汉诺塔递归及非递归解法

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;
}