HDU 1398 Square Coins(母函数)

 

              

                                Square Coins
              Time Limit:1000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u
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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

 

#include<stdio.h>

#define MAX 310

int main(void)

{

    int n,i,j,k;

    int c1[MAX],c2[MAX];

    while(scanf("%d",&n)!=EOF&&n)

    {

        for(i=0;i<=n;i++)

        {

            c1[i]=1;

            c2[i]=0;//当前方程

        }

        for(i=2;i*i<=n;i++){

            for(j=0;j<=n;j++){

                for(k=0;k+j<=n;k+=i*i)

                    c2[k+j]+=c1[j];//当前方程的系数 向下继承k(各种硬币直)+j

            }

            for(j=0;j<=n;j++){

                c1[j]=c2[j];

                c2[j]=0;

            }

        }

        printf("%d\n",c1[n]);

    }

    return 0;

}

 

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