2018行政科推理试题

Posted 2020-10-26 racaljk

最近很火的刑侦推理题，我也试了一下，答案是BCACA CDABA

如果直接推理很难，还要不断试错。既然这样不如借助计算机暴力出结果(因为只有4^9=262144种情况，可以无脑秒出)。具体做法是

1. 首先生成所有可能的答案（递归生成解答树）

2. 筛选掉不符合10个题目要求的（剪枝，剪枝顺序还可以优化）

3. 剩下唯一一个就是答案

附上源代码：

#include <algorithm>  
#include <iostream>  
#define pass  
   
char answers[10];  
   
// Auxiliary functions  
int findMaxCount() {  
    int abcd[4];  
    for (int i = 0; i < 10; i++) {  
        abcd[answers[i] - 'A']++;  
    }  
    return *std::max_element(abcd, abcd + 4);  
};  
int findMinCount() {  
    int abcd[4];  
    for (int i = 0; i < 10; i++) {  
        abcd[answers[i] - 'A']++;  
    }  
    return *std::min_element(abcd, abcd + 4);  
};  
   
bool sameWithProblem8(int prob1, int probl2) {  
    char problem8Anaswer = answers[7];  
    if (problem8Anaswer == 'A') {  
        if (answers[prob1 - 1] != 'A' || answers[probl2 - 1] != 'A')  
            return false;  
    }  
    else if (problem8Anaswer == 'B') {  
        if (answers[prob1 - 1] != 'B' || answers[probl2 - 1] != 'B')  
            return false;  
    }  
    else if (problem8Anaswer == 'C') {  
        if (answers[prob1 - 1] != 'C' || answers[probl2 - 1] != 'C')  
            return false;  
    }  
    else if (problem8Anaswer == 'D') {  
        if (answers[prob1 - 1] != 'D' || answers[probl2 - 1] != 'D')  
            return false;  
    }  
    else {  
        static_assert(true, "should not reach here");  
    }  
    return true;  
};  
   
// BCACA CDABA  
// All 4^9=262144 occurrences could be enumerated in the solution tree  
void enumerateing(int problemCnt) {  
    if (problemCnt == 10) {  
        // Check 1  
        pass;  
        // Check 2  
        if (answers[1] == 'A') {  
            if (answers[4] != 'C')  
                return;  
        }  
        else if (answers[1] == 'B') {  
            if (answers[4] != 'D')  
                return;  
        }  
        else if (answers[1] == 'C') {  
            if (answers[4] != 'A')  
                return;  
        }  
        else if (answers[1] == 'D') {  
            if (answers[4] != 'B')  
                return;  
        }  
        else {  
            static_assert(true, "should not reach here");  
        }  
        // Check 3  
        if (answers[2] == 'A') {  
            if (answers[2] == answers[5] || answers[2] == answers[1] || answers[2] == answers[3])  
                return;  
        }  
        else if (answers[2] == 'B') {  
            if (answers[5] == answers[2] || answers[5] == answers[1] || answers[5] == answers[3])  
                return;  
        }  
        else if (answers[2] == 'C') {  
            if (answers[1] == answers[2] || answers[1] == answers[5] || answers[1] == answers[3])  
                return;  
        }  
        else if (answers[2] == 'D') {  
            if (answers[3] == answers[2] || answers[3] == answers[5] || answers[3] == answers[1])  
                return;  
        }  
        else {  
            static_assert(true, "should not reach here");  
        }  
        // Check 4  
        if (answers[3] == 'A') {  
            if (answers[0] != answers[4])  
                return;  
        }  
        else if (answers[3] == 'B') {  
            if (answers[1] != answers[6])  
                return;  
        }  
        else if (answers[3] == 'C') {  
            if (answers[0] != answers[8])  
                return;  
        }  
        else if (answers[3] == 'D') {  
            if (answers[5] != answers[9])  
                return;  
        }  
        else {  
            static_assert(true, "should  not reach here");  
        }  
        // Check 5  
        if (answers[4] == 'A') {  
            if (answers[7] != 'A')  
                return;  
        }  
        else if (answers[4] == 'B') {  
            if (answers[3] != 'B')  
                return;  
        }  
        else if (answers[4] == 'C') {  
            if (answers[8] != 'C')  
                return;  
        }  
        else if (answers[4] == 'D') {  
            if (answers[6] != 'D')  
                return;  
        }  
        else {  
            static_assert(true, "should not reach here");  
        }  
        // Check 6  
        if (answers[5] == 'A') {  
            if (!sameWithProblem8(2, 4))  
                return;  
        }  
        else if (answers[5] == 'B') {  
            if (!sameWithProblem8(1, 6))  
                return;  
        }  
        else if (answers[5] == 'C') {  
            if (!sameWithProblem8(3, 10))  
                return;  
        }  
        else if (answers[5] == 'D') {  
            if (!sameWithProblem8(5, 9))  
                return;  
        }  
        else {  
            static_assert(true, "should not reach here");  
        }  
   
