题解

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

// 判断是否满足加法表规则
bool check(vector<vector<string>> &table, map<char, int> &mapping, int base) {
    int n = table.size();
    for (int i = 1; i < n; ++i) {
        for (int j = 1; j < n; ++j) {
            int a = mapping[table[i][0][0]];
            int b = mapping[table[0][j][0]];
            int sum = a + b;
            string result = table[i][j];
            if (result.length() == 1) {
                if (mapping[result[0]] != sum % base) {
                    return false;
                }
            } else {
                if (mapping[result[0]] != sum / base || mapping[result[1]] != sum % base) {
                    return false;
                }
            }
        }
    }
    return true;
}

int main() {
    int n;
    cin >> n;
    vector<vector<string>> table(n, vector<string>(n));
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
            cin >> table[i][j];
        }
    }

    vector<char> letters;
    for (int i = 1; i < n; ++i) {
        letters.push_back(table[i][0][0]);
    }

    int base = n - 1;
    do {
        map<char, int> mapping;
        for (int i = 0; i < letters.size(); ++i) {
            mapping[letters[i]] = i;
        }
        if (check(table, mapping, base)) {
            for (int i = 0; i < letters.size(); ++i) {
                cout << letters[i] << "=" << mapping[letters[i]] << " ";
            }
            cout << endl << base << endl;
            return 0;
        }
    } while (next_permutation(letters.begin(), letters.end()));

    cout << "ERROR!" << endl;
    return 0;
}