POJ P1837 Balance

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题目

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

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题目大意

给出n个挂钩，m个钩码，然后分别是n个挂钩的位置的描述（小于0表示在天平左边），m个钩码重量的描述
求出用完所有砝码构成天平平衡的方案数
（天平一臂的长度为15，钩码的重量≤25）

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题解

DP

f[i][j]表示前i个钩码放置使得天平的状态为j的方案数

其中，j=7500，表示平衡，j<7500表示向左倾的力与单位力比值为|j|，j>7500表示向右倾的力与单位力比值为|j|

为什么设7500为平衡点？ 因为max左边=max右边=20*15*25=7500

这道题的代码，我也没交……（POJ维护中……）

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代码

#include<cstdio>#include<cstring>using namespace std;int n,m;int f[25][15005],a[25],b[25];int readln(){    int x=0,f=1;    char ch=getchar();    while (ch<'0'||ch>'9') {if (ch=='-') f=-1;ch=getchar();}    while ('0'<=ch&&ch<='9') x=x*10+ch-48,ch=getchar();    return x*f;}int main(){    while(~scanf("%d%d",&n,&m))    {        for (int i=1;i<=n;i++) a[i]=readln();        for (int i=1;i<=m;i++) b[i]=readln();        memset(f,0,sizeof(f));        f[0][7500]=1;        for (int i=1;i<=m;i++)            for (int j=0;j<=15000;j++)                if (f[i-1][j]!=0)                    for (int k=1;k<=n;k++)                        f[i][j+a[k]*b[i]]+=f[i-1][j];        printf("%d",f[m][7500]);    }    return 0;}