4 Values whose Sum is 0
Time Limit: 15000MS | Memory Limit: 228000K | |
Total Submissions: 20863 | Accepted: 6282 | |
Case Time Limit: 5000MS |
Description
The SUM problem can be formulated as follows: given four lists A, B, C, D of integer values, compute how many quadruplet (a, b, c, d ) ∈ A x B x C x D are such that a + b + c + d = 0 . In the following, we assume that all lists have the same size n .
Input
The first line of the input file contains the size of the lists n (this value can be as large as 4000). We then have n lines containing four integer values (with absolute value as large as 228 ) that belong respectively to A, B, C and D .
Output
For each input file, your program has to write the number quadruplets whose sum is zero.
Sample Input
6 -45 22 42 -16 -41 -27 56 30 -36 53 -37 77 -36 30 -75 -46 26 -38 -10 62 -32 -54 -6 45
Sample Output
5
Hint
Sample Explanation: Indeed, the sum of the five following quadruplets is zero: (-45, -27, 42, 30), (26, 30, -10, -46), (-32, 22, 56, -46),(-32, 30, -75, 77), (-32, -54, 56, 30).
Source
题意:从4列数据每列选1个使之和为0,求可挑选的方案总数。
思路:将第1,2列和第3,4列的和全部求出来,排序,然后二分直至找到和为0。
# include <stdio.h> # include <algorithm> # define MAXN 4000 using namespace std; int a[MAXN][4], b[MAXN*MAXN], c[MAXN*MAXN]; int main() { int n, l, r, sum, tmp, cnt; while(~scanf("%d",&n)) { sum = cnt = 0; for(int i=0; i<n; ++i) scanf("%d%d%d%d",&a[i][0],&a[i][1],&a[i][2],&a[i][3]); for(int i=0; i<n; ++i) for(int j=0; j<n; ++j) { b[cnt] = a[i][0] + a[j][1]; c[cnt++] = a[i][2] + a[j][3]; } sort(b, b+cnt); sort(c, c+cnt); for(int i=0; i<cnt; ++i) { tmp = 0; l = 0; r = cnt-1; while(l<r) { int mid = (l+r)>>1; if(b[i]+c[mid]<0) l = mid + 1; else r = mid; } if(r==0&&(b[i]+c[r]!=0) || l==cnt-1&&(b[i]+c[r]!=0))continue; if(b[i]+c[r]==0) ++tmp; for(int k=r-1; k>=0&&(b[i]+c[k])==0; --k) ++tmp;//符合情况的c[r]可能扎堆在一起,向前搜索。 for(int k=r+1; k<cnt&&(b[i]+c[k])==0; ++k) ++tmp;//向后搜索。 sum += tmp; for(;i+1<cnt&&b[i]==b[i+1]; ++i) sum += tmp;//计算相同的b[i]。 } printf("%d\n",sum); } return 0; }