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题目：这是源自生活中的一个经典小游戏。任意选出四张纸牌，上面有四个数字，（J对应11 Q对应12 K对应13）进行加减乘除运算，最终得到24。

要求：每个纸牌上的数字必须且只能使用一次，可以进行分数运算。不能进行平方、幂运算。

#include <bits/stdc++.h> using namespace std; // 分数结构体 struct Frac { int num, den; Frac(int n = 0, int d = 1) { if (d < 0) { n = -n; d = -d; } int g = __gcd(abs(n), d); num = n / g; den = d / g; } }; // 分数四则运算 Frac add(Frac a, Frac b) { return Frac(a.num*b.den + b.num*a.den, a.den*b.den); } Frac sub(Frac a, Frac b) { return Frac(a.num*b.den - b.num*a.den, a.den*b.den); } Frac mul(Frac a, Frac b) { return Frac(a.num*b.num, a.den*b.den); } Frac divv(Frac a, Frac b) { if (b.num == 0) return Frac(0,1); return Frac(a.num*b.den, a.den*b.num); } int n = 4; Frac a[4]; string expr[4]; // 存储每个数字对应的表达式 bool used[4]; bool found = false; void dfs(int cnt) { if (found) return; if (cnt == 1) { for (int i = 0; i < 4; i++) { if (!used[i]) { if (a[i].num == 24 && a[i].den == 1) { found = true; cout << "可以计算出 24！表达式为：" << endl; cout << expr[i] << " = 24" << endl; } return; } } } for (int i = 0; i < 4; i++) { if (used[i]) continue; for (int j = i+1; j < 4; j++) { if (used[j]) continue; Frac ti = a[i], tj = a[j]; string si = expr[i], sj = expr[j]; used[j] = true; // 1. a + b a[i] = add(ti, tj); expr[i] = "(" + si + "+" + sj + ")"; dfs(cnt-1); // 2. a - b a[i] = sub(ti, tj); expr[i] = "(" + si + "-" + sj + ")"; dfs(cnt-1); // 3. b - a a[i] = sub(tj, ti); expr[i] = "(" + sj + "-" + si + ")"; dfs(cnt-1); // 4. a * b a[i] = mul(ti, tj); expr[i] = "(" + si + "*" + sj + ")"; dfs(cnt-1); // 5. a / b if (tj.num != 0) { a[i] = divv(ti, tj); expr[i] = "(" + si + "/" + sj + ")"; dfs(cnt-1); } // 6. b / a if (ti.num != 0) { a[i] = divv(tj, ti); expr[i] = "(" + sj + "/" + si + ")"; dfs(cnt-1); } // 恢复现场 a[i] = ti; expr[i] = si; a[j] = tj; expr[j] = sj; used[j] = false; } } } int main() { cout << "请输入四个 1-30 之间的自然数："; for (int i = 0; i < 4; i++) { cin >> a[i].num; a[i].den = 1; expr[i] = to_string(a[i].num); } found = false; memset(used, false, sizeof(used)); dfs(4); if (!found) cout << "无法计算出 24。" << endl; return 0; }