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+7 1+2-3-4+5+6-7 1-2 3+4+5+6+7 1-2 3-4 5+6 7 1-2+3+4-5+6-7 1-2-3-4-5+6+7
题解：先对每个数字之间添加'+'或者'-'或者空格。这个可以用深搜实现。然后再对表达式求值，如果表达式的和为零，那么就是符合要求的，输出即可。
丑陋的代码o(╯□╰)o
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1 /* 2 ID:spcjv51 3 PROG:zerosum 4 LANG:C 5 */ 6 #include<stdio.h> 7 #include<string.h> 8 int n; 9 char ss[50]; 10 void print() 11 { 12 char s[50]; 13 int i,len,lr,j,ans; 14 ans=0; 15 strcpy(s,ss); 16 len=strlen(s); 17 i=1; 18 lr=1; 19 if(s[i]==' ') 20 { 21 lr=lr*10+s[i+1]-'0'; 22 j=i+2; 23 while(s[j]==' ') 24 { 25 lr=lr*10+s[j+1]-'0'; 26 j+=2; 27 28 } 29 i=j; 30 } 31 ans+=lr; 32 33 while(i<len) 34 { 35 36 37 if(s[i]=='-') 38 { 39 j=i+2; 40 lr=s[i+1]-'0'; 41 while(s[j]==' ') 42 { 43 lr=lr*10+s[j+1]-'0'; 44 j+=2; 45 46 } 47 i=j; 48 ans-=lr; 49 50 } 51 if(s[i]=='+') 52 { 53 j=i+2; 54 lr=s[i+1]-'0'; 55 while(s[j]==' ') 56 { 57 lr=lr*10+s[j+1]-'0'; 58 j+=2; 59 60 } 61 i=j; 62 ans+=lr; 63 } 64 65 } 66 if(ans==0) 67 printf("%s\n",ss); 68 } 69 void dfs(int step,int last) 70 { 71 char str[3],ssr[50]; 72 if(step==n) 73 { 74 print(); 75 return; 76 } 77 sprintf(str,"%d",step+1); 78 last=last*10+step+1; 79 strcpy(ssr,ss); 80 strcat(ss," "); 81 strcat(ss,str); 82 dfs(step+1,last); 83 strcpy(ss,ssr); 84 strcat(ss,"+"); 85 strcat(ss,str); 86 last=step+1; 87 dfs(step+1,last); 88 strcpy(ss,ssr); 89 strcat(ss,"-"); 90 strcat(ss,str); 91 last=-(step+1); 92 dfs(step+1,last); 93 strcpy(ss,ssr); 94 } 95 96 int main(void) 97 { 98 freopen("zerosum.in","r",stdin); 99 freopen("zerosum.out","w",stdout); 100 scanf("%d",&n); 101 strcpy(ss,"1"); 102 dfs(1,1); 103 return 0; 104 }