动态规划 — 计算二项式系数

#include <iomanip>
#include <iostream>
 
using namespace std;
 
int main()
{
    int n, k;
 
    cout << "求C(n,k)，请输入n和k(k <= n)：";
    cin >> n >> k;
     
    int **p;
    p = new int*[n + 1];
    for (int i = 0; i <= n; i++)
        p[i] = new int[k + 1];
     
    for (int i = 0; i <= n; i++)
        for (int j = 0; j <= k; j++)
            p[i][j] = 0;
     
    for (int i = 0; i <= n; i++)
        p[i][0] = 1;  // C(n,0) = 0
 
    for (int i = 0; i <= k; i++)
        p[i][i] = 1;  // C(n,n) = 1
 
    for (int i = 2; i <= n; i++)
        for (int j = 1; j < (i > k ? k + 1 : i); j++)
            p[i][j] = p[i - 1][j - 1] + p[i - 1][j];
 
    //cout.flags(ios::right);   // 输出对齐
    for (int i = 0; i <= n; i++)
    {
        for (int j = 0; j <= k; j++)
            cout << setw(5) << p[i][j] << ' ';
 
        cout << endl;
    }
     
    // 销毁空间
    for (int i = 0; i <= n; i++)
        delete[] p[i];
 
    delete[] p;
 
    return 0;
}