Find the combination number AcWing 888. Find the combination number IV

Original link

AcWing 888. Find the combination number IV

Algorithm tags

Combinatorial mathematics Combination count High precision

Ideas

Code

#include<bits/stdc++.h>
#define int long long
#define abs fabs
#define rep(i, a, b) for(int i=a;i<b;++i)
#define Rep(i, a, b) for(int i=a;i>=b;--i)
using namespace std;
const int N = 5015;
int pr[N], st[N], s[N], cnt;
inline int read(){
   int s=0,w=1;
   char ch=getchar();
   while(ch<'0'||ch>'9'){if(ch=='-')w=-1;ch=getchar();}
   while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
   return s*w;
}
void put(int x) {
    if(x<0) putchar('-'),x=-x;
    if(x>=10) put(x/10);
    putchar(x%10^48);
}
void pri(int n){
    rep(i, 2, n+1){
        if(!st[i]){
            pr[cnt++]=i;
        }
        for(int j=0; pr[j]<=n/i; ++j){
            st[pr[j]*i]=true;
            if(!(i%pr[j])){
                break;
            }
        }
    }
}
int get(int n, int p){
    int res=0;
    while(n){
        res+=n/p;
        n/=p;
    }
    return res;
}
vector<int> mul(vector<int> a, int b){
    vector<int> c;
    int t=0;
    rep(i, 0, a.size()){
        t+=a[i]*b;
        c.push_back(t%10);
        t/=10;
    }
    while(t){
        c.push_back(t%10);
        t/=10;
    }
    return c;
}
signed main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int a=read(), b=read();
    pri(a);
    rep(i, 0, cnt){
        int p=pr[i];
        s[i]=get(a, p)-get(a-b, p)-get(b, p);
    }
    vector<int> res;
    res.push_back(1);
    rep(i, 0, cnt){
        rep(j, 0, s[i]){
            res=mul(res, pr[i]);
        }
    }
    Rep(i, res.size()-1, 0){
        printf("%lld", res[i]);
    }
}

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