HDU1398(母函数)

大意：有不通面值的硬币，对于给定的值有多少组成方法。

分析：构造母函数(1+x+x^2+x^3+...)(1+x^4+x^8+.....)...(1+x^209+x^508+....)。

代码：

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <cmath>using namespace std;int c1[305], c2[305];int a[17] = { 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289 };int main(){int n;while (scanf("%d", &n) != EOF){for (int i = 0; i <= n; i++)//第一个括号的项数初始化为1{c1[i] = 1;c2[i] = 0;}for (int i = 2; i <= 17; i++)//计算第2到n个式子{for (int j = 0; j <= n; j++)//计算每一项相乘for (int k = 0; k + j <= n; k += a[i-1])//数组下标表示幂c2[k + j] += c1[j];for (int j = 0; j <= n; j++){c1[j] = c2[j];c2[j] = 0;}}printf("%d\n", c1[n]);}return 0;}