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300_A. Array | 1717 | 1717_238 | Vitaly has an array of n distinct integers. Vitaly wants to divide this array into three non-empty sets so as the following conditions hold:
1. The product of all numbers in the first set is less than zero ( < 0).
2. The product of all numbers in the second set is greater than zero ( > 0).
3. The product of all numbers in the third set is equal to zero.
4. Each number from the initial array must occur in exactly one set.
Help Vitaly. Divide the given array.
Input
The first line of the input contains integer n (3 ≤ n ≤ 100). The second line contains n space-separated distinct integers a1, a2, ..., an (|ai| ≤ 103) — the array elements.
Output
In the first line print integer n1 (n1 > 0) — the number of elements in the first set. Then print n1 numbers — the elements that got to the first set.
In the next line print integer n2 (n2 > 0) — the number of elements in the second set. Then print n2 numbers — the elements that got to the second set.
In the next line print integer n3 (n3 > 0) — the number of elements in the third set. Then print n3 numbers — the elements that got to the third set.
The printed sets must meet the described conditions. It is guaranteed that the solution exists. If there are several solutions, you are allowed to print any of them.
Examples
Input
3
-1 2 0
Output
1 -1
1 2
1 0
Input
4
-1 -2 -3 0
Output
1 -1
2 -3 -2
1 0 | #A. Array
n = int(input())
a,b,c =[],[],[]
l = list(map(int,input().split()))
for i in l:
if i<0:
a.append(i)
elif i>0:
b.append(i)
else:
c.append(i)
if len(b)==0 and len(a)>2:
b.append(a.pop())
b.append(a.pop())
if len(a)%2==0:
c.append(a.pop())
print(len(a),*a)
print(len(b),*b)
print(len(c),*c) | import sys
import time
import itertools
from itertools import accumulate, product, permutations, combinations
import collections
from collections import Counter, OrderedDict, deque, defaultdict, ChainMap
from functools import lru_cache
import math
from math import sqrt, sin, cos, tan, ceil, fabs, floor, gcd, exp, log, log2
import fractions
from typing import List, Tuple
import numpy as np
import random
import heapq
from heapq import *
from dataclasses import dataclass
import builtins
import re
def strip(s, characters = None):
if characters is None:
characters = [' ', '\t', '\n', '\r', '\v', '\f']
else:
characters = list(characters)
characters = [x for x in characters if len(x) > 0]
i = 0
while i < len(s):
found_sep_candidate = False
for sep_candidate in characters:
if s[i:i + len(sep_candidate)] == sep_candidate:
found_sep_candidate = True
i += len(sep_candidate)
break
if not found_sep_candidate:
break
j = len(s) - 1
while j >= 0:
found_sep_candidate = False
for sep_candidate in characters:
if s[j + 1 - len(sep_candidate):j+1] == sep_candidate:
found_sep_candidate = True
j -= len(sep_candidate)
break
if not found_sep_candidate:
break
return s[i:j+1]
def split(s, sep=None, maxsplit=-1):
if sep == '':
raise builtins.ValueError('empty separator')
if type(sep) == list and '' in sep:
raise builtins.ValueError('empty separator')
if sep is None:
sep = [' ', '\t', '\n', '\r', '\v', '\f']
result = []
word = ''
count_split = 0
if maxsplit == -1:
maxsplit = len(s) * 1000
i = 0
while i < len(s):
found_sep_candidate = False
for sep_candidate in sep:
if s[i:i + len(sep_candidate)] == sep_candidate:
found_sep_candidate = True
if word:
result.append(word)
count_split += 1
word = ''
i += len(sep_candidate)
break
if not found_sep_candidate and count_split < maxsplit:
word += s[i]
i += 1
elif not found_sep_candidate and count_split >= maxsplit:
word += s[i:]
i = len(s)
if word:
result.append(word)
return result
if type(sep) == str:
sep = [sep]
if maxsplit == -1:
maxsplit = 0
elif maxsplit == 0:
maxsplit = -1
return re.split(re.compile("|".join([re.escape(x) for x in sep])), s, maxsplit=maxsplit)
class str_escaped(str):
def split(self, sep=None, maxsplit=-1):
return split(self, sep=sep, maxsplit=maxsplit)
def strip(self, chars=None):
return strip(self, characters = chars)
from dataclasses import dataclass
from typing import List
@dataclass
class Input:
n: int
a_list: List[int]
@classmethod
def from_str(cls, input_: str):
n, a_list, _ = input_.split('\n')
n = int(n)
a_list = list(map(int, a_list.split()))
assert n == len(a_list)
return cls(n, a_list)
def __repr__(self):
return str(self.n) + '\n' + ' '.join(map(str, self.a_list)) + '\n'
| 4
-1 -2 -3 0
| O(n) | 0.000006 | {
"public_tests": [
{
"input": "4\n-1 -2 -3 0\n",
"output": "1 -1\n2 -3 -2\n1 0\n"
},
{
"input": "3\n-1 2 0\n",
"output": "1 -1\n1 2\n1 0\n"
}
],
"private_tests": [
{
"input": "100\n-34 81 85 -96 50 20 54 86 22 10 -19 52 65 44 30 53 63 71 17 98 -92 4 5 -99 89 -23 48 9 7 33 75 2 47 -56 42 70 -68 57 51 83 82 94 91 45 46 25 95 11 -12 62 -31 -87 58 38 67 97 -60 66 73 -28 13 93 29 59 -49 77 37 -43 -27 0 -16 72 15 79 61 78 35 21 3 8 84 1 -32 36 74 -88 26 100 6 14 40 76 18 90 24 69 80 64 55 41\n",
"output": "19 -34 -96 -19 -92 -99 -23 -56 -68 -12 -31 -87 -60 -28 -49 -43 -27 -16 -32 -88\n80 81 85 50 20 54 86 22 10 52 65 44 30 53 63 71 17 98 4 5 89 48 9 7 33 75 2 47 42 70 57 51 83 82 94 91 45 46 25 95 11 62 58 38 67 97 66 73 13 93 29 59 77 37 72 15 79 61 78 35 21 3 8 84 1 36 74 26 100 6 14 40 76 18 90 24 69 80 64 55 41\n1 0"
},
{
"input": "100\n-87 -48 -76 -1 -10 -17 -22 -19 -27 -99 -43 49 38 -20 -45 -64 44 -96 -35 -74 -65 -41 -21 -75 37 -12 -67 0 -3 5 -80 -93 -81 -97 -47 -63 53 -100 95 -79 -83 -90 -32 88 -77 -16 -23 -54 -28 -4 -73 -98 -25 -39 60 -56 -34 -2 -11 -55 -52 -69 -68 -29 -82 -62 -36 -13 -6 -89 8 -72 18 -15 -50 -71 -70 -92 -42 -78 -61 -9 -30 -85 -91 -94 84 -86 -7 -57 -14 40 -33 51 -26 46 59 -31 -58 -66\n",
"output": "83 -87 -48 -76 -1 -10 -17 -22 -19 -27 -99 -43 -20 -45 -64 -96 -35 -74 -65 -41 -21 -75 -12 -67 -3 -80 -93 -81 -97 -47 -63 -100 -79 -83 -90 -32 -77 -16 -23 -54 -28 -4 -73 -98 -25 -39 -56 -34 -2 -11 -55 -52 -69 -68 -29 -82 -62 -36 -13 -6 -89 -72 -15 -50 -71 -70 -92 -42 -78 -61 -9 -30 -85 -91 -94 -86 -7 -57 -14 -33 -26 -31 -58 -66\n16 49 38 44 37 5 53 95 88 60 8 18 84 40 51 46 59\n1 0"
},
{
"input": "100\n-97 -90 61 78 87 -52 -3 65 83 38 30 -60 35 -50 -73 -77 44 -32 -81 17 -67 58 -6 -34 47 -28 71 -45 69 -80 -4 -7 -57 -79 43 -27 -31 29 16 -89 -21 -93 95 -82 74 -5 -70 -20 -18 36 -64 -66 72 53 62 -68 26 15 76 -40 -99 8 59 88 49 -23 9 10 56 -48 -98 0 100 -54 25 94 13 -63 42 39 -1 55 24 -12 75 51 41 84 -96 -85 -2 -92 14 -46 -91 -19 -11 -86 22 -37\n",
"output": "51 -97 -90 -52 -3 -60 -50 -73 -77 -32 -81 -67 -6 -34 -28 -45 -80 -4 -7 -57 -79 -27 -31 -89 -21 -93 -82 -5 -70 -20 -18 -64 -66 -68 -40 -99 -23 -48 -98 -54 -63 -1 -12 -96 -85 -2 -92 -46 -91 -19 -11 -86\n47 61 78 87 65 83 38 30 35 44 17 58 47 71 69 43 29 16 95 74 36 72 53 62 26 15 76 8 59 88 49 9 10 56 100 25 94 13 42 39 55 24 75 51 41 84 14 22\n2 0 -37\n"
},
{
"input": "4\n0 -1 -2 -3\n",
"output": "1 -1\n2 -3 -2\n1 0\n"
},
{
"input": "5\n-1 -2 -3 -4 0\n",
"output": "1 -1\n2 -4 -3\n2 0 -2\n"
},
{
"input": "100\n3 -66 -17 54 24 -29 76 89 32 -37 93 -16 99 -25 51 78 23 68 -95 59 18 34 -45 77 9 39 -10 19 8 73 -5 60 12 31 0 2 26 40 48 30 52 49 27 4 87 57 85 58 -61 50 83 80 69 67 91 97 -96 11 100 56 82 53 13 -92 -72 70 1 -94 -63 47 21 14 74 7 6 33 55 65 64 -41 81 42 36 28 38 20 43 71 90 -88 22 84 -86 15 75 62 44 35 98 46\n",
"output": "19 -66 -17 -29 -37 -16 -25 -95 -45 -10 -5 -61 -96 -92 -72 -94 -63 -41 -88 -86\n80 3 54 24 76 89 32 93 99 51 78 23 68 59 18 34 77 9 39 19 8 73 60 12 31 2 26 40 48 30 52 49 27 4 87 57 85 58 50 83 80 69 67 91 97 11 100 56 82 53 13 70 1 47 21 14 74 7 6 33 55 65 64 81 42 36 28 38 20 43 71 90 22 84 15 75 62 44 35 98 46\n1 0"
},
{
"input": "100\n-95 -28 -43 -72 -11 -24 -37 -35 -44 -66 -45 -62 -96 -51 -55 -23 -31 -26 -59 -17 77 -69 -10 -12 -78 -14 -52 -57 -40 -75 4 -98 -6 7 -53 -3 -90 -63 -8 -20 88 -91 -32 -76 -80 -97 -34 -27 -19 0 70 -38 -9 -49 -67 73 -36 2 81 -39 -65 -83 -64 -18 -94 -79 -58 -16 87 -22 -74 -25 -13 -46 -89 -47 5 -15 -54 -99 56 -30 -60 -21 -86 33 -1 -50 -68 -100 -85 -29 92 -48 -61 42 -84 -93 -41 -82\n",
"output": "85 -95 -28 -43 -72 -11 -24 -37 -35 -44 -66 -45 -62 -96 -51 -55 -23 -31 -26 -59 -17 -69 -10 -12 -78 -14 -52 -57 -40 -75 -98 -6 -53 -3 -90 -63 -8 -20 -91 -32 -76 -80 -97 -34 -27 -19 -38 -9 -49 -67 -36 -39 -65 -83 -64 -18 -94 -79 -58 -16 -22 -74 -25 -13 -46 -89 -47 -15 -54 -99 -30 -60 -21 -86 -1 -50 -68 -100 -85 -29 -48 -61 -84 -93 -41 -82\n14 77 4 7 88 70 73 2 81 87 5 56 33 92 42\n1 0"
},
{
"input": "100\n-75 -60 -18 -92 -71 -9 -37 -34 -82 28 -54 93 -83 -76 -58 -88 -17 -97 64 -39 -96 -81 -10 -98 -47 -100 -22 27 14 -33 -19 -99 87 -66 57 -21 -90 -70 -32 -26 24 -77 -74 13 -44 16 -5 -55 -2 -6 -7 -73 -1 -68 -30 -95 -42 69 0 -20 -79 59 -48 -4 -72 -67 -46 62 51 -52 -86 -40 56 -53 85 -35 -8 49 50 65 29 11 -43 -15 -41 -12 -3 -80 -31 -38 -91 -45 -25 78 94 -23 -63 84 89 -61\n",
"output": "73 -75 -60 -18 -92 -71 -9 -37 -34 -82 -54 -83 -76 -58 -88 -17 -97 -39 -96 -81 -10 -98 -47 -100 -22 -33 -19 -99 -66 -21 -90 -70 -32 -26 -77 -74 -44 -5 -55 -2 -6 -7 -73 -1 -68 -30 -95 -42 -20 -79 -48 -4 -72 -67 -46 -52 -86 -40 -53 -35 -8 -43 -15 -41 -12 -3 -80 -31 -38 -91 -45 -25 -23 -63\n25 28 93 64 27 14 87 57 24 13 16 69 59 62 51 56 85 49 50 65 29 11 78 94 84 89\n2 0 -61\n"
},
{
"input": "3\n-101 101 0\n",
"output": "1 -101\n1 101\n1 0\n"
},
{
