poj1837

Balance

Time Limit: 1000MS		Memory Limit: 30000K
Total Submissions:17044		Accepted: 10701

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

题意：有一个天平，左臂右臂各长15，然后给出n，m，n代表有几个挂钩，挂钩给出负数代表在左臂的距离，正数则在右臂m代表有m个砝码，要你求出使得这个天平保持平衡有几种方法，要求所有砝码全部使用完。

思路：首先我们先要明确dp数组的作用，dp[i][j]中，i为放置的砝码数量，j为平衡状态，0为平衡,j<0左倾，j>0右倾，由于j作为下标不能是负数，所以我们要找一个新的平衡点，因为15*20*25= 7500，所以平衡点设置为7500
然后我们可以得出动态方程 dp[i][j+w[i]*c[k])+=dp[i-1][j];
（转至）https://blog.csdn.net/libin56842/article/details/21116143

#include<iostream>
#include<cstdio>
#include<string.h>
using namespace std;
int ci[30];
int gi[30];
int dp[30][7500*2+100];///dp[i][j]=k /   i是砝码数量，j为平衡状态，k方法数
int main(){
    int n,m;
    int maxWi=0;
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++){
        scanf("%d",&ci[i]);
    }
    for(int i=1;i<=m;i++){
        scanf("%d",&gi[i]);
    }
    dp[0][7500]=1;//因为数组下表不能为负，所以要让初始状态从20*15*25=7500开始 
    for(int i=1;i<=m;i++){
        for(int j=0;j<=7500*2;j++){// 
                for(int k=1;k<=n;k++){
                    if(j>=gi[i]*ci[k])
                    dp[i][j+gi[i]*ci[k]]+=dp[i-1][j]; //j+gi[i]*ci[k],加上第i个砝码后的状态。 
                }
            }
    }
    cout<<dp[m][7500]<<endl;
    return 0;
}