Square Coins

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 7452 Accepted Submission(s): 5050

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

解題思路：

本題的母函數為 (1+x+x^2+x^3+x^4........) * (1+x^4+x^8+x^12+x^16....) *(1+x^9+x^18+x^27....) * ..............................*(1+x^289+x^(289*2)+..............

1分的硬幣有多少個 4分的硬幣有多少個 9分的硬幣有多少個

這個多了一些限制條件，在母函數模板裡改幾個地方就可以了。重在理解。

代碼：

#include 
using namespace std;
int c[302],temp[302],n;

int main()
{
    while(cin>>n&&n)
    {
        for(int i=0;i<=n;i++)
        {
            c[i]=1;
            temp[i]=0;
        }
        for(int i=2;i*i<=n;i++)//i是代表多少個式子相乘，這裡i*i<=n的意思是比如要求 x^16次方，第一個式子是以1打頭的（1+x+x^2+x^3...)，1*x^16,所有的式子中最後一次出現x^16次方的是(1+x^16+x^32..)這是第4個式子。
        {
            for(int j=0;j<=n;j++)
                for(int k=0;k+j<=n;k+=i*i)//注意 k+=i*i ,因為比如當i等於2時，代表第2個式子1+x^4+x^8+x^12+x^16..，注意指數。
                    temp[j+k]+=c[j];
            for(int i=0;i<=n;i++)
            {
                c[i]=temp[i];
                temp[i]=0;
            }
        }
        cout<