"input": "100\n-64 -51 -75 -98 74 -26 -1 -8 -99 -76 -53 -80 -43 -22 -100 -62 -34 -5 -65 -81 -18 -91 -92 -16 -23 -95 -9 -19 -44 -46 -79 52 -35 4 -87 -7 -90 -20 -71 -61 -67 -50 -66 -68 -49 -27 -32 -57 -85 -59 -30 -36 -3 -77 86 -25 -94 -56 60 -24 -37 -72 -41 -31 11 -48 28 -38 -42 -39 -33 -70 -84 0 -93 -73 -14 -69 -40 -97 -6 -55 -45 -54 -10 -29 -96 -12 -83 -15 -21 -47 17 -2 -63 -89 88 13 -58 -82\n",
"output": "89 -64 -51 -75 -98 -26 -1 -8 -99 -76 -53 -80 -43 -22 -100 -62 -34 -5 -65 -81 -18 -91 -92 -16 -23 -95 -9 -19 -44 -46 -79 -35 -87 -7 -90 -20 -71 -61 -67 -50 -66 -68 -49 -27 -32 -57 -85 -59 -30 -36 -3 -77 -25 -94 -56 -24 -37 -72 -41 -31 -48 -38 -42 -39 -33 -70 -84 -93 -73 -14 -69 -40 -97 -6 -55 -45 -54 -10 -29 -96 -12 -83 -15 -21 -47 -2 -63 -89 -58 -82\n10 74 52 4 86 60 11 28 17 88 13\n1 0"
},
{
"input": "21\n-100 -200 -300 -400 -500 -600 -700 -800 -900 -1000 0 100 200 300 400 500 600 700 800 900 1000\n",
"output": "9 -100 -200 -300 -400 -500 -600 -700 -800 -900\n10 100 200 300 400 500 600 700 800 900 1000\n2 0 -1000\n"
},
{
"input": "100\n-1000 -986 -979 -955 -966 -963 -973 -959 -972 -906 -924 -927 -929 -918 -977 -967 -921 -989 -911 -995 -945 -919 -971 -913 -912 -933 -969 -975 -920 -988 -997 -994 -953 -962 -940 -905 -978 -948 -957 -996 0 -976 -949 -931 -903 -985 -923 -993 -944 -909 -938 -946 -934 -992 -904 -980 -954 -943 -917 -968 -991 -956 -902 -942 -999 -998 -908 -928 -930 -914 -922 -936 -960 -937 -939 -926 -965 -925 -951 -910 -907 -970 -990 -984 -964 -987 -916 -947 -982 -950 -974 -915 -932 -958 -981 -941 -961 -983 -952 -935\n",
"output": "97 -1000 -986 -979 -955 -966 -963 -973 -959 -972 -906 -924 -927 -929 -918 -977 -967 -921 -989 -911 -995 -945 -919 -971 -913 -912 -933 -969 -975 -920 -988 -997 -994 -953 -962 -940 -905 -978 -948 -957 -996 -976 -949 -931 -903 -985 -923 -993 -944 -909 -938 -946 -934 -992 -904 -980 -954 -943 -917 -968 -991 -956 -902 -942 -999 -998 -908 -928 -930 -914 -922 -936 -960 -937 -939 -926 -965 -925 -951 -910 -907 -970 -990 -984 -964 -987 -916 -947 -982 -950 -974 -915 -932 -958 -981 -941 -961 -983\n2 -935 -952\n1 0\n"
},
{
"input": "64\n502 885 -631 -906 735 687 642 -29 -696 -165 -524 15 -129 -663 -846 -501 -651 895 -341 -833 -142 33 -847 688 945 -192 -587 -930 603 849 736 676 788 256 863 -509 319 -49 -807 -158 218 -886 -143 -639 118 -156 -291 325 892 -916 -622 -960 -959 -731 -943 436 -535 861 745 589 -159 376 -182 0\n",
"output": "35 -631 -906 -29 -696 -165 -524 -129 -663 -846 -501 -651 -341 -833 -142 -847 -192 -587 -930 -509 -49 -807 -158 -886 -143 -639 -156 -291 -916 -622 -960 -959 -731 -943 -535 -159\n27 502 885 735 687 642 15 895 33 688 945 603 849 736 676 788 256 863 319 218 118 325 892 436 861 745 589 376\n2 0 -182\n"
},
{
"input": "100\n-12 -41 57 13 83 -36 53 69 -6 86 -75 87 11 -5 -4 -14 -37 -84 70 2 -73 16 31 34 -45 94 -9 26 27 52 -42 46 96 21 32 7 -18 61 66 -51 95 -48 -76 90 80 -40 89 77 78 54 -30 8 88 33 -24 82 -15 19 1 59 44 64 -97 -60 43 56 35 47 39 50 29 28 -17 -67 74 23 85 -68 79 0 65 55 -3 92 -99 72 93 -71 38 -10 -100 -98 81 62 91 -63 -58 49 -20 22\n",
"output": "35 -12 -41 -36 -6 -75 -5 -4 -14 -37 -84 -73 -45 -9 -42 -18 -51 -48 -76 -40 -30 -24 -15 -97 -60 -17 -67 -68 -3 -99 -71 -10 -100 -98 -63 -58\n63 57 13 83 53 69 86 87 11 70 2 16 31 34 94 26 27 52 46 96 21 32 7 61 66 95 90 80 89 77 78 54 8 88 33 82 19 1 59 44 64 43 56 35 47 39 50 29 28 74 23 85 79 65 55 92 72 93 38 81 62 91 49 22\n2 0 -20\n"
},
{
"input": "100\n-17 16 -70 32 -60 75 -100 -9 -68 -30 -42 86 -88 -98 -47 -5 58 -14 -94 -73 -80 -51 -66 -85 -53 49 -25 -3 -45 -69 -11 -64 83 74 -65 67 13 -91 81 6 -90 -54 -12 -39 0 -24 -71 -41 -44 57 -93 -20 -92 18 -43 -52 -55 -84 -89 -19 40 -4 -99 -26 -87 -36 -56 -61 -62 37 -95 -28 63 23 35 -82 1 -2 -78 -96 -21 -77 -76 -27 -10 -97 -8 46 -15 -48 -34 -59 -7 -29 50 -33 -72 -79 22 38\n",
"output": "75 -17 -70 -60 -100 -9 -68 -30 -42 -88 -98 -47 -5 -14 -94 -73 -80 -51 -66 -85 -53 -25 -3 -45 -69 -11 -64 -65 -91 -90 -54 -12 -39 -24 -71 -41 -44 -93 -20 -92 -43 -52 -55 -84 -89 -19 -4 -99 -26 -87 -36 -56 -61 -62 -95 -28 -82 -2 -78 -96 -21 -77 -76 -27 -10 -97 -8 -15 -48 -34 -59 -7 -29 -33 -72 -79\n24 16 32 75 86 58 49 83 74 67 13 81 6 57 18 40 37 63 23 35 1 46 50 22 38\n1 0"
},
{
"input": "5\n-1 -2 1 2 0\n",
"output": "1 -1\n2 1 2\n2 0 -2\n"
},
{
"input": "99\n-1000 -986 -979 -955 -966 -963 -973 -959 -972 -906 -924 -927 -929 -918 -977 -967 -921 -989 -911 -995 -945 -919 -971 -913 -912 -933 -969 -975 -920 -988 -997 -994 -953 -962 -940 -905 -978 -948 -957 -996 0 -976 -949 -931 -903 -985 -923 -993 -944 -909 -938 -946 -934 -992 -904 -980 -954 -943 -917 -968 -991 -956 -902 -942 -999 -998 -908 -928 -930 -914 -922 -936 -960 -937 -939 -926 -965 -925 -951 -910 -907 -970 -990 -984 -964 -987 -916 -947 -982 -950 -974 -915 -932 -958 -981 -941 -961 -983 -952\n",
"output": "1 -1000\n2 -999 -998\n96 -997 -996 -995 -994 -993 -992 -991 -990 -989 -988 -987 -986 -985 -984 -983 -982 -981 -980 -979 -978 -977 -976 -975 -974 -973 -972 -971 -970 -969 -968 -967 -966 -965 -964 -963 -962 -961 -960 -959 -958 -957 -956 -955 -954 -953 -952 -951 -950 -949 -948 -947 -946 -945 -944 -943 -942 -941 -940 -939 -938 -937 -936 -934 -933 -932 -931 -930 -929 -928 -927 -926 -925 -924 -923 -922 -921 -920 -919 -918 -917 -916 -915 -914 -913 -912 -911 -910 -909 -908 -907 -906 -905 -904 -903 -902 0\n"
},
{
"input": "59\n-990 -876 -641 -726 718 -53 803 -954 894 -265 -587 -665 904 349 754 -978 441 794 -768 -428 -569 -476 188 -620 -290 -333 45 705 -201 109 165 446 13 122 714 -562 -15 -86 -960 43 329 578 287 -776 -14 -71 915 886 -259 337 -495 913 -498 -669 -673 818 225 647 0\n",
"output": "29 -990 -876 -641 -726 -53 -954 -265 -587 -665 -978 -768 -428 -569 -476 -620 -290 -333 -201 -562 -15 -86 -960 -776 -14 -71 -259 -495 -498 -669\n28 718 803 894 904 349 754 441 794 188 45 705 109 165 446 13 122 714 43 329 578 287 915 886 337 913 818 225 647\n2 0 -673\n"
}
],
"generated_tests": [
{
"input": "100\n-34 81 85 -96 50 20 54 86 22 10 -19 52 65 44 30 53 63 71 17 98 -92 4 5 -99 89 -23 48 9 7 33 75 2 47 -56 42 70 -68 57 51 83 82 94 91 45 46 25 95 11 -12 62 -31 -87 58 38 67 97 -60 66 73 -28 13 93 29 59 -49 77 37 -43 -27 0 -16 72 15 79 61 78 35 21 3 8 84 1 -32 36 74 -88 26 100 6 14 40 76 18 162 24 69 80 64 55 41\n",
"output": "19 -34 -96 -19 -92 -99 -23 -56 -68 -12 -31 -87 -60 -28 -49 -43 -27 -16 -32 -88\n80 81 85 50 20 54 86 22 10 52 65 44 30 53 63 71 17 98 4 5 89 48 9 7 33 75 2 47 42 70 57 51 83 82 94 91 45 46 25 95 11 62 58 38 67 97 66 73 13 93 29 59 77 37 72 15 79 61 78 35 21 3 8 84 1 36 74 26 100 6 14 40 76 18 162 24 69 80 64 55 41\n1 0\n"
},
{
"input": "100\n-87 -48 -76 -1 -10 -17 -22 -19 -27 -99 -43 49 38 -20 -45 -64 44 -96 -35 -74 -65 -41 -21 -75 37 -12 -67 0 -3 5 -80 -93 -81 -97 -47 -63 53 -100 95 -79 -83 -90 -32 88 -77 -16 -23 -54 -28 -4 -73 -98 -25 -39 60 -56 -34 -2 -11 -55 -52 -69 -68 -29 -82 -62 -36 -13 -6 -89 8 -72 18 -15 -50 -71 -70 -92 -37 -78 -61 -9 -30 -85 -91 -94 84 -86 -7 -57 -14 40 -33 51 -26 46 59 -31 -58 -66\n",
"output": "83 -87 -48 -76 -1 -10 -17 -22 -19 -27 -99 -43 -20 -45 -64 -96 -35 -74 -65 -41 -21 -75 -12 -67 -3 -80 -93 -81 -97 -47 -63 -100 -79 -83 -90 -32 -77 -16 -23 -54 -28 -4 -73 -98 -25 -39 -56 -34 -2 -11 -55 -52 -69 -68 -29 -82 -62 -36 -13 -6 -89 -72 -15 -50 -71 -70 -92 -37 -78 -61 -9 -30 -85 -91 -94 -86 -7 -57 -14 -33 -26 -31 -58 -66\n16 49 38 44 37 5 53 95 88 60 8 18 84 40 51 46 59\n1 0\n"
},
{
"input": "100\n-97 -90 61 78 146 -52 -3 65 83 38 30 -60 35 -50 -73 -77 44 -32 -81 17 -67 58 -6 -34 47 -28 71 -45 69 -80 -4 -7 -57 -79 43 -27 -31 29 16 -89 -21 -93 95 -82 74 -5 -70 -20 -18 36 -64 -66 72 53 62 -68 26 15 76 -40 -99 8 59 88 49 -23 9 10 56 -48 -98 0 100 -54 25 94 13 -63 42 39 -1 55 24 -12 75 51 41 84 -96 -85 -2 -92 14 -46 -91 -19 -11 -86 22 -37\n",
"output": "51 -97 -90 -52 -3 -60 -50 -73 -77 -32 -81 -67 -6 -34 -28 -45 -80 -4 -7 -57 -79 -27 -31 -89 -21 -93 -82 -5 -70 -20 -18 -64 -66 -68 -40 -99 -23 -48 -98 -54 -63 -1 -12 -96 -85 -2 -92 -46 -91 -19 -11 -86\n47 61 78 146 65 83 38 30 35 44 17 58 47 71 69 43 29 16 95 74 36 72 53 62 26 15 76 8 59 88 49 9 10 56 100 25 94 13 42 39 55 24 75 51 41 84 14 22\n2 0 -37\n"
},
{
"input": "4\n0 -1 -1 -3\n",
"output": "1 -1\n2 -3 -1\n1 0\n"
},
{
"input": "5\n-2 -2 -3 -4 0\n",
"output": "1 -2\n2 -4 -3\n2 0 -2\n"
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0.0000038081443673513994,
0.0000038061494482080424,
0.000003660373156140735,
0.0000035743453753277973,
0.00000348891915701486,
0.0000033876273082386362,
0.0000033356311325393365,
0.000003330587002840909,
0.0000032976050180288463,
0.000003289384984156469,
0.000003233523300917832,
0.000003032051272945804,
0.0000029971998743444058,
0.0000029961048404720284,
0.0000029302086565777967,
0.000002837364442198427,
0.000002833609456949301,
0.000001809557596700175,
0.0000016848219788024475,
2.9716318837412587e-8,
2.6259410511363636e-8,
4.617207987325174e-9,
2.367720170454546e-9,
1.3772126311188794e-9,
1.3565067744755246e-9,
6.864688046328674e-10,
2.331730769230768e-10,
1.8926873907342664e-10,
1.3354321459790206e-10,
1.247063483391608e-10,
9.971181162587414e-11,
9.271197552447555e-11,
6.633795891608386e-11,
5.011199737762238e-11,
3.796301354895108e-11
] |
300_A. Array | 1717 | 1717_175 | Vitaly has an array of n distinct integers. Vitaly wants to divide this array into three non-empty sets so as the following conditions hold:
