2018行政科推理试题
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
-
首先生成所有可能的答案（递归生成解答树）
-
筛选掉不符合10个题目要求的（剪枝，剪枝顺序还可以优化）
-
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;
}
版权声明：本文为racaljk原创文章，遵循 CC 4.0 BY-SA 版权协议，转载请附上原文出处链接和本声明。