usaco - Zero Sum

Consider the sequence of digits from 1 through N (where N=9) in increasing order: 1 2 3 ... N.
Now insert either a `+' for addition or a `-' for subtraction or a ` ' [blank] to run the digits together between each pair of digits (not in front of the first digit). Calculate the result that of the expression
and see if you get zero.
Write a program that will find all sequences of length N that produce a zero sum.

PROGRAM NAME: zerosum

INPUT FORMAT

A single line with the integer N (3 <= N <= 9).

SAMPLE INPUT (file zerosum.in)

7

OUTPUT FORMAT

In ASCII order, show each sequence that can create 0 sum with a `+', `-', or ` ' between each pair of numbers.

SAMPLE OUTPUT (file zerosum.out)

1+2-3+4-5-6+71+2-3-4+5+6-71-2 3+4+5+6+71-2 3-4 5+6 71-2+3+4-5+6-71-2-3-4-5+6+7

k：表示数字几
sum：表示当前的和
num：表示当前加到的数
eg：dfs(2,1,2)表示当前加完了1，该加数2了
犯的错误：
之前写dfs结束条件的时候写成

if(k==n&&sum+num==0){
puts(a);
return ;
}

这样是错误的，因为(k==n&&sum+num!=0)这个情况没有考虑，k会一直增大。

所以dfs要保证有结束的条件。
另外初始化字符数组用memset。

/*
ID:
LANG:C++
PROG:zerosum
*/
#include<iostream>
#include<cstdio>
#include<cstring>
char a[50];
int n;
void dfs(int k,int sum,int num){
if(k==n){
if(sum+num==0)puts(a);
return ;
}
a[2*k-1]=' ';
dfs(k+1,sum,num>0?num*10+k+1:10*num-k-1);
a[2*k-1]='+';
dfs(k+1,sum+num,k+1);
a[2*k-1]='-';
dfs(k+1,sum+num,-k-1);
}

int main()
{
freopen("zerosum.in", "r", stdin);
freopen("zerosum.out", "w", stdout);
scanf("%d",&n);
memset(a,0,sizeof(a));
for(int i=0;i<n;i++){
a[2*i]=i+'1';
}
dfs(1,0,1);
return 0;
}