1. The product of all numbers in the first set is less than zero ( < 0).
2. The product of all numbers in the second set is greater than zero ( > 0).
3. The product of all numbers in the third set is equal to zero.
4. Each number from the initial array must occur in exactly one set.
Help Vitaly. Divide the given array.
Input
The first line of the input contains integer n (3 ≤ n ≤ 100). The second line contains n space-separated distinct integers a1, a2, ..., an (|ai| ≤ 103) — the array elements.
Output
In the first line print integer n1 (n1 > 0) — the number of elements in the first set. Then print n1 numbers — the elements that got to the first set.
In the next line print integer n2 (n2 > 0) — the number of elements in the second set. Then print n2 numbers — the elements that got to the second set.
In the next line print integer n3 (n3 > 0) — the number of elements in the third set. Then print n3 numbers — the elements that got to the third set.
The printed sets must meet the described conditions. It is guaranteed that the solution exists. If there are several solutions, you are allowed to print any of them.
Examples
Input
3
-1 2 0
Output
1 -1
1 2
1 0
Input
4
-1 -2 -3 0
Output
1 -1
2 -3 -2
1 0 | (input())
a=sorted(map(int,input().split()))
b=[a.pop(0)]
c=a[-1]>0 and [a.pop()] or [a.pop(0),a.pop(0)]
for l in b,c,a:
print(len(l),*l) | import sys
import time
import itertools
from itertools import accumulate, product, permutations, combinations
import collections
from collections import Counter, OrderedDict, deque, defaultdict, ChainMap
from functools import lru_cache
import math
from math import sqrt, sin, cos, tan, ceil, fabs, floor, gcd, exp, log, log2
import fractions
from typing import List, Tuple
import numpy as np
import random
import heapq
from heapq import *
from dataclasses import dataclass
import builtins
import re
def strip(s, characters = None):
if characters is None:
characters = [' ', '\t', '\n', '\r', '\v', '\f']
else:
characters = list(characters)
characters = [x for x in characters if len(x) > 0]
i = 0
while i < len(s):
found_sep_candidate = False
for sep_candidate in characters:
if s[i:i + len(sep_candidate)] == sep_candidate:
found_sep_candidate = True
i += len(sep_candidate)
break
if not found_sep_candidate:
break
j = len(s) - 1
while j >= 0:
found_sep_candidate = False
for sep_candidate in characters:
if s[j + 1 - len(sep_candidate):j+1] == sep_candidate:
found_sep_candidate = True
j -= len(sep_candidate)
break
if not found_sep_candidate:
break
return s[i:j+1]
def split(s, sep=None, maxsplit=-1):
if sep == '':
raise builtins.ValueError('empty separator')
if type(sep) == list and '' in sep:
raise builtins.ValueError('empty separator')
if sep is None:
sep = [' ', '\t', '\n', '\r', '\v', '\f']
result = []
word = ''
count_split = 0
if maxsplit == -1:
maxsplit = len(s) * 1000
i = 0
while i < len(s):
found_sep_candidate = False
for sep_candidate in sep:
if s[i:i + len(sep_candidate)] == sep_candidate:
found_sep_candidate = True
if word:
result.append(word)
count_split += 1
word = ''
i += len(sep_candidate)
break
if not found_sep_candidate and count_split < maxsplit:
word += s[i]
i += 1
elif not found_sep_candidate and count_split >= maxsplit:
word += s[i:]
i = len(s)
if word:
result.append(word)
return result
if type(sep) == str:
sep = [sep]
if maxsplit == -1:
maxsplit = 0
elif maxsplit == 0:
maxsplit = -1
return re.split(re.compile("|".join([re.escape(x) for x in sep])), s, maxsplit=maxsplit)
class str_escaped(str):
def split(self, sep=None, maxsplit=-1):
return split(self, sep=sep, maxsplit=maxsplit)
def strip(self, chars=None):
return strip(self, characters = chars)
from dataclasses import dataclass
from typing import List
@dataclass
class Input:
n: int
a_list: List[int]
@classmethod
def from_str(cls, input_: str):
n, a_list, _ = input_.split('\n')
n = int(n)
a_list = list(map(int, a_list.split()))
assert n == len(a_list)
return cls(n, a_list)
def __repr__(self):
return str(self.n) + '\n' + ' '.join(map(str, self.a_list)) + '\n'
| 4
-1 -2 -3 0
| O(nlogn) | 0.000012 | {
"public_tests": [
{
"input": "4\n-1 -2 -3 0\n",
"output": "1 -1\n2 -3 -2\n1 0\n"
},
{
"input": "3\n-1 2 0\n",
"output": "1 -1\n1 2\n1 0\n"
}
],
"private_tests": [
{
"input": "100\n-34 81 85 -96 50 20 54 86 22 10 -19 52 65 44 30 53 63 71 17 98 -92 4 5 -99 89 -23 48 9 7 33 75 2 47 -56 42 70 -68 57 51 83 82 94 91 45 46 25 95 11 -12 62 -31 -87 58 38 67 97 -60 66 73 -28 13 93 29 59 -49 77 37 -43 -27 0 -16 72 15 79 61 78 35 21 3 8 84 1 -32 36 74 -88 26 100 6 14 40 76 18 90 24 69 80 64 55 41\n",
"output": "19 -34 -96 -19 -92 -99 -23 -56 -68 -12 -31 -87 -60 -28 -49 -43 -27 -16 -32 -88\n80 81 85 50 20 54 86 22 10 52 65 44 30 53 63 71 17 98 4 5 89 48 9 7 33 75 2 47 42 70 57 51 83 82 94 91 45 46 25 95 11 62 58 38 67 97 66 73 13 93 29 59 77 37 72 15 79 61 78 35 21 3 8 84 1 36 74 26 100 6 14 40 76 18 90 24 69 80 64 55 41\n1 0"
},
{
"input": "100\n-87 -48 -76 -1 -10 -17 -22 -19 -27 -99 -43 49 38 -20 -45 -64 44 -96 -35 -74 -65 -41 -21 -75 37 -12 -67 0 -3 5 -80 -93 -81 -97 -47 -63 53 -100 95 -79 -83 -90 -32 88 -77 -16 -23 -54 -28 -4 -73 -98 -25 -39 60 -56 -34 -2 -11 -55 -52 -69 -68 -29 -82 -62 -36 -13 -6 -89 8 -72 18 -15 -50 -71 -70 -92 -42 -78 -61 -9 -30 -85 -91 -94 84 -86 -7 -57 -14 40 -33 51 -26 46 59 -31 -58 -66\n",
"output": "83 -87 -48 -76 -1 -10 -17 -22 -19 -27 -99 -43 -20 -45 -64 -96 -35 -74 -65 -41 -21 -75 -12 -67 -3 -80 -93 -81 -97 -47 -63 -100 -79 -83 -90 -32 -77 -16 -23 -54 -28 -4 -73 -98 -25 -39 -56 -34 -2 -11 -55 -52 -69 -68 -29 -82 -62 -36 -13 -6 -89 -72 -15 -50 -71 -70 -92 -42 -78 -61 -9 -30 -85 -91 -94 -86 -7 -57 -14 -33 -26 -31 -58 -66\n16 49 38 44 37 5 53 95 88 60 8 18 84 40 51 46 59\n1 0"
},
{
"input": "100\n-97 -90 61 78 87 -52 -3 65 83 38 30 -60 35 -50 -73 -77 44 -32 -81 17 -67 58 -6 -34 47 -28 71 -45 69 -80 -4 -7 -57 -79 43 -27 -31 29 16 -89 -21 -93 95 -82 74 -5 -70 -20 -18 36 -64 -66 72 53 62 -68 26 15 76 -40 -99 8 59 88 49 -23 9 10 56 -48 -98 0 100 -54 25 94 13 -63 42 39 -1 55 24 -12 75 51 41 84 -96 -85 -2 -92 14 -46 -91 -19 -11 -86 22 -37\n",
"output": "51 -97 -90 -52 -3 -60 -50 -73 -77 -32 -81 -67 -6 -34 -28 -45 -80 -4 -7 -57 -79 -27 -31 -89 -21 -93 -82 -5 -70 -20 -18 -64 -66 -68 -40 -99 -23 -48 -98 -54 -63 -1 -12 -96 -85 -2 -92 -46 -91 -19 -11 -86\n47 61 78 87 65 83 38 30 35 44 17 58 47 71 69 43 29 16 95 74 36 72 53 62 26 15 76 8 59 88 49 9 10 56 100 25 94 13 42 39 55 24 75 51 41 84 14 22\n2 0 -37\n"
},
{
"input": "4\n0 -1 -2 -3\n",
"output": "1 -1\n2 -3 -2\n1 0\n"
},
{
"input": "5\n-1 -2 -3 -4 0\n",
"output": "1 -1\n2 -4 -3\n2 0 -2\n"
},
{
"input": "100\n3 -66 -17 54 24 -29 76 89 32 -37 93 -16 99 -25 51 78 23 68 -95 59 18 34 -45 77 9 39 -10 19 8 73 -5 60 12 31 0 2 26 40 48 30 52 49 27 4 87 57 85 58 -61 50 83 80 69 67 91 97 -96 11 100 56 82 53 13 -92 -72 70 1 -94 -63 47 21 14 74 7 6 33 55 65 64 -41 81 42 36 28 38 20 43 71 90 -88 22 84 -86 15 75 62 44 35 98 46\n",
"output": "19 -66 -17 -29 -37 -16 -25 -95 -45 -10 -5 -61 -96 -92 -72 -94 -63 -41 -88 -86\n80 3 54 24 76 89 32 93 99 51 78 23 68 59 18 34 77 9 39 19 8 73 60 12 31 2 26 40 48 30 52 49 27 4 87 57 85 58 50 83 80 69 67 91 97 11 100 56 82 53 13 70 1 47 21 14 74 7 6 33 55 65 64 81 42 36 28 38 20 43 71 90 22 84 15 75 62 44 35 98 46\n1 0"
},
{
"input": "100\n-95 -28 -43 -72 -11 -24 -37 -35 -44 -66 -45 -62 -96 -51 -55 -23 -31 -26 -59 -17 77 -69 -10 -12 -78 -14 -52 -57 -40 -75 4 -98 -6 7 -53 -3 -90 -63 -8 -20 88 -91 -32 -76 -80 -97 -34 -27 -19 0 70 -38 -9 -49 -67 73 -36 2 81 -39 -65 -83 -64 -18 -94 -79 -58 -16 87 -22 -74 -25 -13 -46 -89 -47 5 -15 -54 -99 56 -30 -60 -21 -86 33 -1 -50 -68 -100 -85 -29 92 -48 -61 42 -84 -93 -41 -82\n",
"output": "85 -95 -28 -43 -72 -11 -24 -37 -35 -44 -66 -45 -62 -96 -51 -55 -23 -31 -26 -59 -17 -69 -10 -12 -78 -14 -52 -57 -40 -75 -98 -6 -53 -3 -90 -63 -8 -20 -91 -32 -76 -80 -97 -34 -27 -19 -38 -9 -49 -67 -36 -39 -65 -83 -64 -18 -94 -79 -58 -16 -22 -74 -25 -13 -46 -89 -47 -15 -54 -99 -30 -60 -21 -86 -1 -50 -68 -100 -85 -29 -48 -61 -84 -93 -41 -82\n14 77 4 7 88 70 73 2 81 87 5 56 33 92 42\n1 0"
