24点计算

• 规则
  随机输入四个1到13(也就是扑克牌中A-K)的数字，利用加、减、乘和除对这四个数做运算最终计算得到24，这四个数都需要用到，而且只能使用一次。

• 思路

  • 四个[1 - 13]的数字，a、b、c、d，可用符号+、-、*、/
  • 两两数字之间存在6个结果：{a+b},{a-b},{b-a},{a*b},{a/b},{b/a}
  • 四个数存在三个符号，也就是存在6*6*6=216种结果
  • 四个数字存在4的阶乘=24种组合:
    {a,b,c,d},{a,b,d,c},{a,c,b,d},{a,c,d,b},{a,d,b,c},{a,d,c,b},
    {b,a,c,d},{b,a,d,c},{b,c,d,a},{b,c,a,d},{b,d,a,c},{b,d,c,a},
    {c,a,b,d},{c,a,d,b},{c,b,d,a},{c,b,a,d},{c,d,a,b},{c,d,b,a},
    {d,a,b,c},{d,a,c,b},{d,b,c,a},{d,b,a,c},{d,c,b,a},{d,c,a,b},
  • 24种组合，每种组合存在216种结果，也就是存在24*216=5184种结果（当两数字相同存在相同结果的情况）

• 代码：

/*************************************************************************    > File Name: twentyfour.cc    > Mail: [e-mail] ************************************************************************/#include <set>#include <vector>#include <iostream>#include <utility>#include <stdio.h>#include <stdlib.h>// 记录两数的操作，例如 "（4 + 3）"std::string tostring(float a, float b, char c){    char buf[32] = {0};    sprintf(buf, "(%.0f %c %.0f)", a, c, b);    return std::string(buf);}// 记录前面两数的操作与第三数的操作，或者前面三数与第四个数的操作// 例如 "（（4 + 3） * 2）"std::string tostring(std::string a, std::string b, char c){    char buf[32] = {0};    sprintf(buf, "(%s %c %s)", a.c_str(), c, b.c_str());    return std::string(buf);}// 把浮点数变为字符串，例如 3.5 -> "3.5"std::string tostring(float a){    char buf[32] = {0};    sprintf(buf, "%.0f", a);    return std::string(buf);}// 把两数的结果，一共6钟结果和他们的操作返回出去// 例如：<7, "3 + 4">,<-1,"3 - 4">,<1, "4 - 3">,<12, "3 * 4">,<0.75, "3 / 4">,<1.33333,"4/3">std::vector<std::pair<float, std::string>> result(float a, float b){    std::vector<std::pair<float, std::string>> r;    r.push_back(std::pair<float, std::string>(a + b, tostring(a, b, '+')));    r.push_back(std::pair<float, std::string>(a * b, tostring(a, b, '*')));    r.push_back(std::pair<float, std::string>(a - b, tostring(a, b, '-')));    r.push_back(std::pair<float, std::string>(b - a, tostring(b, a, '-')));    r.push_back(std::pair<float, std::string>(a / b, tostring(a, b, '/')));    r.push_back(std::pair<float, std::string>(b / a, tostring(b, a, '/')));    return r;}std::vector<std::pair<float, std::string>> result(float a, float b, std::string s){    std::vector<std::pair<float, std::string>> r;    r.push_back(std::pair<float, std::string>(a + b, tostring(s, tostring(b), '+')));    r.push_back(std::pair<float, std::string>(a * b, tostring(s, tostring(b), '*')));    r.push_back(std::pair<float, std::string>(a - b, tostring(s, tostring(b), '-')));    r.push_back(std::pair<float, std::string>(b - a, tostring(tostring(b), s, '-')));    r.push_back(std::pair<float, std::string>(a / b, tostring(s, tostring(b), '/')));    r.push_back(std::pair<float, std::string>(b / a, tostring(tostring(b), s, '/')));    return r;}std::vector<std::pair<float, std::string>> result(std::vector<std::pair<float, std::string>> array, float b){    std::vector<std::pair<float, std::string>> r;    for (auto m : array) {        std::vector<std::pair<float, std::string>> rr = result(m.first, b, m.second);        r.insert(r.end(), rr.begin(), rr.end());    }    return r;}std::set<std::string> all_result;void show_result(std::vector<float> v){    std::vector<std::pair<float, std::string>> r;    if (v.size() < 2) {        return;    }    r = result(v[0], v[1]);    for (auto it = v.begin() + 2; it != v.end(); ++it) {        r = result(r, *it);    }    for (auto m : r) {        if (24 == m.first) {            all_result.insert(m.second);        }    }}std::vector<std::vector<int>> four_factorial(){    std::vector<std::vector<int>> vv;    for (int i = 0; i < 4; ++i) {        for (int j = 0; j < 4; ++j) {            for (int k = 0; k < 4; ++k) {                for (int z = 0; z < 4; ++z) {                    if (i != j && i != k && i != z &&                            j != k && j != z &&                            k != z) {                        std::vector<int> v;                        v.push_back(i);                        v.push_back(j);                        v.push_back(k);                        v.push_back(z);                        vv.push_back(v);                    }                }            }        }    }    return vv;}std::vector<float> bind(float* user_input, std::vector<int> order){    std::vector<float> v;    for (int index : order) {        v.push_back(user_input[index]);    }    return v;}int main(int argc, char* argv[]){    if (argc != 5) {        printf("%s four valid digital\n", argv[0]);        return 1;    }    float input_digital[32] = {0};    printf("input number is :");    for (int i = 1; i < 5; ++i) {        int number = atoi(argv[i]);        if (number < 1 || number > 13) {            std::cout << "Invalid digital " << number << "\n";            return -1;        }        printf(" %d ", number);        input_digital[i - 1] = static_cast<float>(number);    }    printf("\n");    for (std::vector<int> v : four_factorial()) {        show_result(bind(&input_digital[0], v));    }    for (std::string s : all_result) {        std::cout << s << std::endl;    }    return 0;}