给定一个整数数组，检测是否存在一个和为零的子数组_C/C++_编程开发_程序员俱乐部

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)
Copyright 2004 Free Software Foundation, Inc.
GDB is free software, covered by the GNU General Public License, and you are
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Type "show copying" to see the conditions.
There is absolutely no warranty for GDB.  Type "show warranty" for details.
This GDB was configured as "x86_64-apple-darwin".tty /dev/ttys002
[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