},
{
"input": "100\n-75 -60 -18 -92 -71 -9 -37 -34 -82 28 -54 93 -83 -76 -58 -88 -17 -97 64 -39 -96 -81 -10 -98 -47 -100 -22 27 14 -33 -19 -99 87 -66 57 -21 -90 -70 -32 -26 24 -77 -74 13 -44 16 -5 -55 -2 -6 -7 -73 -1 -68 -30 -95 -42 69 0 -20 -79 59 -48 -4 -72 -67 -46 62 51 -52 -86 -40 56 -53 85 -35 -8 49 50 65 29 11 -43 -15 -41 -12 -3 -80 -31 -38 -91 -45 -25 78 94 -23 -63 84 89 -61\n",
"output": "73 -75 -60 -18 -92 -71 -9 -37 -34 -82 -54 -83 -76 -58 -88 -17 -97 -39 -96 -81 -10 -98 -47 -100 -22 -33 -19 -99 -66 -21 -90 -70 -32 -26 -77 -74 -44 -5 -55 -2 -6 -7 -73 -1 -68 -30 -95 -42 -20 -79 -48 -4 -72 -67 -46 -52 -86 -40 -53 -35 -8 -43 -15 -41 -12 -3 -80 -31 -38 -91 -45 -25 -23 -63\n25 28 93 64 27 14 87 57 24 13 16 69 59 62 51 56 85 49 50 65 29 11 78 94 84 89\n2 0 -61\n"
},
{
"input": "3\n-101 101 0\n",
"output": "1 -101\n1 101\n1 0\n"
},
{
"input": "100\n-64 -51 -75 -98 74 -26 -1 -8 -99 -76 -53 -80 -43 -22 -100 -62 -34 -5 -65 -81 -18 -91 -92 -16 -23 -95 -9 -19 -44 -46 -79 52 -35 4 -87 -7 -90 -20 -71 -61 -67 -50 -66 -68 -49 -27 -32 -57 -85 -59 -30 -36 -3 -77 86 -25 -94 -56 60 -24 -37 -72 -41 -31 11 -48 28 -38 -42 -39 -33 -70 -84 0 -93 -73 -14 -69 -40 -97 -6 -55 -45 -54 -10 -29 -96 -12 -83 -15 -21 -47 17 -2 -63 -89 88 13 -58 -82\n",
"output": "89 -64 -51 -75 -98 -26 -1 -8 -99 -76 -53 -80 -43 -22 -100 -62 -34 -5 -65 -81 -18 -91 -92 -16 -23 -95 -9 -19 -44 -46 -79 -35 -87 -7 -90 -20 -71 -61 -67 -50 -66 -68 -49 -27 -32 -57 -85 -59 -30 -36 -3 -77 -25 -94 -56 -24 -37 -72 -41 -31 -48 -38 -42 -39 -33 -70 -84 -93 -73 -14 -69 -40 -97 -6 -55 -45 -54 -10 -29 -96 -12 -83 -15 -21 -47 -2 -63 -89 -58 -82\n10 74 52 4 86 60 11 28 17 88 13\n1 0"
},
{
"input": "21\n-100 -200 -300 -400 -500 -600 -700 -800 -900 -1000 0 100 200 300 400 500 600 700 800 900 1000\n",
"output": "9 -100 -200 -300 -400 -500 -600 -700 -800 -900\n10 100 200 300 400 500 600 700 800 900 1000\n2 0 -1000\n"
},
{
"input": "100\n-1000 -986 -979 -955 -966 -963 -973 -959 -972 -906 -924 -927 -929 -918 -977 -967 -921 -989 -911 -995 -945 -919 -971 -913 -912 -933 -969 -975 -920 -988 -997 -994 -953 -962 -940 -905 -978 -948 -957 -996 0 -976 -949 -931 -903 -985 -923 -993 -944 -909 -938 -946 -934 -992 -904 -980 -954 -943 -917 -968 -991 -956 -902 -942 -999 -998 -908 -928 -930 -914 -922 -936 -960 -937 -939 -926 -965 -925 -951 -910 -907 -970 -990 -984 -964 -987 -916 -947 -982 -950 -974 -915 -932 -958 -981 -941 -961 -983 -952 -935\n",
"output": "97 -1000 -986 -979 -955 -966 -963 -973 -959 -972 -906 -924 -927 -929 -918 -977 -967 -921 -989 -911 -995 -945 -919 -971 -913 -912 -933 -969 -975 -920 -988 -997 -994 -953 -962 -940 -905 -978 -948 -957 -996 -976 -949 -931 -903 -985 -923 -993 -944 -909 -938 -946 -934 -992 -904 -980 -954 -943 -917 -968 -991 -956 -902 -942 -999 -998 -908 -928 -930 -914 -922 -936 -960 -937 -939 -926 -965 -925 -951 -910 -907 -970 -990 -984 -964 -987 -916 -947 -982 -950 -974 -915 -932 -958 -981 -941 -961 -983\n2 -935 -952\n1 0\n"
},
{
"input": "64\n502 885 -631 -906 735 687 642 -29 -696 -165 -524 15 -129 -663 -846 -501 -651 895 -341 -833 -142 33 -847 688 945 -192 -587 -930 603 849 736 676 788 256 863 -509 319 -49 -807 -158 218 -886 -143 -639 118 -156 -291 325 892 -916 -622 -960 -959 -731 -943 436 -535 861 745 589 -159 376 -182 0\n",
"output": "35 -631 -906 -29 -696 -165 -524 -129 -663 -846 -501 -651 -341 -833 -142 -847 -192 -587 -930 -509 -49 -807 -158 -886 -143 -639 -156 -291 -916 -622 -960 -959 -731 -943 -535 -159\n27 502 885 735 687 642 15 895 33 688 945 603 849 736 676 788 256 863 319 218 118 325 892 436 861 745 589 376\n2 0 -182\n"
},
{
"input": "100\n-12 -41 57 13 83 -36 53 69 -6 86 -75 87 11 -5 -4 -14 -37 -84 70 2 -73 16 31 34 -45 94 -9 26 27 52 -42 46 96 21 32 7 -18 61 66 -51 95 -48 -76 90 80 -40 89 77 78 54 -30 8 88 33 -24 82 -15 19 1 59 44 64 -97 -60 43 56 35 47 39 50 29 28 -17 -67 74 23 85 -68 79 0 65 55 -3 92 -99 72 93 -71 38 -10 -100 -98 81 62 91 -63 -58 49 -20 22\n",
"output": "35 -12 -41 -36 -6 -75 -5 -4 -14 -37 -84 -73 -45 -9 -42 -18 -51 -48 -76 -40 -30 -24 -15 -97 -60 -17 -67 -68 -3 -99 -71 -10 -100 -98 -63 -58\n63 57 13 83 53 69 86 87 11 70 2 16 31 34 94 26 27 52 46 96 21 32 7 61 66 95 90 80 89 77 78 54 8 88 33 82 19 1 59 44 64 43 56 35 47 39 50 29 28 74 23 85 79 65 55 92 72 93 38 81 62 91 49 22\n2 0 -20\n"
},
{
"input": "100\n-17 16 -70 32 -60 75 -100 -9 -68 -30 -42 86 -88 -98 -47 -5 58 -14 -94 -73 -80 -51 -66 -85 -53 49 -25 -3 -45 -69 -11 -64 83 74 -65 67 13 -91 81 6 -90 -54 -12 -39 0 -24 -71 -41 -44 57 -93 -20 -92 18 -43 -52 -55 -84 -89 -19 40 -4 -99 -26 -87 -36 -56 -61 -62 37 -95 -28 63 23 35 -82 1 -2 -78 -96 -21 -77 -76 -27 -10 -97 -8 46 -15 -48 -34 -59 -7 -29 50 -33 -72 -79 22 38\n",
"output": "75 -17 -70 -60 -100 -9 -68 -30 -42 -88 -98 -47 -5 -14 -94 -73 -80 -51 -66 -85 -53 -25 -3 -45 -69 -11 -64 -65 -91 -90 -54 -12 -39 -24 -71 -41 -44 -93 -20 -92 -43 -52 -55 -84 -89 -19 -4 -99 -26 -87 -36 -56 -61 -62 -95 -28 -82 -2 -78 -96 -21 -77 -76 -27 -10 -97 -8 -15 -48 -34 -59 -7 -29 -33 -72 -79\n24 16 32 75 86 58 49 83 74 67 13 81 6 57 18 40 37 63 23 35 1 46 50 22 38\n1 0"
},
{
"input": "5\n-1 -2 1 2 0\n",
"output": "1 -1\n2 1 2\n2 0 -2\n"
},
{
"input": "99\n-1000 -986 -979 -955 -966 -963 -973 -959 -972 -906 -924 -927 -929 -918 -977 -967 -921 -989 -911 -995 -945 -919 -971 -913 -912 -933 -969 -975 -920 -988 -997 -994 -953 -962 -940 -905 -978 -948 -957 -996 0 -976 -949 -931 -903 -985 -923 -993 -944 -909 -938 -946 -934 -992 -904 -980 -954 -943 -917 -968 -991 -956 -902 -942 -999 -998 -908 -928 -930 -914 -922 -936 -960 -937 -939 -926 -965 -925 -951 -910 -907 -970 -990 -984 -964 -987 -916 -947 -982 -950 -974 -915 -932 -958 -981 -941 -961 -983 -952\n",
"output": "1 -1000\n2 -999 -998\n96 -997 -996 -995 -994 -993 -992 -991 -990 -989 -988 -987 -986 -985 -984 -983 -982 -981 -980 -979 -978 -977 -976 -975 -974 -973 -972 -971 -970 -969 -968 -967 -966 -965 -964 -963 -962 -961 -960 -959 -958 -957 -956 -955 -954 -953 -952 -951 -950 -949 -948 -947 -946 -945 -944 -943 -942 -941 -940 -939 -938 -937 -936 -934 -933 -932 -931 -930 -929 -928 -927 -926 -925 -924 -923 -922 -921 -920 -919 -918 -917 -916 -915 -914 -913 -912 -911 -910 -909 -908 -907 -906 -905 -904 -903 -902 0\n"
},
{
"input": "59\n-990 -876 -641 -726 718 -53 803 -954 894 -265 -587 -665 904 349 754 -978 441 794 -768 -428 -569 -476 188 -620 -290 -333 45 705 -201 109 165 446 13 122 714 -562 -15 -86 -960 43 329 578 287 -776 -14 -71 915 886 -259 337 -495 913 -498 -669 -673 818 225 647 0\n",
"output": "29 -990 -876 -641 -726 -53 -954 -265 -587 -665 -978 -768 -428 -569 -476 -620 -290 -333 -201 -562 -15 -86 -960 -776 -14 -71 -259 -495 -498 -669\n28 718 803 894 904 349 754 441 794 188 45 705 109 165 446 13 122 714 43 329 578 287 915 886 337 913 818 225 647\n2 0 -673\n"
}
],
"generated_tests": [
{
"input": "100\n-34 81 85 -96 50 20 54 86 22 10 -19 52 65 44 30 53 63 71 17 98 -92 4 5 -99 89 -23 48 9 7 33 75 2 47 -56 42 70 -68 57 51 83 82 94 91 45 46 25 95 11 -12 62 -31 -87 58 38 67 97 -60 66 73 -28 13 93 29 59 -49 77 37 -43 -27 0 -16 72 15 79 61 78 35 21 3 8 84 1 -32 36 74 -88 26 100 6 14 40 76 18 162 24 69 80 64 55 41\n",
"output": "19 -34 -96 -19 -92 -99 -23 -56 -68 -12 -31 -87 -60 -28 -49 -43 -27 -16 -32 -88\n80 81 85 50 20 54 86 22 10 52 65 44 30 53 63 71 17 98 4 5 89 48 9 7 33 75 2 47 42 70 57 51 83 82 94 91 45 46 25 95 11 62 58 38 67 97 66 73 13 93 29 59 77 37 72 15 79 61 78 35 21 3 8 84 1 36 74 26 100 6 14 40 76 18 162 24 69 80 64 55 41\n1 0\n"
},
{
"input": "100\n-87 -48 -76 -1 -10 -17 -22 -19 -27 -99 -43 49 38 -20 -45 -64 44 -96 -35 -74 -65 -41 -21 -75 37 -12 -67 0 -3 5 -80 -93 -81 -97 -47 -63 53 -100 95 -79 -83 -90 -32 88 -77 -16 -23 -54 -28 -4 -73 -98 -25 -39 60 -56 -34 -2 -11 -55 -52 -69 -68 -29 -82 -62 -36 -13 -6 -89 8 -72 18 -15 -50 -71 -70 -92 -37 -78 -61 -9 -30 -85 -91 -94 84 -86 -7 -57 -14 40 -33 51 -26 46 59 -31 -58 -66\n",
"output": "83 -87 -48 -76 -1 -10 -17 -22 -19 -27 -99 -43 -20 -45 -64 -96 -35 -74 -65 -41 -21 -75 -12 -67 -3 -80 -93 -81 -97 -47 -63 -100 -79 -83 -90 -32 -77 -16 -23 -54 -28 -4 -73 -98 -25 -39 -56 -34 -2 -11 -55 -52 -69 -68 -29 -82 -62 -36 -13 -6 -89 -72 -15 -50 -71 -70 -92 -37 -78 -61 -9 -30 -85 -91 -94 -86 -7 -57 -14 -33 -26 -31 -58 -66\n16 49 38 44 37 5 53 95 88 60 8 18 84 40 51 46 59\n1 0\n"
