4. 位运算（快速幂）

1.

typedef long long ll;
ll mod_pow(ll x, ll n, ll mod){
    ll res = 1;
    while(n > 0){
        if(n & 1) res = res * x % mod;
        x = x * x % mod;
        n >>= 1;
    }
    return res;
}

 

2.

ll mod_pow(ll x, ll n, ll mod){
    if(n == 0) return 1 % mod;
    ll res = mod_pow(x * x % mod, n/2, mod);
    if(n & 1) res = res * x % mod;
    return res;
}

 3.当 x, n, p都在10^18级别，改为加法

typedef long long LL;

LL mod_pow(LL x, LL n, LL mod){
    LL ans = 0;
    while (n > 0){
        if (n & 1) ans = (ans + x) % mod;
        x = x * 2 % p;
        n >> 1
    }
    return ans;
}