Binomial coefficient O(N) && O(N^2) - YessineJallouli/Competitive-Programming GitHub Wiki

#include <bits/stdc++.h>
using namespace std;

const int mod = 1e9 + 7;
const int mx = 1e5+7;

long long fact[mx];
long long invfact[mx];

long long fast_pow(long long a, long long b) {
   long long ans = 1;
   while (b > 0) {
      if (b & 1)
         ans = (ans*a)%mod;
      a = (a*a)%mod;
      b/= 2;
   }
   return ans;
}

long long modinv(long long a) {
   return fast_pow(a, mod-2);
}

void precompute() {
   fact[0] = 1;
   for (int i = 1; i < mx; i++)
      fact[i] = fact[i-1] * i % mod;
   for (int i = 0; i < mx; i++)
      invfact[i] = modinv(fact[i]);
}

long long C(int n, int k) {
   if (k > n)
      return 0;
   return fact[n] * invfact[n-k] % mod * invfact[k] % mod;
}

int main() {
   precompute();
}

#include <bits/stdc++.h>
using namespace std;

const int mod = 1e9 + 7;
const int mx = 2e3 + 7;

long long dp[mx][mx];

long long C(int n, int k) {
   if (dp[n][k] != -1)
      return dp[n][k];
   if (k == n || k == 0)
      return dp[n][k] = 1;
   return dp[n][k] = (C(n-1, k) + C(n-1, k-1)) % mod;
}

int main() {
   memset(dp, -1, sizeof dp);
}