},
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"output": "97 -1000 -986 -979 -955 -966 -963 -973 -959 -972 -906 -924 -927 -929 -1697 -553 -967 -921 -989 -911 -995 -945 -919 -971 -913 -912 -933 -969 -1908 -920 -988 -997 -994 -953 -962 -940 -905 -978 -948 -957 -996 -976 -949 -931 -903 -985 -923 -993 -448 -909 -938 -946 -934 -992 -904 -980 -954 -943 -917 -968 -991 -956 -902 -942 -999 -998 -908 -928 -930 -914 -922 -936 -960 -937 -939 -926 -965 -925 -481 -910 -907 -970 -990 -984 -964 -987 -916 -947 -982 -827 -974 -915 -932 -958 -981 -941 -961 -983\n2 -935 -952\n1 0\n"
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{
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"output": "35 -631 -906 -29 -696 -165 -524 -185 -663 -846 -501 -651 -341 -833 -142 -847 -192 -587 -930 -509 -49 -807 -158 -886 -143 -639 -156 -291 -916 -622 -960 -678 -731 -943 -535 -159\n27 348 885 735 687 642 15 895 12 688 945 603 849 736 676 788 256 863 319 218 118 172 1460 436 861 745 589 376\n2 0 -182\n"
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"output": "35 -22 -41 -36 -6 -75 -5 -4 -14 -37 -84 -73 -45 -6 -42 -18 -51 -48 -76 -40 -30 -24 -15 -97 -60 -31 -67 -68 -3 -99 -71 -10 -116 -98 -63 -58\n63 57 13 83 53 69 86 87 11 70 2 16 31 34 94 26 27 52 46 96 21 32 7 61 66 114 90 80 89 77 78 54 8 88 33 12 19 1 59 44 64 43 56 35 47 39 50 29 28 74 23 85 79 65 55 92 72 93 38 81 62 91 49 22\n2 0 -20\n"
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"output": "75 -17 -70 -60 -80 -9 -68 -30 -42 -106 -98 -47 -5 -14 -94 -73 -80 -27 -66 -85 -53 -25 -3 -45 -69 -11 -64 -65 -91 -90 -54 -12 -39 -24 -71 -41 -44 -93 -20 -92 -43 -52 -55 -84 -89 -19 -4 -99 -26 -87 -36 -56 -120 -62 -95 -28 -82 -2 -78 -96 -21 -77 -76 -27 -10 -97 -8 -15 -48 -34 -59 -7 -51 -33 -72 -79\n24 16 32 75 86 58 49 83 74 67 13 81 6 57 18 40 37 63 23 63 1 46 50 22 38\n1 0\n"
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{
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"output": "29 -660 -876 -641 -726 -53 -954 -265 -587 -665 -1336 -768 -428 -569 -476 -620 -290 -333 -201 -562 -15 -86 -960 -665 -14 -71 -259 -495 -498 -669\n28 718 803 894 904 349 754 441 794 188 45 705 109 165 446 25 122 1089 43 329 578 287 915 886 337 913 818 225 647\n2 0 -658\n"
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{
"input": "100\n-34 81 85 -96 50 20 54 86 22 16 -19 52 65 44 30 53 63 71 17 99 -92 4 5 -99 89 -23 48 9 7 33 75 2 47 -56 42 70 -126 57 51 83 82 94 91 45 46 25 95 21 -12 62 -31 -87 58 38 67 97 -60 66 73 -28 13 93 29 59 -49 77 37 -43 -27 0 -16 72 15 79 61 78 35 21 3 8 84 1 -32 36 74 -88 26 100 4 14 40 76 18 162 24 69 80 64 55 26\n",
"output": "19 -34 -96 -19 -92 -99 -23 -56 -126 -12 -31 -87 -60 -28 -49 -43 -27 -16 -32 -88\n80 81 85 50 20 54 86 22 16 52 65 44 30 53 63 71 17 99 4 5 89 48 9 7 33 75 2 47 42 70 57 51 83 82 94 91 45 46 25 95 21 62 58 38 67 97 66 73 13 93 29 59 77 37 72 15 79 61 78 35 21 3 8 84 1 36 74 26 100 4 14 40 76 18 162 24 69 80 64 55 26\n1 0\n"
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"output": "51 -97 -90 -52 -3 -60 -50 -73 -77 -32 -81 -67 -6 -34 -28 -45 -80 -4 -7 -57 -79 -7 -31 -89 -21 -93 -82 -5 -70 -20 -18 -64 -66 -68 -40 -99 -23 -2 -98 -54 -63 -1 -12 -96 -85 -2 -92 -46 -91 -19 -11 -86\n47 61 114 146 65 83 38 30 35 44 17 58 47 71 69 43 29 16 95 74 36 72 53 62 7 15 76 10 59 88 49 9 10 56 100 25 94 13 42 39 55 24 75 51 41 84 14 13\n2 0 -37\n"
},
{
"input": "5\n-2 -2 -1 -16 0\n",
"output": "1 -2\n2 -16 -1\n2 0 -2\n"
},
{
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"output": "19 -66 -17 -29 -37 -16 -25 -95 -45 -10 -5 -61 -96 -92 -72 -55 -63 -41 -88 -86\n80 3 54 24 76 89 32 93 99 51 78 23 68 59 18 34 77 9 39 19 8 73 14 12 31 2 26 40 48 30 52 49 13 4 87 114 85 58 50 83 80 69 116 91 97 11 100 56 82 53 13 70 1 47 21 12 74 7 6 33 55 65 64 81 42 36 28 38 20 43 71 12 22 84 15 75 62 44 35 98 46\n1 0\n"
},
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"output": "85 -95 -28 -43 -72 -11 -24 -37 -35 -44 -66 -45 -84 -96 -51 -55 -23 -31 -4 -59 -17 -69 -10 -12 -78 -14 -52 -57 -40 -75 -98 -6 -53 -3 -90 -63 -8 -20 -91 -32 -76 -80 -49 -43 -27 -19 -38 -9 -49 -67 -36 -39 -65 -83 -64 -18 -94 -79 -58 -16 -22 -74 -25 -13 -46 -89 -47 -15 -54 -99 -30 -109 -21 -86 -1 -50 -68 -100 -85 -29 -48 -50 -84 -93 -41 -82\n14 11 4 7 88 70 73 2 81 87 5 56 33 92 42\n1 0\n"
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"output": "73 -75 -60 -18 -92 -71 -9 -37 -34 -82 -54 -83 -76 -58 -88 -17 -97 -39 -96 -81 -10 -98 -47 -131 -22 -33 -19 -99 -66 -21 -90 -70 -32 -26 -77 -74 -44 -5 -55 -2 -6 -7 -73 -1 -9 -30 -95 -42 -20 -79 -48 -4 -72 -67 -46 -52 -86 -40 -53 -35 -8 -43 -15 -49 -12 -3 -80 -31 -47 -91 -45 -24 -23 -63\n25 28 93 64 27 14 87 57 24 12 16 12 59 62 51 56 85 49 50 65 29 11 78 94 84 89\n2 0 -61\n"
},
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"output": "89 -64 -51 -36 -98 -26 -1 -8 -99 -76 -53 -80 -43 -22 -100 -62 -34 -5 -65 -81 -18 -91 -92 -16 -23 -95 -9 -19 -11 -46 -79 -35 -87 -7 -26 -20 -71 -61 -67 -50 -66 -68 -49 -35 -32 -57 -85 -59 -30 -36 -3 -77 -25 -94 -56 -24 -19 -72 -41 -31 -48 -38 -26 -39 -33 -70 -84 -93 -73 -14 -69 -40 -97 -7 -55 -45 -54 -10 -29 -96 -12 -83 -15 -21 -47 -2 -63 -89 -58 -82\n10 74 52 4 86 60 11 28 17 88 13\n1 0\n"
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"output": "97 -1000 -986 -979 -955 -966 -963 -973 -896 -972 -906 -924 -927 -929 -1697 -553 -967 -921 -989 -911 -995 -945 -919 -971 -913 -912 -933 -969 -1908 -920 -988 -997 -994 -953 -962 -940 -905 -978 -948 -957 -996 -976 -949 -931 -903 -985 -923 -993 -448 -909 -938 -946 -934 -992 -904 -980 -954 -943 -917 -968 -991 -956 -902 -942 -999 -998 -908 -928 -930 -914 -922 -936 -960 -937 -939 -926 -965 -925 -481 -910 -907 -970 -990 -984 -964 -987 -916 -947 -982 -827 -974 -915 -932 -958 -981 -941 -961 -983\n2 -935 -952\n1 0\n"
},
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"output": "35 -631 -906 -29 -696 -165 -524 -185 -663 -846 -501 -651 -341 -833 -142 -847 -192 -587 -930 -509 -49 -807 -158 -886 -143 -639 -156 -291 -916 -622 -960 -678 -731 -943 -535 -159\n27 348 885 735 687 642 15 895 12 688 945 603 849 736 676 861 256 863 319 218 118 172 1460 436 861 745 589 376\n2 0 -182\n"
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"output": "35 -22 -41 -36 -6 -75 -5 -4 -14 -37 -84 -73 -45 -6 -42 -18 -51 -48 -76 -40 -30 -24 -15 -97 -60 -31 -67 -68 -3 -99 -71 -10 -116 -98 -63 -58\n63 57 13 83 53 69 86 87 11 70 2 16 31 40 94 26 27 52 46 96 21 32 7 61 66 114 90 80 89 77 78 54 8 88 33 12 19 1 59 44 64 43 56 35 47 39 50 29 28 74 23 85 79 65 55 92 72 93 38 81 62 91 49 22\n2 0 -20\n"
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"output": "75 -17 -70 -60 -80 -9 -68 -30 -42 -106 -98 -47 -5 -14 -94 -73 -80 -27 -66 -85 -53 -25 -3 -45 -69 -11 -64 -65 -91 -90 -54 -12 -39 -24 -71 -41 -44 -93 -20 -92 -43 -52 -55 -84 -89 -19 -4 -99 -26 -87 -36 -56 -120 -62 -95 -28 -82 -2 -78 -96 -21 -77 -76 -27 -10 -97 -8 -15 -48 -34 -59 -7 -51 -33 -72 -79\n24 4 32 75 86 58 49 83 74 67 13 81 6 57 18 40 37 63 23 63 1 46 50 22 38\n1 0\n"
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137_B. Permutation | 1413 | 1413_222 | "Hey, it's homework time" — thought Polycarpus and of course he started with his favourite subject, IT. Polycarpus managed to solve all tasks but for the last one in 20 minutes. However, as he failed to solve the last task after some considerable time, the boy asked you to help him.
The sequence of n integers is called a permutation if it contains all integers from 1 to n exactly once.
You are given an arbitrary sequence a1, a2, ..., an containing n integers. Each integer is not less than 1 and not greater than 5000. Determine what minimum number of elements Polycarpus needs to change to get a permutation (he should not delete or add numbers). In a single change he can modify any single sequence element (i. e. replace it with another integer).
