UVa 10105 Polynomial Coefficients（排列组合）

题意：

求x₁ⁿ¹x₂ⁿ²...x_k^nk的系数

思路：

排列组合知识。

#include <cstdio>

#include <cstdlib>

#include <cstring>



const int MAXN = 20;

int c[MAXN][MAXN];



void init()

{

    for (int i = 0; i < MAXN; ++i)

        c[i][0] = c[i][i] = 1;



    for (int i = 2; i < MAXN; ++i)

        for (int j = 1; j < i; ++j)

            c[i][j] = c[i-1][j] + c[i-1][j-1];

}



int main()

{

    int n, k;

    init();

    while (scanf("%d %d", &n, &k) != EOF)

    {

        int a[MAXN];

        for (int i = 0; i < k; ++i)

            scanf("%d", &a[i]);



        int ans = 1;

        for (int i = 0; i < k; ++i)

            ans *= c[n][a[i]], n -= a[i];



        printf("%d\n", ans);

    }

    return 0;

}