汉诺塔递归及非递归解法

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1. 经典递归解法

#include <iostream>void mov(char a, char b){std::cout << a << " -> " << b << std::endl;}void recursive_hanoi(int n, char a, char b, char c){if (n == 0) return;recursive_hanoi(n - 1, a, c, b);mov(a, c);recursive_hanoi(n - 1, b, a, c);}int main() {recursive_hanoi(3, '1', '2', '3');return 0;}

2. 非递归解法

从汉诺塔的递归解法可以看出，它跟二叉树中序遍历递归解法是一个道理。既然二叉树非递归解法能写出来，那么汉诺塔非递归解法也不难写出来。

#include <iostream>#include <stack>struct HanoiNode{private:int num = 0;char a, b, c;public:HanoiNode() = default;HanoiNode(int n_, char a_, char b_, char c_): num(n_), a(a_), b(b_), c(c_) {}bool is_null(){return num == 0;}HanoiNode left(){if (is_null()) return *this;return HanoiNode(num - 1, a, c, b);}HanoiNode right(){if (is_null()) return *this;return HanoiNode(num - 1, b, a, c);}void mov() const { std::cout << a << " -> " << c << std::endl; }};void nonrecursive_hanoi(int n, char a, char b, char c){if (n < 0) return;std::stack<HanoiNode> hn;HanoiNode hnd(n, a, b, c);while (!hnd.is_null() || !hn.empty()){if (!hnd.is_null()){hn.push(hnd);hnd = hnd.left();}else{hnd = hn.top();hn.pop();hnd.mov();hnd = hnd.right();}}}int main() {nonrecursive_hanoi(3, '1', '2', '3');return 0;}

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