ZOJ1711-sum it up(DFS+去重)

Sum It Up

Time Limit: 2 Seconds Memory Limit: 65536 KB
Given a specified total t and a list of n integers, find all distinct sums using numbers from the list that add up to t. For example, if t = 4, n = 6, and the list is [4, 3, 2, 2, 1, 1], then there are four different sums that equal 4: 4, 3+1, 2+2, and 2+1+1. (A number can be used within a sum as many times as it appears in the list, and a single number counts as a sum.) Your job is to solve this problem in general. #include<stdio.h>

Input

The input file will contain one or more test cases, one per line. Each test case contains t, the total, followed by n, the number of integers in the list, followed by n integers x 1 , . . . , x n . If n = 0 it signals the end of the input; otherwise, t will be a positive integer less than 1000, n will be an integer between 1 and 12 (inclusive), and x 1 , . . . , x n will be positive integers less than 100. All numbers will be separated by exactly one space. The numbers in each list appear in nonincreasing order, and there may be repetitions.


Output

For each test case, first output a line containing `Sums of', the total, and a colon. Then output each sum, one per line; if there are no sums, output the line `NONE'. The numbers within each sum must appear in nonincreasing order. A number may be repeated in the sum as many times as it was repeated in the original list. The sums themselves must be sorted in decreasing order based on the numbers appearing in the sum. In other words, the sums must be sorted by their first number; sums with the same first number must be sorted by their second number; sums with the same first two numbers must be sorted by their third number; and so on. Within each test case, all sums must be distinct; the same sum cannot appear twice.


Sample Input

4 6 4 3 2 2 1 1


5 3 2 1 1
400 12 50 50 50 50 50 50 25 25 25 25 25 25
0 0

Sample Output

Sums of 4:
4
3+1
2+2
2+1+1
Sums of 5:
NONE
Sums of 400:
50+50+50+50+50+50+25+25+25+25
50+50+50+50+50+25+25+25+25+25+25

题目大意：给你n个正整数，用这些数凑成t,输出所有的方法，不能重复，每一个表达式为非递增的，表达式之间为递减的。这道题主要是深搜，然后判重。我们可以先排序，然后相同的数字就在相邻位置上了，如果上一个没有用，而当前的有和上一个相同，则当前也不能用。

代码：

#include<stdio.h>#include<string.h>#include<stdlib.h>#define N 100int a[N],b[N],n,flag,left,top;int cmp(const void *x, const void *y){return *(int *)y-*(int *)x;}void fun(int sum,int cur){    int i;if(sum==0){        flag=1;        for(i=0;i<top-1;i++){            printf("%d+",b[i]);        }        printf("%d\n",b[i]);        return;    }    if(sum<0||cur==n)        return;            if(sum>=a[cur]&&a[cur]!=left){        b[top++]=a[cur];        fun(sum-a[cur],cur+1);        b[top--]=0;    }    left=a[cur];    fun(sum,cur+1);}int main(){    int i,t;    while(scanf("%d %d",&t,&n),t||n){        for(i=0;i<n;i++){            scanf("%d",&a[i]);        }        left=top=flag=0;qsort(a,n,sizeof(int),cmp);printf("Sums of %d:\n",t);        fun(t,0);        if(flag==0) printf("NONE\n");    }    return 0;}