Misc/Formula.h

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• Last update: 2025-07-06 11:39:53+07:00
• Link: https://cp-algorithms.com/algebra/factorial-divisors.html

Depends on

• template.h

Code

#include "../template.h"


// https://cp-algorithms.com/algebra/factorial-divisors.html
// Legendre's formula
// only for case k is prime
// n/k + n/(k^2) + n/(k^3) + ...
// return largest x that n! % k^x = 0
// O(logk (n))
int fact_pow(int n, int k) {
    int res = 0;
    while (n) {
        n /= k;
        res += n;
    }
    return res;
}

#line 2 "template.h"

#include <bits/stdc++.h>
using namespace std;
 
#define ll long long
#define MOD (ll)(1e9+7)
#define all(x) (x).begin(),(x).end()
#define unique(x) x.erase(unique(all(x)), x.end())
#define INF32 ((1ull<<31)-1)
#define INF64 ((1ull<<63)-1)
#define inf (ll)1e18

#define vi vector<int>
#define pii pair<int, int>
#define pll pair<ll, ll>
#define fi first
#define se second

const int mod = 998244353;

void solve();

int main(){
    ios_base::sync_with_stdio(false);cin.tie(NULL);
    // cin.exceptions(cin.failbit);
    // int t; cin >> t;
    // while(t--)
        solve();
    cerr << "\nTime run: " << 1000 * clock() / CLOCKS_PER_SEC << "ms" << '\n';
    return 0;
}
#line 2 "Misc/Formula.h"


// https://cp-algorithms.com/algebra/factorial-divisors.html
// Legendre's formula
// only for case k is prime
// n/k + n/(k^2) + n/(k^3) + ...
// return largest x that n! % k^x = 0
// O(logk (n))
int fact_pow(int n, int k) {
    int res = 0;
    while (n) {
        n /= k;
        res += n;
    }
    return res;
}

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