MOOC清华《程序设计基础》第6章第2题：求f(a,b)问题（动态规划）

题目描述

已知f(n, 0) = 1, f(n,n) = 1

当n>m>0时，f(n,m) = f(n-1,m-1) + f(n-1, m)

求f(a, b)

输入格式

多行输入，每一行输入两个正整数a, b (1 <= b <= a <= 10),a，b以空格隔开

输出格式

每一行输出f（a，b）值

样例输入

2 23 2

样例输出

13

#include <iostream>using namespace std;int main(){int a[20] = {0};int b[20] = {0};int i = 0;while(cin >> a[i] >> b[i])i++;int f[11][11] = {0};for(int j = 0; j < i; j++){for(int k = 0; k <= a[j]; k++)f[k][0] = 1;for(int k = 0; k <= a[j]; k++)f[k][k] = 1;for(int m = 1; m <= b[j]; m++)for(int n = m; n <= a[j]; n++){if(n == m)f[n][m] = 1;elseif(n > m)f[n][m] = f[n - 1][m - 1] + f[n - 1][m];}cout << f[a[j]][b[j]] << endl;}return 0;}