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;
}

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