最幸运的数字(The Luckiest Number) 题解

思路分析

按题目要求使用对应数据结构与算法模拟/递推求解，注意数据范围边界与时间复杂度。

参考代码

#include <algorithm>
#include <iostream>
#include <numeric>
#include <vector>
using namespace std;

using i128 = __int128_t;

long long qpow(long long a, long long b, long long mod) {
    long long res = 1 % mod;
    a %= mod;
    while (b > 0) {
        if (b & 1) res = (long long)((i128)res * a % mod);
        a = (long long)((i128)a * a % mod);
        b >>= 1;
    }
    return res;
}

long long get_phi(long long n) {
    long long res = n;
    for (long long i = 2; i * i <= n; ++i) {
        if (n % i == 0) {
            while (n % i == 0) n /= i;
            res = res / i * (i - 1);
        }
    }
    if (n > 1) res = res / n * (n - 1);
    return res;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    long long L;
    int tc = 1;
    while (cin >> L && L != 0) {
        long long g = std::gcd(L, 8LL);
        long long M = 9LL * (L / g);
        if (std::gcd(10LL, M) != 1) {
            cout << "Case " << tc++ << ": 0\n";
            continue;
        }
        long long phi = get_phi(M);
        vector<long long> divs;
        for (long long d = 1; d * d <= phi; ++d) {
            if (phi % d == 0) {
                divs.push_back(d);
                if (d * d != phi) divs.push_back(phi / d);
            }
        }
        sort(divs.begin(), divs.end());
        long long ans = 0;
        for (long long d : divs) {
            if (qpow(10, d, M) == 1) {
                ans = d;
                break;
            }
        }
        cout << "Case " << tc++ << ": " << ans << "\n";
    }
    return 0;
}