2018刑偵科推理試題
阿新 • • 發佈：2018-12-31
最近很火的刑偵推理題，我也試了一下，答案是BCACA CDABA
如果直接推理很難，還要不斷試錯。既然這樣不如藉助計算機暴力出結果(因為只有4^9=262144種情況，可以無腦秒出)。具體做法是
1.首先生成所有可能的答案（遞迴生成解答樹）
2.篩選掉不符合10個題目要求的（剪枝，剪枝順序還可以優化）
3.剩下唯一一個就是答案
附上原始碼：
#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; }