topic:
Interview Question 08.06. The Tower of Hanoi Question
In the classic Tower of Hanoi problem, there are 3 pillars and N perforated discs of different sizes, and the plate can slide into any pillar. At the beginning, all the plates are placed on the first pillar in ascending order from top to bottom (that is, each plate can only be placed on a larger plate). The following restrictions apply when moving the disc:
(1) Only one plate can be moved at a time;
(2) The plate can only slide from the top of the column to the next column;
(3) The plate can only be stacked on a plate larger than it on.
Please write a program to use the stack to move all the plates from the first pillar to the last pillar.
You need to modify the stack in place.
Example 1:
Input: A = [2, 1, 0], B = [], C = []
Output: C = [2, 1, 0]
Example 2:
Input: A = [1, 0], B = [], C = []
Output: C = [1, 0]
prompt:
The number of plates in A is not more than 14.
Problem solution ideas:
Recursion and Divide and Conquer
This is a classic topic of recursive methods, it is quite difficult to sort out the clues at first thought, we might as well start with the simple ones.
(1)
Assuming n = 1, there is only one plate, it is very simple, just take it out of A and move it to C;
（2）
What if n = 2? At this time we have to use B, because the small plate must always be on top of the large plate, a total of 4 steps are required.
（3）
What if n> 2? The idea is the same as the above. We also regard n plates as two parts, one part has 1 plate and the other part has n-1 plates.
Looking at the picture above, you may ask: "How did n-1 plates move from A to C?"
Note that when you are thinking about this problem, the problem of moving the first n plates from A to C is transformed into the problem of moving n-1 plates from A to C , and so on, until it becomes 1 The problem is solved when the problem is with a plate. This is the idea of divide and conquer .
The common way to realize the idea of divide and conquer is recursion. It is not difficult to find that if the original problem can be decomposed into several smaller sub-problems with the same structure as the original problem, it can often be solved by recursive methods. The specific solutions are as follows:
When n = 1, directly move the plate from A to C;
——————————————————————————————————
n> 1:00:
1. First move the above n-1 plates from A to B (sub-problem, recursion);
2. Then move the largest plate from A to C;
3. Then move n-1 plates on B from B moves to C (subproblem, recursion).
Problem solution python code:
class Solution:
def hanota(self, A: List[int], B: List[int], C: List[int]) -> None:
n = len(A)
self.move(n, A, B, C)
# 定义move 函数移动汉诺塔
def move(self,n, A, B, C):
if n == 1:
C.append(A[-1])
A.pop()
return
else:
self.move(n-1, A, C, B) # 将A上面n-1个通过C移到B
C.append(A[-1]) # 将A最后一个移到C
A.pop() # 这时，A空了
self.move(n-1,B, A, C) # 将B上面n-1个通过空的A移到C
Complexity analysis:
Time complexity: O(2^n-1). The total number of moves required.
Space complexity: O(1).
Author: z1m
link: https://leetcode-cn.com/problems/hanota-lcci/solution/tu-jie-yi-nuo-ta-de-gu-shi-ju-shuo-dang-64ge-pan-z /
Source: LeetCode https://leetcode-cn.com/problems/hanota-lcci/