POJ 1837-Balance 動態規劃

題目來源：http://acm.pku.edu.cn/JudgeOnline/problem?id=1837

 

解題報告：

 

想了很久，還是看了別人的解題報告

背包問題的形式吧

設f[i][j]代表掛了前i個砝碼時，平衡度為j的方法的個數。
顯然，平衡度的範圍為[-25*20*15,25*20*15]，即[-7500,7500]，但是要使天平保持平衡，
一旦平衡度超過3750，或小於-3750，那麼剩下的砝碼無論如何放，天平都無法平衡，所以這種情況可以不用考慮。

當然，實際時，由於不允許有負數，所以f[i][j]需要進行必要的修改。

 

#include <iostream><br />using namespace std;</p><p>int main()<br />{<br />int C,G;<br />cin >> C >> G;<br />int *c=new int[C];<br />int *w=new int[G];<br />for(int i=0;i<C;i++)<br />cin >> c[i];<br />for(int i=0;i<G;i++)<br />cin >> w[i];<br />int f[21][7501]={0};<br />f[0][3750]=1;<br />for(int i=1;i<=G;i++)<br />{<br />for(int j=0;j<7501;j++)<br />{<br />if(f[i-1][j]!=0)<br />{<br />for(int k=0;k<C;k++)<br />f[i][j+c[k]*w[i-1]]+=f[i-1][j];<br />}<br />}<br />}<br />cout << f[G][3750] << endl;<br />}

 

附錄：

Balance

Time Limit: 1000MS		Memory Limit: 30000K
Total Submissions: 3771		Accepted: 2141

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