Input
The first line of the input data contains an integer n (1 ≤ n ≤ 5000) which represents how many numbers are in the sequence. The second line contains a sequence of integers ai (1 ≤ ai ≤ 5000, 1 ≤ i ≤ n).
Output
Print the only number — the minimum number of changes needed to get the permutation.
Examples
Input
3
3 1 2
Output
0
Input
2
2 2
Output
1
Input
5
5 3 3 3 1
Output
2
Note
The first sample contains the permutation, which is why no replacements are required.
In the second sample it is enough to replace the first element with the number 1 and that will make the sequence the needed permutation.
In the third sample we can replace the second element with number 4 and the fourth element with number 2. | n = int(input())
x = list(map(int, input().split()))
a, list_of_set = n * [0], n * [0]
ans = 0
for i in range(1, n + 1):
a[i - 1] = i
for j in range(n):
if j + 1 in set(x):
list_of_set[j] = j + 1
for k in range(n):
if list_of_set[k] != a[k]:
ans += 1
print(ans)
| import sys
import time
import itertools
from itertools import accumulate, product, permutations, combinations
import collections
from collections import Counter, OrderedDict, deque, defaultdict, ChainMap
from functools import lru_cache
import math
from math import sqrt, sin, cos, tan, ceil, fabs, floor, gcd, exp, log, log2
import fractions
from typing import List, Tuple
import numpy as np
import random
import heapq
from heapq import *
from dataclasses import dataclass
import builtins
import re
def strip(s, characters = None):
if characters is None:
characters = [' ', '\t', '\n', '\r', '\v', '\f']
else:
characters = list(characters)
characters = [x for x in characters if len(x) > 0]
i = 0
while i < len(s):
found_sep_candidate = False
for sep_candidate in characters:
if s[i:i + len(sep_candidate)] == sep_candidate:
found_sep_candidate = True
i += len(sep_candidate)
break
if not found_sep_candidate:
break
j = len(s) - 1
while j >= 0:
found_sep_candidate = False
for sep_candidate in characters:
if s[j + 1 - len(sep_candidate):j+1] == sep_candidate:
found_sep_candidate = True
j -= len(sep_candidate)
break
if not found_sep_candidate:
break
return s[i:j+1]
def split(s, sep=None, maxsplit=-1):
if sep == '':
raise builtins.ValueError('empty separator')
if type(sep) == list and '' in sep:
raise builtins.ValueError('empty separator')
if sep is None:
sep = [' ', '\t', '\n', '\r', '\v', '\f']
result = []
word = ''
count_split = 0
if maxsplit == -1:
maxsplit = len(s) * 1000
i = 0
while i < len(s):
found_sep_candidate = False
for sep_candidate in sep:
if s[i:i + len(sep_candidate)] == sep_candidate:
found_sep_candidate = True
if word:
result.append(word)
count_split += 1
word = ''
i += len(sep_candidate)
break
if not found_sep_candidate and count_split < maxsplit:
word += s[i]
i += 1
elif not found_sep_candidate and count_split >= maxsplit:
word += s[i:]
i = len(s)
if word:
result.append(word)
return result
if type(sep) == str:
sep = [sep]
if maxsplit == -1:
maxsplit = 0
elif maxsplit == 0:
maxsplit = -1
return re.split(re.compile("|".join([re.escape(x) for x in sep])), s, maxsplit=maxsplit)
class str_escaped(str):
def split(self, sep=None, maxsplit=-1):
return split(self, sep=sep, maxsplit=maxsplit)
def strip(self, chars=None):
return strip(self, characters = chars)
from dataclasses import dataclass
from typing import List
@dataclass
class Input:
n: int
values: List[int]
@classmethod
def from_str(cls, input_: str):
n, values, _ = input_.split('\n')
n = int(n)
values = [int(x) for x in values.split(' ')]
return cls(n, values)
def __repr__(self):
return str(self.n) + '\n' + ' '.join([str(x) for x in self.values]) + '\n'
| 2
2 2
| O(n**2) | 0 | {
"public_tests": [
{
"input": "2\n2 2\n",
"output": "1\n"
},
{
"input": "3\n3 1 2\n",
"output": "0\n"
},
{
"input": "5\n5 3 3 3 1\n",
"output": "2\n"
}
],
"private_tests": [
{
"input": "100\n340 14 3275 2283 2673 1107 817 2243 1226 32 2382 3638 4652 418 68 4962 387 764 4647 159 1846 225 2760 4904 3150 403 3 2439 91 4428 92 4705 75 348 1566 1465 69 6 49 4 62 4643 564 1090 3447 1871 2255 139 24 99 2669 969 86 61 4550 158 4537 3993 1589 872 2907 1888 401 80 1825 1483 63 1 2264 4068 4113 2548 41 885 4806 36 67 167 4447 34 1248 2593 82 202 81 1783 1284 4973 16 43 95 7 865 2091 3008 1793 20 947 4912 3604\n",
"output": "70\n"
},
{
"input": "10\n1 1 2 2 8 8 7 7 9 9\n",
"output": "5\n"
},
{
"input": "5\n6 6 6 6 6\n",
"output": "5\n"
},
{
"input": "2\n2 3\n",
"output": "1\n"
},
{
"input": "1\n2\n",
"output": "1\n"
},
{
"input": "30\n28 1 3449 9 3242 4735 26 3472 15 21 2698 7 4073 3190 10 3 29 1301 4526 22 345 3876 19 12 4562 2535 2 630 18 27\n",
"output": "14\n"
},
{
"input": "10\n1 2 3 4 5 6 7 1000 10 10\n",
"output": "2\n"
},
{
"input": "2\n1 1\n",
"output": "1\n"
},
{
"input": "10\n8 2 10 3 4 6 1 7 9 5\n",
"output": "0\n"
},
{
"input": "10\n551 3192 3213 2846 3068 1224 3447 1 10 9\n",
"output": "7\n"
},
{
"input": "15\n2436 2354 4259 1210 2037 2665 700 3578 2880 973 1317 1024 24 3621 4142\n",
"output": "15\n"
},
{
"input": "5\n3366 3461 4 5 4370\n",
"output": "3\n"
},
{
"input": "2\n5000 5000\n",
"output": "2\n"
},
{
"input": "2\n1 2\n",
"output": "0\n"
},
{
"input": "15\n4 1459 12 4281 3241 2748 10 3590 14 845 3518 1721 2 2880 1974\n",
"output": "10\n"
},
{
"input": "1\n1\n",
"output": "0\n"
},
{
"input": "8\n9 8 7 6 5 4 3 2\n",
"output": "1\n"
},
{
"input": "15\n15 1 8 2 13 11 12 7 3 14 6 10 9 4 5\n",
"output": "0\n"
},
{
"input": "100\n50 39 95 30 66 78 2169 4326 81 31 74 34 80 40 19 48 97 63 82 6 88 16 21 57 92 77 10 1213 17 93 32 91 38 4375 29 75 44 22 4 45 14 2395 3254 59 3379 2 85 96 8 83 27 94 1512 2960 100 9 73 79 7 25 55 69 90 99 51 87 98 62 18 35 43 4376 4668 28 72 56 4070 61 65 36 54 4106 11 24 15 86 70 71 4087 23 13 76 20 4694 26 4962 4726 37 14 64\n",
"output": "18\n"
},
{
"input": "2\n3 4\n",
"output": "2\n"
},
{
"input": "15\n1 2 3 4 5 5 4 3 2 1 1 2 3 4 5\n",
"output": "10\n"
},
{
"input": "1\n5000\n",
"output": "1\n"
},
{
"input": "4\n5000 5000 5000 5000\n",
"output": "4\n"
}
],
"generated_tests": [
{
"input": "100\n340 14 3275 2283 2673 1107 817 3847 1226 32 2382 3638 4652 418 68 4962 387 764 4647 159 1846 225 2760 4904 3150 403 3 2439 91 4428 92 4705 75 348 1566 1465 69 6 49 4 62 4643 564 1090 3447 1871 2255 139 24 99 2669 969 86 61 4550 158 4537 3993 1589 872 2907 1888 401 80 1825 1483 63 1 2264 4068 4113 2548 41 885 4806 36 67 167 4447 34 1248 2593 82 202 81 1783 1284 4973 16 43 95 7 865 2091 3008 1793 20 947 4912 3604\n",
"output": "70\n"
},
{
"input": "10\n1 1 2 2 8 8 7 7 3 9\n",
"output": "4\n"
},
{
"input": "2\n3 3\n",
"output": "2\n"
},
{
"input": "30\n28 1 3449 9 3242 4735 26 3472 15 21 2698 7 4073 3190 10 4 29 1301 4526 22 345 3876 19 12 4562 2535 2 630 18 27\n",
"output": "14\n"
},
{
"input": "10\n8 2 10 3 4 6 1 9 9 5\n",
"output": "1\n"
},
{
"input": "10\n666 3192 3213 2846 3068 1224 3447 1 10 9\n",
"output": "7\n"
},
{
"input": "15\n2436 2354 4259 1210 2037 2665 700 3578 2880 973 1317 1024 30 3621 4142\n",
"output": "15\n"
},
{
"input": "5\n3366 3461 4 2 4370\n",
"output": "3\n"
},
{
"input": "15\n4 1459 12 4281 3241 2748 20 3590 14 845 3518 1721 2 2880 1974\n",
"output": "11\n"
},
{
"input": "100\n50 39 95 30 66 78 2169 4326 81 31 74 34 80 40 19 48 97 63 82 6 88 16 21 57 92 77 10 1213 17 93 32 91 38 4375 29 75 44 22 4 45 14 2395 3254 59 3379 2 85 96 8 83 27 94 1512 2960 100 9 73 79 7 25 55 69 90 99 51 87 98 62 18 35 43 4376 4668 28 72 56 4070 61 65 36 54 4106 11 24 8 86 70 71 4087 23 13 76 20 4694 26 4962 4726 37 14 64\n",
"output": "19\n"
},
{
"input": "15\n1 3 3 4 5 5 4 3 2 1 1 2 3 4 5\n",
"output": "10\n"
},
{
"input": "100\n50 39 95 30 66 78 2169 4326 81 31 74 34 80 40 19 48 97 63 82 6 88 16 21 57 92 27 10 1213 17 93 32 91 38 4375 29 75 44 22 4 45 14 2395 3254 59 3379 2 85 96 8 83 27 94 1512 2960 100 9 73 79 7 25 55 69 90 99 51 87 98 62 18 35 43 4376 4668 28 72 56 4070 61 65 36 54 4106 11 24 8 86 70 71 4087 23 13 76 20 4694 26 4962 4726 37 14 64\n",
"output": "20\n"
},
{
"input": "15\n1 3 3 4 5 7 4 3 2 1 1 2 3 4 5\n",
"output": "9\n"
},
{
"input": "100\n340 14 1203 2283 2673 1107 817 3847 1226 32 2382 3638 4652 418 68 4962 387 764 4647 159 1846 225 2760 4904 3150 403 3 2439 91 4428 92 4705 75 348 1566 1465 69 6 49 4 62 4643 564 1090 3447 1871 2255 139 24 99 2669 969 86 61 4550 158 4537 3993 1589 872 2907 1888 401 80 1825 1483 63 1 2264 4068 4113 2548 41 885 4806 36 67 167 4447 34 1248 2593 82 202 81 1783 1284 4973 24 43 95 7 865 2091 3008 1793 20 947 4912 3604\n",
"output": "71\n"
},
{
"input": "100\n50 39 95 30 66 78 2169 4326 81 31 74 34 80 40 19 48 97 63 82 6 88 16 21 57 92 27 10 1213 17 93 32 91 38 4375 29 75 44 22 4 45 14 2395 3254 59 3379 2 85 96 8 83 27 94 1512 2960 100 9 73 79 7 25 55 69 90 99 31 87 98 62 18 35 43 4376 4668 28 72 56 4070 61 65 36 54 4106 11 24 8 86 70 71 4087 23 13 76 20 4694 26 4962 4726 37 14 64\n",
"output": "21\n"
},
{
"input": "100\n50 39 95 30 66 78 2169 4326 81 31 74 34 80 40 19 48 97 63 82 6 88 16 21 57 92 27 10 1213 17 93 32 91 38 4375 29 75 44 22 4 45 14 2395 3254 59 3379 2 85 96 8 83 27 94 1512 2960 100 9 73 79 7 25 55 69 90 99 31 87 98 62 18 35 43 4376 4668 28 72 56 4070 61 65 36 54 4106 11 24 8 86 70 71 4087 23 20 76 20 4694 26 4962 4726 37 14 64\n",
"output": "22\n"
},
{
"input": "15\n4 1459 18 4281 3241 2469 20 3590 14 845 4623 1721 2 2880 2630\n",
"output": "12\n"
},
{
"input": "5\n1 5 4 3 2\n",
"output": "0\n"
},
{
"input": "10\n184 1711 1226 4196 3068 1224 3447 1 9 9\n",
"output": "8\n"
},
{
"input": "5\n2 6 6 6 6\n",
"output": "4\n"
},
{
"input": "2\n3297 5000\n",
"output": "2\n"
},
{
"input": "2\n1 4\n",
"output": "1\n"
},
{
"input": "8\n13 8 7 6 5 4 3 2\n",
"output": "1\n"
},
{
"input": "15\n15 1 8 2 13 11 12 7 3 14 6 10 6 4 5\n",
"output": "1\n"
},
{
"input": "2\n5 4\n",
"output": "2\n"
},
{
"input": "4\n5000 5000 2454 5000\n",
"output": "4\n"
},
{
"input": "3\n1 1 2\n",
"output": "1\n"
},
{
"input": "5\n1 3 3 3 1\n",
"output": "3\n"
},
{
"input": "100\n340 14 1203 2283 2673 1107 817 3847 1226 32 2382 3638 4652 418 68 4962 387 764 4647 159 1846 225 2760 4904 3150 403 3 2439 91 4428 92 4705 75 348 1566 1465 69 6 49 4 62 4643 564 1090 3447 1871 2255 139 24 99 2669 969 86 61 4550 158 4537 3993 1589 872 2907 1888 401 80 1825 1483 63 1 2264 4068 4113 2548 41 885 4806 36 67 167 4447 34 1248 2593 82 202 81 1783 1284 4973 16 43 95 7 865 2091 3008 1793 20 947 4912 3604\n",
