问题：给定一个整数数组，写一个算法实现判断是否存在一个和为零的子数组。

答：算法思路：计算数组的前缀和，然后将前缀和进行排序，如果存在连续两个元素相同的情况即存在一个和为零的子数组，否则不存在。

算法的代码实现：

// // main.cpp // MyProjectForCPP // // Created by labuser on 11/2/11. // Copyright 2011 __MyCompanyName__. All rights reserved. // #include <iostream> #include <math.h> #define YES 1 #define NO 0 using namespace std; void sort(int x[],int n); int zero_sum(int x[],int n){ int i; for(i=1;i<n;i++){ x[i]+=x[i-1]; } sort(x,n); for(i=1;i<n && x[i]!=x[i-1];i++); return (i==n) ? NO : YES; } void sort(int x[],int n){ int i,j; int temp; for(i=0;i<n;i++){ for(j=i+1;j<n;j++){ if(x[i]>x[j]){ temp = x[i]; x[i]=x[j]; x[j]=temp; } } } } int main (int argc, const char * argv[]) { int x[] = {4,-1,2,1,-2,-1,5}; int n = sizeof(x)/sizeof(int); int i; printf("\nZero Sum Sunarray Check Program"); printf("\n==============================="); printf("\n\nGiven Array : "); for(i=0;i<n;i++) printf("%4d",x[i]); if (zero_sum(x, n)==YES) { printf("\n\nYES, there is some range summing up to 0"); }else{ printf("\n\nNO! no such subarray found!"); } printf("\n\n"); return 0; }

运行结果：
GNU gdb 6.3.50-20050815 (Apple version gdb-1705) (Fri Jul  1 10:44:54 UTC 2011)
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[Switching to process 17846 thread 0x0]

Zero Sum Sunarray Check Program
===============================

Given Array :    4  -1   2   1  -2  -1   5

YES, there is some range summing up to 0

Program ended with exit code: 0