Square Coins

最新推荐文章于 2024-08-25 08:45:00 发布

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最新推荐文章于 2024-08-25 08:45:00 发布

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分类专栏：母函数

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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
Source
Asia 1999
Uploader

crq

#include<stdio.h>

#define max 310
int main()
{
    int coin[17] = {1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289}; //列出所有coin的面值
    int n,i,j,k, an[max], bn[max]; //an[]记录结果，bn[]记录中间值
    while(scanf("%d", &n) && n)
    {
        for(i = 0; i <= n; i ++) //赋初值
        {
            an[i] = 1;
            bn[i] = 0;
        }
        for(j = 1; j < 17; j ++) 
        {
            for(i = 0; i <= n; i ++)
            {
                for(k = 0; k + i <= n; k += coin[j])
                    bn[k + i] += an[i];
            }
            for(i = 0; i <= n; i ++)
            {
                an[i] = bn[i];
                bn[i] = 0;
            }
        }
        printf("%d\n", an[n]);
    }
    return 0;
}