URAL 1055 Combinations

URAL_1055

    将组合数展开后的每个数依次分解素因子，最后再统计一下有多少种素因子就可以了。

#include<stdio.h>

#include<string.h>

#define MAXD 1010

#define MAXN 50010

int N, M, isprime[MAXD], prime[MAXD], P, h[MAXN];

void prepare()

{

    int i, j;

    P = 0;

    memset(isprime, -1, sizeof(isprime));

    for(i = 2; i <= 1000; i ++)

        if(isprime[i])

        {

            prime[P ++] = i;

            for(j = i * i; j <= 1000; j += i)

                isprime[j] = 0;

        }

}

void deal(int n, int d)

{

    int i;;

    for(i = 0; prime[i] * prime[i] <= n; i ++)

        while(n % prime[i] == 0)

            h[prime[i]] += d, n /= prime[i];

    h[n] += d;

}

void solve()

{

    int i, ans = 0;

    memset(h, 0, sizeof(h));

    for(i = N - M + 1; i <= N; i ++)

        deal(i, 1);

    for(i = 1; i <= M; i ++)

        deal(i, -1);

    for(i = 2; i <= N; i ++)

        if(h[i])

            ++ ans;

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

}

int main()

{

    prepare();

    while(scanf("%d%d", &N, &M) == 2)

    {

        solve();

    }

    return 0;

}