"output": "70\n"
},
{
"input": "10\n1 1 2 2 8 8 9 7 3 9\n",
"output": "4\n"
},
{
"input": "5\n2 6 3 6 6\n",
"output": "3\n"
},
{
"input": "2\n1 3\n",
"output": "1\n"
},
{
"input": "10\n8 2 10 3 4 6 1 9 9 8\n",
"output": "2\n"
},
{
"input": "10\n666 3192 3125 2846 3068 1224 3447 1 10 9\n",
"output": "7\n"
},
{
"input": "15\n2436 2354 4259 1210 2037 2665 700 3578 2880 973 607 1024 30 3621 4142\n",
"output": "15\n"
},
{
"input": "5\n3366 3461 4 3 4370\n",
"output": "3\n"
},
{
"input": "2\n3867 5000\n",
"output": "2\n"
},
{
"input": "2\n2 4\n",
"output": "1\n"
},
{
"input": "15\n4 1459 12 4281 3241 2748 20 3590 14 845 4623 1721 2 2880 1974\n",
"output": "11\n"
},
{
"input": "8\n22 8 7 6 5 4 3 2\n",
"output": "1\n"
},
{
"input": "15\n15 1 8 2 5 11 12 7 3 14 6 10 6 4 5\n",
"output": "2\n"
},
{
"input": "2\n8 4\n",
"output": "2\n"
},
{
"input": "3\n2 1 2\n",
"output": "1\n"
},
{
"input": "5\n1 4 3 3 1\n",
"output": "2\n"
},
{
"input": "10\n1 1 2 2 8 1 9 7 3 9\n",
"output": "4\n"
},
{
"input": "5\n2 6 4 6 6\n",
"output": "3\n"
},
{
"input": "10\n8 2 20 3 4 6 1 9 9 8\n",
"output": "3\n"
},
{
"input": "10\n184 3192 3125 2846 3068 1224 3447 1 10 9\n",
"output": "7\n"
},
{
"input": "15\n2436 2354 4259 1210 2037 2665 700 3578 2880 973 607 1024 3 3621 4142\n",
"output": "14\n"
},
{
"input": "5\n4120 3461 4 3 4370\n",
"output": "3\n"
},
{
"input": "2\n3633 5000\n",
"output": "2\n"
},
{
"input": "2\n4 4\n",
"output": "2\n"
},
{
"input": "15\n4 1459 12 4281 3241 2469 20 3590 14 845 4623 1721 2 2880 1974\n",
"output": "11\n"
},
{
"input": "8\n22 8 7 6 5 4 4 2\n",
"output": "2\n"
},
{
"input": "15\n15 1 8 2 5 11 12 7 3 17 6 10 6 4 5\n",
"output": "3\n"
},
{
"input": "2\n12 4\n",
"output": "2\n"
},
{
"input": "15\n1 3 3 4 5 7 4 3 2 1 1 2 4 4 5\n",
"output": "9\n"
},
{
"input": "5\n1 5 3 3 1\n",
"output": "2\n"
},
{
"input": "100\n340 14 1203 2283 2673 1107 817 3847 1226 32 2382 3638 4652 418 68 4962 387 764 4647 159 1846 225 2760 4904 3150 323 3 2439 91 4428 92 4705 75 348 1566 1465 69 6 49 4 62 4643 564 1090 3447 1871 2255 139 24 99 2669 969 86 61 4550 158 4537 3993 1589 872 2907 1888 401 80 1825 1483 63 1 2264 4068 4113 2548 41 885 4806 36 67 167 4447 34 1248 2593 82 202 81 1783 1284 4973 24 43 95 7 865 2091 3008 1793 20 947 4912 3604\n",
"output": "71\n"
},
{
"input": "10\n1 1 2 2 8 1 1 7 3 9\n",
"output": "4\n"
},
{
"input": "5\n2 6 7 6 6\n",
"output": "4\n"
},
{
"input": "10\n8 2 20 3 1 6 1 9 9 8\n",
"output": "4\n"
},
{
"input": "10\n184 3192 2273 2846 3068 1224 3447 1 10 9\n",
"output": "7\n"
},
{
"input": "15\n4450 2354 4259 1210 2037 2665 700 3578 2880 973 607 1024 3 3621 4142\n",
"output": "14\n"
},
{
"input": "5\n3306 3461 4 3 4370\n",
"output": "3\n"
},
{
"input": "15\n4 1459 12 4281 3241 2469 20 3590 14 845 4623 1721 2 2880 2630\n",
"output": "11\n"
},
{
"input": "8\n34 8 7 6 5 4 4 2\n",
"output": "2\n"
},
{
"input": "5\n1 5 3 3 2\n",
"output": "1\n"
},
{
"input": "100\n340 14 1203 2283 2673 1107 817 787 1226 32 2382 3638 4652 418 68 4962 387 764 4647 159 1846 225 2760 4904 3150 323 3 2439 91 4428 92 4705 75 348 1566 1465 69 6 49 4 62 4643 564 1090 3447 1871 2255 139 24 99 2669 969 86 61 4550 158 4537 3993 1589 872 2907 1888 401 80 1825 1483 63 1 2264 4068 4113 2548 41 885 4806 36 67 167 4447 34 1248 2593 82 202 81 1783 1284 4973 24 43 95 7 865 2091 3008 1793 20 947 4912 3604\n",
"output": "71\n"
},
{
"input": "10\n1 1 2 2 8 2 1 7 3 9\n",
"output": "4\n"
},
{
"input": "10\n8 2 14 3 1 6 1 9 9 8\n",
"output": "4\n"
},
{
"input": "10\n184 3192 2273 4196 3068 1224 3447 1 10 9\n",
"output": "7\n"
},
{
"input": "15\n4450 2354 4259 1210 2037 2665 255 3578 2880 973 607 1024 3 3621 4142\n",
"output": "14\n"
},
{
"input": "5\n3306 3461 5 3 4370\n",
"output": "3\n"
},
{
"input": "8\n34 8 7 11 5 4 4 2\n",
"output": "3\n"
},
{
"input": "100\n340 14 1203 2283 2673 1107 817 787 1226 32 2382 3638 4652 418 68 4962 387 764 4647 159 1846 225 2760 4904 3150 323 3 2439 91 4428 92 4705 75 348 1566 1465 69 6 49 4 62 4643 564 1090 3447 1871 2255 139 24 99 2669 969 86 61 4550 158 4537 3993 1589 872 2907 1888 401 80 1825 1483 63 1 2264 4068 4113 2548 41 885 4806 36 67 167 4447 34 1248 2593 82 202 81 1783 1284 4973 24 43 95 7 865 2091 3008 1793 20 947 3278 3604\n",
"output": "71\n"
},
{
"input": "10\n1 1 2 2 8 4 1 7 3 9\n",
"output": "3\n"
},
{
"input": "10\n8 2 5 3 1 6 1 9 9 8\n",
"output": "3\n"
},
{
"input": "10\n184 1711 2273 4196 3068 1224 3447 1 10 9\n",
"output": "7\n"
},
{
"input": "15\n4450 2354 3296 1210 2037 2665 255 3578 2880 973 607 1024 3 3621 4142\n",
"output": "14\n"
},
{
"input": "5\n3306 3461 5 3 3923\n",
"output": "3\n"
},
{
"input": "15\n4 1459 18 4281 3241 2469 20 3590 14 745 4623 1721 2 2880 2630\n",
"output": "12\n"
},
{
"input": "8\n34 8 7 11 9 4 4 2\n",
"output": "4\n"
},
{
"input": "5\n1 2 4 3 2\n",
"output": "1\n"
},
{
"input": "100\n340 14 1203 2283 2673 1107 817 787 1226 32 2382 3638 4652 418 68 4962 387 764 4647 159 1846 225 2760 4904 3150 323 3 2439 91 4428 92 4705 75 348 1566 2308 69 6 49 4 62 4643 564 1090 3447 1871 2255 139 24 99 2669 969 86 61 4550 158 4537 3993 1589 872 2907 1888 401 80 1825 1483 63 1 2264 4068 4113 2548 41 885 4806 36 67 167 4447 34 1248 2593 82 202 81 1783 1284 4973 24 43 95 7 865 2091 3008 1793 20 947 3278 3604\n",
"output": "71\n"
},
{
"input": "10\n1 1 2 2 8 2 2 7 3 9\n",
"output": "4\n"
},
{
"input": "10\n8 2 5 3 2 6 1 9 9 8\n",
"output": "3\n"
},
{
"input": "10\n184 1711 1226 4196 3068 1224 3447 1 10 9\n",
"output": "7\n"
},
{
"input": "15\n4450 2354 3296 1210 2037 2665 255 4415 2880 973 607 1024 3 3621 4142\n",
"output": "14\n"
},
{
"input": "15\n4 1459 18 4281 3241 2469 20 3590 14 745 4623 1721 2 2919 2630\n",
"output": "12\n"
},
{
"input": "8\n34 1 7 11 9 4 4 2\n",
"output": "4\n"
},
{
"input": "100\n340 14 1203 2283 2673 1107 817 787 1226 32 2382 3638 4652 418 68 4962 387 379 4647 159 1846 225 2760 4904 3150 323 3 2439 91 4428 92 4705 75 348 1566 2308 69 6 49 4 62 4643 564 1090 3447 1871 2255 139 24 99 2669 969 86 61 4550 158 4537 3993 1589 872 2907 1888 401 80 1825 1483 63 1 2264 4068 4113 2548 41 885 4806 36 67 167 4447 34 1248 2593 82 202 81 1783 1284 4973 24 43 95 7 865 2091 3008 1793 20 947 3278 3604\n",
"output": "71\n"
},
{
"input": "10\n8 2 5 3 2 6 1 9 11 8\n",
"output": "3\n"
},
{
"input": "15\n4450 2354 3296 1210 2037 2665 255 4415 2880 973 607 1024 3 4567 4142\n",
"output": "14\n"
},
{
"input": "15\n4 1459 18 4281 3241 1040 20 3590 14 745 4623 1721 2 2919 2630\n",
"output": "12\n"
}
]
} | [
0.00001752841712194056,
0.00000924227734375,
0.000006904312418050699,
0.000006892622377622378,
0.000006889492747486887,
0.000006609331949300701,
8.84411264773725e-8,
4.624087106753035e-8,
4.045804122207912e-8,
3.0479932450166966e-8,
5.1464285185353154e-9,
2.4291092962001724e-9,
2.418851692162863e-9,
2.272762963198693e-9,
2.26749632010222e-9,
1.7628217140101037e-9,
1.6801292921630974e-9,
1.4586189040035957e-9
] |
137_B. Permutation | 1413 | 1413_104 | "\"Hey, it's homework time\" — thought Polycarpus and of course he started with his favourite subj(...TRUNCATED) | "n = int(input())\nns = [int(x) for x in input().split()]\nok = [False]*n\nfor ni in ns:\n ni-=1\(...TRUNCATED) | "import sys\nimport time\nimport itertools\nfrom itertools import accumulate, product, permutations,(...TRUNCATED) | 2
2 2
| O(n) | 0.000001 | {"public_tests":[{"input":"2\n2 2\n","output":"1\n"},{"input":"3\n3 1 2\n","output":"0\n"},{"input":(...TRUNCATED) | [2.8812745574737766e-6,2.488892837631119e-6,2.292101862980769e-6,2.1158861997377623e-6,2.05915405102(...TRUNCATED) |
1102_C. Doors Breaking and Repairing | 2982 | 2982_323 | "You are policeman and you are playing a game with Slavik. The game is turn-based and each turn cons(...TRUNCATED) | "from math import ceil\nn, x, y = map(int, input().split())\nli = list(map(int, input().split()))\ni(...TRUNCATED) | "import sys\nimport time\nimport itertools\nfrom itertools import accumulate, product, permutations,(...TRUNCATED) | 5 5 6
1 2 6 10 3
| O(n) | 0.000003 | {"public_tests":[{"input":"5 5 6\n1 2 6 10 3\n","output":"2\n"},{"input":"6 3 2\n2 3 1 3 4 2\n","out(...TRUNCATED) | [0.042477502218309864,4.523451526988637e-6,4.4658248606861895e-6,4.092630886691434e-6,4.070891157670(...TRUNCATED) |
1102_C. Doors Breaking and Repairing | 2982 | 2982_103 | "You are policeman and you are playing a game with Slavik. The game is turn-based and each turn cons(...TRUNCATED) | "n,x,y=input().split()\nn=int(n)\nx=int(x)\ny=int(y)\n\nl=[int(x) for x in input().split()]\n\nl.sor(...TRUNCATED) | "import sys\nimport time\nimport itertools\nfrom itertools import accumulate, product, permutations,(...TRUNCATED) | 5 5 6
1 2 6 10 3
| O(nlogn) | 0.000014 | {"public_tests":[{"input":"5 5 6\n1 2 6 10 3\n","output":"2\n"},{"input":"6 3 2\n2 3 1 3 4 2\n","out(...TRUNCATED) | [0.00001896206035324976,0.00001715002833060554,0.00001555067730383755,0.000015251951034254272,0.0000(...TRUNCATED) |
499_A. Watching a movie | 1138 | 1138_83 | "You have decided to watch the best moments of some movie. There are two buttons on your player: \n\(...TRUNCATED) | "n,x = map(int, input().split())\ndata = []\nresult = 0\n\nfor _ in range(n):\n data.append(list((...TRUNCATED) | "import sys\nimport time\nimport itertools\nfrom itertools import accumulate, product, permutations,(...TRUNCATED) | 2 3
5 6
10 12
| O(n*m) | 0.000002 | {"public_tests":[{"input":"2 3\n5 6\n10 12\n","output":"6\n"},{"input":"1 1\n1 100000\n","output":"1(...TRUNCATED) | [5.614333342438811e-6,2.2258838368662593e-6,1.9078166520979018e-6,1.8696114510489515e-6,1.8089166029(...TRUNCATED) |
499_A. Watching a movie | 1138 | 1138_66 | "You have decided to watch the best moments of some movie. There are two buttons on your player: \n\(...TRUNCATED) | "n,x=map(int, input().split())\nw=0\nm=1\nfor i in range(n):\n\tl,r=map(int, input().split())\n\tk=r(...TRUNCATED) | "import sys\nimport time\nimport itertools\nfrom itertools import accumulate, product, permutations,(...TRUNCATED) | 2 3
5 6
10 12
