CSES · 1712

Exponentiation II

This C++ solution uses modular exponentiation for CSES 1712 Exponentiation II. Read the reasoning, inspect the code, or try your own test case below.

1712MathModular exponentiationC++30 lines
Solution088of 248
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Approach

Modular exponentiation

Exponentiation II task requires a^(b^c) modulo 1e9+7; the nested modular exponentiation matches.

Math

Problem and code

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Written by benbenyaojifen. Try the problem first, then compare your approach with the code.

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Implementation

Exponentiation_II.cpp

C++

    #include <bits/stdc++.h>
    using namespace std;
    using ll = long long;
    using i128 = __int128;
    const int inf = 1e9;
    const ll INF = 1e18; //❄️
    ll power(ll a, ll b, int mod) {
        ll res = 1;
        a %= mod;
        while (b) {
            if (b & 1) res = ((res % mod) * (a % mod)) % mod;
            a = ((a % mod) * (a % mod)) % mod;
            b >>= 1LL;
        }
        return res;
    }
    int main() {
        ios::sync_with_stdio(0); cin.tie(0); 
        int n; cin >> n;
        while (n--) {
            ll a, b, c; cin >> a >> b >> c;
            if (b == 0 && c == 0) {
                cout << a << '\n';
                continue;
            }
            ll p = power(b, c, 1e9 + 6); // by fermats little theorem
            cout << power(a, p, 1e9 + 7) << '\n';
        }
        return 0;
    }
        

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