题干

思路

直接暴力枚举即可，用c++要模拟大数的乘法，否则会溢出

code

// 972
#include <bits/stdc++.h>

using namespace std;

using ll = long long;

string mul(const string &num1, int num2) {
	int carry = 0; // 进位
	string ans;
	for (int i = num1.size() - 1; i >= 0; --i) {
		int tmp = (num1[i] - '0') * num2 + carry;
		ans += (tmp % 10) + '0';
		carry = tmp / 10;
	}
	while (carry > 0) {
		ans += (carry % 10) + '0';
		carry /= 10;
	}
	reverse(ans.begin(), ans.end());
	return ans;
}

int digsum(const string &num) {
	int ans = 0;
	for (char c : num) {
		ans += c - '0';
	}
	return ans;
}

void solve() {
	ll ans = 0;
	for (int a = 1; a < 100; ++a) {
		string power = "1";
		for (int b = 1; b < 100; ++b) {
			power = mul(power, a);
			int sum = digsum(power);
			if (sum > ans) {
				ans = sum;
			}
		}
	}
	cout << ans << "\n";

	
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int tt = 1; // cin >> tt;
	while (tt--) {
		solve();
	}

	return 0;
}