| O(n) | 0.000007 | {"public_tests":[{"input":"2 3\n5 6\n10 12\n","output":"6\n"},{"input":"1 1\n1 100000\n","output":"1(...TRUNCATED) | [0.00001486612691215035,0.000011527583752185316,0.000010805071705638112,0.00001031349651715472,0.000(...TRUNCATED) |
725_A. Jumping Ball | 410 | 410_105 | "In a new version of the famous Pinball game, one of the most important parts of the game field is a(...TRUNCATED) | "n = int(input())\ns = input()\n\nbegin = True\ncounter = 0\nans = 0\n\nfor i in range(n):\n if b(...TRUNCATED) | "import sys\nimport time\nimport itertools\nfrom itertools import accumulate, product, permutations,(...TRUNCATED) | 5
>>>>>
| O(n) | 0.000001 | {"public_tests":[{"input":"5\n>>>>>\n","output":"0"},{"input":"4\n<<><\n"(...TRUNCATED) | [0.000022257482613090036,0.000022010910606971156,0.000015191888371394233,0.000014906069096918707,0.0(...TRUNCATED) |
725_A. Jumping Ball | 410 | 410_176 | "In a new version of the famous Pinball game, one of the most important parts of the game field is a(...TRUNCATED) | "n, s = int(input()), input()\nif '<' not in s or '>' not in s:\n print(n)\nelse:\n print(s.fi(...TRUNCATED) | "import sys\nimport time\nimport itertools\nfrom itertools import accumulate, product, permutations,(...TRUNCATED) | 5
>>>>>
| O(1) | 0.000001 | {"public_tests":[{"input":"5\n>>>>>\n","output":"0"},{"input":"4\n<<><\n"(...TRUNCATED) | [5.731500000000001e-6,4.074500000000003e-6,3.9795000000000015e-6,3.951000000000003e-6,3.732999999999(...TRUNCATED) |
End of preview. Expand
in Data Studio
👋 Overview
🚀 Introduction
📋 Getting Started with the data
🔥
problem_and_human_solutions_list.jsonl🔥
complexity_labels_light.jsonl🔥
complexity_labels_full.jsonl🔥
time_complexity_test_set.jsonl🔥
space_complexity_test_set.jsonlLicense
📝 Citation
🚀 Introduction
BigO(Bench) is a benchmark of ~300 code problems to be solved in Python, along with 3,105 coding problems and 1,190,250 solutions for training purposes, that evaluates whether LLMs can find the time-space complexity of code solutions or generate code solutions themselves that respect a time-space complexity requirement. This benchmark addresses the gap in current evaluations that often overlook the ability of models to comprehend and produce code constrained by computational complexity. BigO(Bench) includes a complexity inference framework that can run any Python code snippet, measure multiple runtime and memory footprint values, and infer its algorithmic time-space complexity. It also includes of set of 3,105 coding problems and 1,190,250 solutions from Code Contests annotated with inferred (synthetic) time and space complexity labels from the complexity framework, as well as corresponding runtime and memory footprint values for a large set of input sizes.
For more details, see our Paper, GitHub repository and Website.
📋 Getting Started with the data
The data is available as a Huggingface dataset. You can directly download it from the HuggingFace website, or use the CLI
huggingface-cli download facebook/BigOBench --repo-type dataset --local-dir ./temp_dir
It can also be loaded in a Python script using
from datasets import load_dataset
# Change the second parameter to the sub-dataset you would like to use
df_bb = load_dataset("facebook/BigOBench", 'time_complexity_test_set')
You will find 5 files, whose content is detailed below.
🔥 problem_and_human_solutions_list.jsonl
This gathers the general information about the coding problems and human solutions on which BigO(Bench) is built, from the problem descriptions to the public and private tests. There is also a lot of metadata used for postprocessing the results of BigO(Bench) and further analyze where models are strong and where they struggle.
In addition, you will find added data from BigO(Bench), first in the field dataclass that shares added value about the inputs of a problem, and the code of the dataclass corresponding to this problem as generated by ourselves using a LLM. Some metadata from the complexity framework is also available in complexity_framework, such as the fail rates and inputs metadata as parsed by the framework itself (which can differ from what the dataclass parsed):
dataclass.input_type_listgives the list of arguments, listed as their data type, as inferred by a LLM. This comes along the dataclass code, that is also inferred by the LLM. The LLM uses the problem description and a reference solution to try to understand the data types. This field was used to create filters on the problems and solutions, to create the base dataset of BigO(Bench).complexity_framework.measures_set_id_to_input_properties.framework_input_typeis instead the data type of each argument as inferred by the framework. The framework uses the dataclass code generated by the LLM to split the input stream (string that represents all the inputs of the problem all together), and then each input is parsed into a data type using rules. This means that sometimes a LLM can correctly understand that there are two arguments, but mistake them for string arguments, whereas the framework will use the LLM-generated dataclass to split the input stream into the two arguments, but using rules will correctly infer that each argument is an integer. To understand fully the complexity framework outputs, use this field. The previous one was only used for filters on the base Code Contests dataset, but were not used within the complexity framework itself to generate the complexity output.
problem_and_human_solutions_list: dict list
problem_id: strproblem_name: strdescription: dicttext: stris_description_translated: booluntranslated_text: str
correct_solution_list: dict listsolution_id: strsolution_code: str
data_source: strsource_specific_limits: dicttime_limit: dictseconds: intnanos: int
memory_limit_bytes: int
codeforces_specific_metadata: dictcf_contest_id: intcf_index: strcf_points: floatcf_rating: intcf_tags: str listdifficulty: str
tests: dictpublic_tests: dict listinput: stroutput: str
private_tests: dict listinput: stroutput: str
generated_tests: dict listinput: stroutput: str
human_accuracy_rate: floatdataclass: dictdataclass_code: strinput_type_list: str listnumber_inputs: int
complexity_framework: dicttime_complexity_fail_ratespace_complexity_fail_ratetime_or_space_complexity_fail_ratemeasures_set_id_to_input_properties: dict- (measures_set_id) str: dict
input_id: strframework_input_type: strinput_dimension: int
- (measures_set_id) str: dict
🔥 complexity_labels_light.jsonl
Light outputs of the complexity framework, as detailed in the module src/complexity, when run on all problems and solutions from problem_and_human_solutions_list.jsonl.
complexity_labels_light: dict list
problem_id: strproblem_name: strsolution_id: strtime_complexity_inferred: strspace_complexity_inferred: strtime_curve_coefficient: floatspace_curve_coefficient: float
🔥 complexity_labels_full.jsonl
Full outputs of the complexity framework, as detailed in the module src/complexity, when run on all problems and solutions from problem_and_human_solutions_list.jsonl.
complexity_labels_full_n-m: dict list
problem_id: strproblem_name: strsolution_id: strtime_complexity_inferred: strspace_complexity_inferred: strtime_curve_coefficient: floatspace_curve_coefficient: floatquery_dataclass_code: strquery_code: strquery_inputs_example: strruntime_measures: dict listmeasures_set_id: strmeasures_per_expansion_multiplier: dict listexpansion_multiplier: intmeasures_per_expansion_method: dict listvalue_list: float listexpansion_method: strmeasures_set_id_list: str listmeasures_priority: int
memory_footprint_measures: dict listmeasures_set_id: strmeasures_per_expansion_multiplier: dict listexpansion_multiplier: intmeasures_per_expansion_method: dict listvalue_list: float listexpansion_method: strmeasures_set_id_list: str listmeasures_priority: int
🔥 time_complexity_test_set.jsonl
The time complexity test set is made out of 311 problems and 640 corresponding solutions covering 11 different classes (the most represented ones being O(n), O(n.log(n)), O(n2), O(1), O(n ×m) and the least represented O((n + m)log(n + m))).
It was created from problem_and_human_solutions_list.jsonl and the complexity framework outputs on this dataset, complexity_labels_full.jsonl. Filtering was applied to nail down the test set of problems and solutions.
time_complexity_test_set: dict list
problem_name: strproblem_id: strsolution_id: strdescription: strsolution_code: strdataclass_code: strinputs_example: strtime_complexity_inferred: strtime_curve_coefficient: floattests: dictpublic_tests: dict listinput: stroutput: str
private_tests: dict listinput: stroutput: str
generated_tests: dict listinput: stroutput: str
problem_time_curve_coefficient_list: float list
🔥 space_complexity_test_set.jsonl
The space complexity test set consists in 308 problems and 636 solutions covering 5 different classes (by order of popularity O(n), O(1), O(n**2), O(n + m), O(n×m)).
It was created from problem_and_human_solutions_list.jsonl and the complexity framework outputs on this dataset, complexity_labels_full.jsonl. Filtering was applied to nail down the test set of problems and solutions.
space_complexity_test_set: dict list
problem_name: strproblem_id: strsolution_id: strdescription: strsolution_code: strdataclass_code: strinputs_example: strspace_complexity_inferred: strspace_curve_coefficient: floattests: dictpublic_tests: dict listinput: stroutput: str
private_tests: dict listinput: stroutput: str
generated_tests: dict listinput: stroutput: str
problem_space_curve_coefficient_list: float list
License
The majority of BigO(Bench) is licensed under CC-BY-NC (see LICENCE), however portions of the project are available under separate license terms: https://github.com/pberkes/big_O is licensed under the BSD-3 license.
📝 Citation
If you find our project useful and/or are using its data, please cite our paper:
@misc{chambon2025bigobenchllmsgenerate,
title={BigO(Bench) -- Can LLMs Generate Code with Controlled Time and Space Complexity?},
author={Pierre Chambon and Baptiste Roziere and Benoit Sagot and Gabriel Synnaeve},
year={2025},
eprint={2503.15242},
archivePrefix={arXiv},
primaryClass={cs.CL},
url={https://arxiv.org/abs/2503.15242},
}
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