杭电ACM hdu 1398 Square Coins 解题报告（母函数）

Problem Description

People in Silverland use square coins. Not only they have square shapes but also their values are square numbers. Coins with values of all square numbers up to 289 (=17^2), i.e., 1-credit coins, 4-credit coins, 9-credit coins, ..., and 289-credit coins, are available in Silverland. 
There are four combinations of coins to pay ten credits: 
ten 1-credit coins,
one 4-credit coin and six 1-credit coins,
two 4-credit coins and two 1-credit coins, and
one 9-credit coin and one 1-credit coin. 
Your mission is to count the number of ways to pay a given amount using coins of Silverland.

Input
The input consists of lines each containing an integer meaning an amount to be paid, followed by a line containing a zero. You may assume that all the amounts are positive and less than 300.

Output
For each of the given amount, one line containing a single integer representing the number of combinations of coins should be output. No other characters should appear in the output. 

Sample Input
2
10
30
0

Sample Output
1
4
27

Source
Asia 1999, Kyoto (Japan)

Recommend
Ignatius.L

Solution

以下部分的版权归本人（小飞）所有。所有权利保留。

欢迎转载，转载时请注明出处：

http://blog.csdn.net/xiaofei_it/article/details/17041815

本题直接套用母函数模板即可。关于母函数的详细解释请看：

http://blog.csdn.net/xiaofei_it/article/details/17042651

代码如下：

#include <iostream>
#include <cstring>
using namespace std;
#define MAX 301
int n,a[MAX],b[MAX],i,j,k,v[18];
int main()
{
	for (i=1;i<=17;i++)
		v[i]=i*i;
	while ((cin>>n)&&n>0)
	{
		memset(a,0,sizeof(a));
		a[0]=1;
		for (i=1;i<=17;i++)
		{
			memset(b,0,sizeof(b));
			for (j=0;j*v[i]<=n;j++)
				for (k=0;k+j*v[i]<=n;k++)
					b[k+j*v[i]]+=a[k];
			memcpy(a,b,sizeof(b));
		}
		cout<<a[n]<<endl;
	}
	return 0;
}