POJ 1837 天平

Balance

Time Limit: 1000MS Memory Limit: 30000KTotal Submissions: 12867 Accepted: 8071

Description

Gigel has a strange "balance" and he wants to poise it. Actually, the device is different from any other ordinary balance. 
It orders two arms of negligible weight and each arm's length is 15. Some hooks are attached to these arms and Gigel wants to hang up some weights from his collection of G weights (1 <= G <= 20) knowing that these weights have distinct values in the range 1..25. Gigel may droop any weight of any hook but he is forced to use all the weights. 
Finally, Gigel managed to balance the device using the experience he gained at the National Olympiad in Informatics. Now he would like to know in how many ways the device can be balanced. 

Knowing the repartition of the hooks and the set of the weights write a program that calculates the number of possibilities to balance the device. 
It is guaranteed that will exist at least one solution for each test case at the evaluation. 

Input

The input has the following structure: 
• the first line contains the number C (2 <= C <= 20) and the number G (2 <= G <= 20); 
• the next line contains C integer numbers (these numbers are also distinct and sorted in ascending order) in the range -15..15 representing the repartition of the hooks; each number represents the position relative to the center of the balance on the X axis (when no weights are attached the device is balanced and lined up to the X axis; the absolute value of the distances represents the distance between the hook and the balance center and the sign of the numbers determines the arm of the balance to which the hook is attached: '-' for the left arm and '+' for the right arm); 
• on the next line there are G natural, distinct and sorted in ascending order numbers in the range 1..25 representing the weights' values. 

Output

The output contains the number M representing the number of possibilities to poise the balance.

Sample Input

2 4-2 3 3 4 5 8

Sample Output

2

Source

Romania OI 2002

题目大意：

有一个天平，天平左右两边各有若干个钩子，总共有C个钩子，有G个钩码，求将钩码全部挂到钩子上使天平平衡的方法的总数。

其中可以把天枰看做一个以x轴0点作为平衡点的横轴

输入：

2 4 //C 钩子数 与 G钩码数

-2 3 //负数：左边的钩子距离天平中央的距离；正数：右边的钩子距离天平中央的距离c[k]

3 4 5 8 //G个重物的质量w[i]

#include<stdio.h>#include<string.h>int dp[25][15010];///dp[i][j]数组中存的是挂到第i个挂钩达到j状态的方法数                  ///i表示挂钩的位置,j表示当前的平衡状态int main(){    int n,m;    int c[25];///挂钩的位置    int w[25];///钩码的重量    while(~scanf("%d%d",&n,&m))    {        memset(dp,0,sizeof(dp));        for(int i=1; i<=n; i++)            scanf("%d",&c[i]);        for(int j=1; j<=m; j++)            scanf("%d",&w[j]);        dp[0][7500]=1;///j=7500是平衡的时候,方法数是1,,即不挂钩码        for(int i=1; i<=m; i++) ///枚举每一个钩码        {            for(int j=0; j<=15000; j++)///所有的状态                if(dp[i-1][j])                    for(int k=1; k<=n; k++)///枚举第i个钩码挂在的位置                        dp[i][j+c[k]*w[i]]+=dp[i-1][j];        }        printf("%d\n",dp[m][7500]);///m个钩码达到平衡时的方法数    }    return 0;}