[leetcode] 289. Game of Life @ python

最新推荐文章于 2025-01-08 21:01:27 发布

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最新推荐文章于 2025-01-08 21:01:27 发布

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本文链接：https://blog.youkuaiyun.com/danspace1/article/details/86632904

本文详细解析了Conway生命游戏的规则与实现，通过深度复制当前状态并计算每个细胞周围活细胞数量，来决定其生死状态。算法遵循四条基本规则进行迭代，实现了细胞状态的更新。

原题

According to the Wikipedia’s article: “The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970.”

Given a board with m by n cells, each cell has an initial state live (1) or dead (0). Each cell interacts with its eight neighbors (horizontal, vertical, diagonal) using the following four rules (taken from the above Wikipedia article):

Any live cell with fewer than two live neighbors dies, as if caused by under-population.
Any live cell with two or three live neighbors lives on to the next generation.
Any live cell with more than three live neighbors dies, as if by over-population…
Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.
Write a function to compute the next state (after one update) of the board given its current state. The next state is created by applying the above rules simultaneously to every cell in the current state, where births and deaths occur simultaneously.

Example:

Input:
[
[0,1,0],
[0,0,1],
[1,1,1],
[0,0,0]
]
Output:
[
[0,0,0],
[1,0,1],
[0,1,1],
[0,1,0]
]
Follow up:

Could you solve it in-place? Remember that the board needs to be updated at the same time: You cannot update some cells first and then use their updated values to update other cells.
In this question, we represent the board using a 2D array. In principle, the board is infinite, which would cause problems when the active area encroaches the border of the array. How would you address these problems?

解法

将board深度复制给prev, 然后遍历prev, 计算每个格子周围活的邻居的个数, 然后分类讨论, 直接在board上重新赋值.

代码

class Solution(object):
    def gameOfLife(self, board):
        """
        :type board: List[List[int]]
        :rtype: void Do not return anything, modify board in-place instead.
        """
        def countNeighbors(x, y):
            directions = [(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 0), (1, 1)]
            res = 0
            for dx,dy in directions:
                if 0<= x+dx < row and 0<= y+dy < col and prev[x+dx][y+dy] == 1:
                    res += 1
            return res
            
        prev = copy.deepcopy(board)        
        row, col = len(prev), len(prev[0])
        for i in range(row):
            for j in range(col):
                # count the live neighbors
                count = countNeighbors(i, j)
                if prev[i][j] == 1 and (count < 2 or count > 3):
                    board[i][j] = 0
                if prev[i][j] == 0 and count== 3:
                    board[i][j] = 1