AcWing 888. 求组合数 IV（高精度求组合数问题）

Posted 2022-02-21 MangataTS

题面连接

https://www.acwing.com/problem/content/890/

思路

因为要用到高精度，那我们直接使用python就好，如果不使用python，那么我们可以将$a!$和$b!$进行一个质因子拆分操作，最后再使用高精度乘法将这些质数的质因子质数的值全部乘上就好

代码

python

import math
a,b=map(int,input().split());
b=max(b,a-b);
ans=1;
for i in range(a-b+1,a+1):
    ans=ans*i;
for i in range(1,b+1):
    ans=ans//i;
print(ans)

C++

#include <iostream>
#include <algorithm>
#include <vector>

using namespace std;


const int N = 5010;

int primes[N], cnt;
int sum[N];
bool st[N];


void get_primes(int n)

    for (int i = 2; i <= n; i ++ )
    
        if (!st[i]) primes[cnt ++ ] = i;
        for (int j = 0; primes[j] <= n / i; j ++ )
        
            st[primes[j] * i] = true;
            if (i % primes[j] == 0) 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;
    for (int i = 0; i < a.size(); i ++ )
    
        t += a[i] * b;
        c.push_back(t % 10);
        t /= 10;
    
    while (t)
    
        c.push_back(t % 10);
        t /= 10;
    
    return c;



int main()

    int a, b;
    cin >> a >> b;

    get_primes(a);

    for (int i = 0; i < cnt; i ++ )
    
        int p = primes[i];
        sum[i] = get(a, p) - get(a - b, p) - get(b, p);
    

    vector<int> res;
    res.push_back(1);

    for (int i = 0; i < cnt; i ++ )
        for (int j = 0; j < sum[i]; j ++ )
            res = mul(res, primes[i]);

    for (int i = res.size() - 1; i >= 0; i -- ) printf("%d", res[i]);
    puts("");

    return 0;