HDU-1398-Square Coins（母函数）

链接：

https://vjudge.net/problem/HDU-1398

题意：

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.

思路：

母函数模板， 枚举平方

代码：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
#include<math.h>
#include<vector>

using namespace std;
typedef long long LL;
const int INF = 1e9;

const int MAXN = 300+10;
int c1[MAXN], c2[MAXN];
int n;

void Init()
{
    c1[0] = 1;
    for (int i = 1;i <= 17;i++)
    {
        for (int j = 0;j < MAXN;j+=i*i)
        {
            for (int k = 0;k+j < MAXN;k++)
                c2[j+k] += c1[k];
        }
        for (int j = 0;j < MAXN;j++)
        {
            c1[j] = c2[j];
            c2[j] = 0;
        }
    }
}

int main()
{
    Init();
    while(~scanf("%d", &n) && n)
    {
        printf("%d\n", c1[n]);
    }

    return 0;
}