        // Check 7  
        int abcd[4];  
        for (int i = 0; i < 10; i++) {  
            abcd[answers[i] - 'A']++;  
        }  
        char whichCharMinCount = 'A';  
        int min = abcd[0];  
        for (int k = 1; k < 4; k++) {  
            if (abcd[k] < min) {  
                min = abcd[k];  
                whichCharMinCount = 'A' + k;  
            }  
        }  
        if (answers[6] == 'A') {  
            if (whichCharMinCount != 'C')  
                return;  
        }  
        else if (answers[6] == 'B') {  
            if (whichCharMinCount != 'B')  
                return;  
        }  
        else if (answers[6] == 'C') {  
            if (whichCharMinCount != 'A')  
                return;  
        }  
        else if (answers[6] == 'D') {  
            if (whichCharMinCount != 'D')  
                return;  
        }  
        else {  
            static_assert(true, "should not reach here");  
        }  
        // Check 8  
        auto nearProblem1 = [=](int prob1)->bool {  
            char problem1Answer = answers[0];  
            if ((answers[prob1 - 1] - 1) == problem1Answer || (answers[prob1 - 1] + 1) == problem1Answer)  
                return true;  
            return false;  
        };  
        if (answers[7] == 'A') {  
            if (nearProblem1(7))  
                return;  
        }  
        else if (answers[7] == 'B') {  
            if (nearProblem1(5))  
                return;  
        }  
        else if (answers[7] == 'C') {  
            if (nearProblem1(2))  
                return;  
        }  
        else if (answers[7] == 'D') {  
            if (nearProblem1(10))  
                return;  
        }  
        else {  
            static_assert(true, "should not reach here");  
        }  
        // Check 9  
        if (answers[8] == 'A') {  
            if ((answers[0] == answers[5] && answers[5] == answers[4]) ||  
                (answers[0] != answers[5] && answers[5] != answers[4]))  
                return;  
        }  
        else if (answers[8] == 'B') {  
            if ((answers[0] == answers[5] && answers[9] == answers[4]) ||  
                (answers[0] != answers[5] && answers[9] != answers[4]))  
                return;  
        }  
        else if (answers[8] == 'C') {  
            if ((answers[0] == answers[5] && answers[1] == answers[4]) ||  
                (answers[0] != answers[5] && answers[1] != answers[4]))  
                return;  
        }  
        else if (answers[8] == 'D') {  
            if ((answers[0] == answers[5] && answers[8] == answers[4]) ||  
                (answers[0] != answers[5] && answers[8] != answers[4]))  
                return;  
        }  
        else {  
            static_assert(true, "should not reach here");  
        }  
   
        // Check 10  
        int diff = findMaxCount() - findMinCount();  
        if (answers[9] == 'A') {  
            if (diff != 3)  
                return;  
        }  
        else if (answers[9] == 'B') {  
            if (diff != 2)  
                return;  
        }  
        else if (answers[9] == 'C') {  
            if (diff != 4)  
                return;  
        }  
        else if (answers[9] == 'D') {  
            if (diff != 1)  
                return;  
        }  
        else {  
            static_assert(true, "should not reach here");  
        }  
        // Finally, we got the unique solution and print it  
        std::cout << "Finally we got the unqiue solution:\n";  
        for (auto x : answers) {  
            std::cout << x;  
        }  
        std::cout << "\n";  
        return;  
    }  
    for (char i = 0; i < 4; i++) {  
        answers[problemCnt] = i + 'A';  
        enumerateing(problemCnt + 1);  
    }  
}  
   
int main() {  
    enumerateing(0);  
    getchar();  
    return 0;  
}