C. On Number of Decompositions into Multipliers

https://codeforces.com/problemset/problem/397/C

思路

Code

https://codeforces.com/contest/397/submission/185147057

#include<bits/stdc++.h>
using namespace std;
#define int long long
const int mod=1e9+7;
const int MAXV=20000;
int inv[MAXV+10],jc[MAXV+10],invjc[MAXV+10];
int ksm(int a,int b,int res=1) {
    for(;b;a=a*a%mod,b>>=1)
        if(b&1) res=res*a%mod;
    return res;
}
void init() {
    jc[0]=1;
    for(int i=1;i<=MAXV;i++)
        jc[i]=jc[i-1]*i%mod;
    invjc[MAXV]=ksm(jc[MAXV],mod-2);
    for(int i=MAXV;i>0;i--)
        invjc[i-1]=invjc[i]*i%mod;
    for(int i=1;i<=MAXV;i++)
        inv[i]=jc[i-1]*invjc[i]%mod;
}
int C(int x,int y) {
    return jc[x]*invjc[y]%mod*invjc[x-y]%mod;
}
signed main() {
    init();
    int n;
    cin>>n;
    map<int,int> mp;
    for(int i=1;i<=n;i++) {
        int x;
        cin>>x;
        for(int j=2;j*j<=x;j++)
            while(x%j==0) x/=j,mp[j]++;
        if(x>1) mp[x]++;
    }
    int ans=1;
    for(auto tmp:mp)
        (ans*=C(tmp.second+n-1,n-1))%=mod;
    cout<<ans<<endl;
    return 0;
}

组合数解释

https://www.cnblogs.com/ke-xin/p/13532206.html

 

 

C(n+m−1,m−1)