欧拉计划 Project Euler56（幂的数字和）题解

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;
}