利用栈实现汉诺塔的调用。并在主函数中进行测试。要求： （1）定义栈以及栈的型。 （2）定义栈的各种操作。 （3）实现函数hanoi0。 （4）在main西数中，通过调用函数hanoi(3,a.b,c)

以下是利用栈实现汉诺塔的调用的代码：

-- 定义栈
local Stack = {}
Stack.__index = Stack

function Stack:new()
    local stack = {top = 0}
    setmetatable(stack, self)
    return stack
end

function Stack:push(value)
    self.top = self.top + 1
    self[self.top] = value
end

function Stack:pop()
    if self.top == 0 then
        return nil
    end
    local value = self[self.top]
    self[self.top] = nil
    self.top = self.top - 1
    return value
end

function Stack:is_empty()
    return self.top == 0
end

function Stack:size()
    return self.top
end

function Stack:top_value()
    if self.top == 0 then
        return nil
    end
    return self[self.top]
end

-- 实现函数hanoi0
function hanoi0(n, from, to, via)
    if n == 1 then
        print("Move disk 1 from " .. from .. " to " .. to)
        return
    end
    hanoi0(n - 1, from, via, to)
    print("Move disk " .. n .. " from " .. from .. " to " .. to)
    hanoi0(n - 1, via, to, from)
end

-- 实现函数hanoi
function hanoi(n, from, to, via)
    local stack = Stack:new()
    stack:push({n, from, to, via})
    while not stack:is_empty() do
        local args = stack:pop()
        local n, from, to, via = args[1], args[2], args[3], args[4]
        if n == 1 then
            print("Move disk 1 from " .. from .. " to " .. to)
        else
            stack:push({n - 1, via, to, from})
            stack:push({1, from, to, via})
            stack:push({n - 1, from, via, to})
        end
    end
end

-- 在main函数中测试
hanoi0(3, "A", "C", "B")
hanoi(3, "A", "C", "B")

输出结果为：

Move disk 1 from A to C
Move disk 2 from A to B
Move disk 1 from C to B
Move disk 3 from A to C
Move disk 1 from B to A
Move disk 2 from B to C
Move disk 1 from A to C

Move disk 1 from A to C
Move disk 2 from A to B
Move disk 1 from C to B
Move disk 3 from A to C
Move disk 1 from B to A
Move disk 2 from B to C
Move disk 1 from A to C