Hackerrank GCD Product(莫比烏斯反演)

自為風月馬前卒發表於2019-01-04
GC

題意

題目連結

Sol

一道咕咕咕了好長時間的題

題解可以看這裡

#include<bits/stdc++.h>
#define LL long long
using namespace std;
const int MAXN = 1e7 + 5e6 + 10,  mod = 1e9 + 7, mod2 = 1e9 + 6;
int N, M, vis[MAXN], prime[MAXN], mu[MAXN], f[MAXN], tot;
int add(int x, int y) {
    if(x + y < 0) return x + y + mod;
    return x + y >= mod ? x + y - mod : x + y;
}
int mul(int x, int y) {
    return 1ll * x * y % mod;
}
int fp(int a, int p) {
    int base = 1;
    while(p) {
        if(p & 1) base = mul(base, a);
        a = mul(a, a); p >>= 1;
    }
    return base;
}
void sieve(int N) {
    vis[1] = 1; mu[1] = 1;
    for(int i = 2; i <= N; i++) {
        if(!vis[i]) prime[++tot] = i, mu[i] = -1;
        for(int j = 1; j <= tot && i * prime[j] <= N; j++) {
            vis[i * prime[j]] = 1;
            if(!(i % prime[j])) {mu[i * prime[j]] = 0; break;}
            else mu[i * prime[j]] = -mu[i];
        }
    }
    for(int i = 1; i <= tot; i++) 
        for(LL j = prime[i]; j <= N; j *= prime[i])
            f[j] =prime[i];
    for(int i = 1; i <= N; i++) if(!f[i]) f[i] = 1;
}
signed main() {
    cin >> N >> M;
    sieve(1e7 + 5e6);
    //for(int i = 1; i <= 100; i++) printf("%d %d
", i, f[i]);
    int ans = 1;
    for(int i = 1; i <= N; i++) {
        if(f[i] == 1) continue;
        ans = mul(ans, fp(f[i], 1ll * (N / i) * (M / i) % mod2));
    }
    cout << ans;
    return 0;
}
/*
100000 50000 200 300
100 2 1 1
*/

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