hdoj 1709 The Balance(母函数)

因为是天平，所以组合之间的差值也都是可以得到的，这差值也是新的组合数。

代码：

#include<iostream>#include<cstdio>#include<cstring>using namespace std;const int maxn = 1e4+5;int n, c1[maxn], c2[maxn], num[maxn], ans[maxn];int main(void){    while(cin >> n)    {        int sum = 0;        for(int i = 1; i <= n; i++)            scanf("%d", &num[i]), sum += num[i];        memset(c1, 0, sizeof(c1));        memset(c2, 0, sizeof(c2));        c1[0] = c1[num[1]] = 1;        for(int i = 2; i <= n; i++)        {            for(int j = 0; j <= sum; j++)                for(int k = 0; k+j <= sum && k <= num[i]; k += num[i])                {                    if(k > j) c2[k-j] += c1[j];                    else c2[j-k] += c1[j];                    c2[k+j] += c1[j];                }            for(int j = 0; j <= sum; j++)                c1[j] = c2[j], c2[j] = 0;        }        int count = 0;        for(int i = 1; i <= sum; i++)            if(!c1[i]) ans[count++] = i;        if(!count) puts("0");        else        {            printf("%d\n", count);            for(int i = 0; i < count; i++)                printf("%d%c", ans[i], i==count-1? '\n' : ' ');        }    }    return 0;}

The Balance

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 7615    Accepted Submission(s): 3165

Problem Description

Now you are asked to measure a dose of medicine with a balance and a number of weights. Certainly it is not always achievable. So you should find out the qualities which cannot be measured from the range [1,S]. S is the total quality of all the weights.

 

Input

The input consists of multiple test cases, and each case begins with a single positive integer N (1<=N<=100) on a line by itself indicating the number of weights you have. Followed by N integers Ai (1<=i<=N), indicating the quality of each weight where 1<=Ai<=100.

 

Output

For each input set, you should first print a line specifying the number of qualities which cannot be measured. Then print another line which consists all the irrealizable qualities if the number is not zero.

 

Sample Input

31 2 439 2 1

 

Sample Output

024 5

 

Source

HDU 2007-Spring Programming Contest

 

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