What is the primary approach for solving the Check Knight Tour Configuration problem?

The primary approach involves Depth-First Search (DFS) to validate the sequence of knight's moves and ensure each move follows the valid L-shaped movement pattern.

How can I verify the knight's moves efficiently in this problem?

You can efficiently verify the knight's moves by checking the difference in indices between two consecutive moves and ensuring they follow the valid L-shaped pattern.

What are the key challenges in solving the Knight's Tour configuration?

Key challenges include ensuring the knight's moves are valid at each step and managing the complexity of larger grid sizes (up to 7x7).

Why is boundary checking crucial in this problem?

Boundary checking ensures the knight does not move off the board, preventing invalid configurations and out-of-bound errors during the move validation process.

What role does the array representation of the grid play in solving this problem?

The array representation of the grid allows you to track the knight's exact movement order and easily validate if each move is valid based on the knight's L-shaped movement pattern.

#2596

Medium

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LeetCode 题解工作台

检查骑士巡视方案

骑士在一张 n x n 的棋盘上巡视。在有效的巡视方案中，骑士会从棋盘的左上角出发，并且访问棋盘上的每个格子恰好一次。给你一个 n x n 的整数矩阵 grid ，由范围 [0, n * n - 1] 内的不同整数组成，其中 grid[row][col] 表示单元格 (row, col…

数组深度优先搜索广度优先搜索矩阵模拟

题目描述

骑士在一张 n x n 的棋盘上巡视。在有效的巡视方案中，骑士会从棋盘的 左上角 出发，并且访问棋盘上的每个格子 恰好一次 。

给你一个 n x n 的整数矩阵 grid ，由范围 [0, n * n - 1] 内的不同整数组成，其中 grid[row][col] 表示单元格 (row, col) 是骑士访问的第 grid[row][col] 个单元格。骑士的行动是从下标 0 开始的。

如果 grid 表示了骑士的有效巡视方案，返回 true；否则返回 false。

注意，骑士行动时可以垂直移动两个格子且水平移动一个格子，或水平移动两个格子且垂直移动一个格子。下图展示了骑士从某个格子出发可能的八种行动路线。

示例 1：

输入：grid = [[0,11,16,5,20],[17,4,19,10,15],[12,1,8,21,6],[3,18,23,14,9],[24,13,2,7,22]]
输出：true
解释：grid 如上图所示，可以证明这是一个有效的巡视方案。

示例 2：

输入：grid = [[0,3,6],[5,8,1],[2,7,4]]
输出：false
解释：grid 如上图所示，考虑到骑士第 7 次行动后的位置，第 8 次行动是无效的。

提示：

n == grid.length == grid[i].length
3 <= n <= 7
0 <= grid[row][col] < n * n
grid 中的所有整数 互不相同

lightbulb

解题思路

方法一：模拟

我们先用数组 $\textit{pos}$ 记录骑士访问的每个格子的坐标，然后遍历 $\textit{pos}$ 数组，检查相邻两个格子的坐标差是否为 $(1, 2)$ 或 $(2, 1)$ 即可。若不满足，则返回 $\textit{false}$ 。

否则遍历结束后，返回 $\textit{true}$

时间复杂度 $O(n^2)$ ，空间复杂度 $O(n^2)$ 。其中 $n$ 为棋盘的边长。

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class Solution:
    def checkValidGrid(self, grid: List[List[int]]) -> bool:
        if grid[0][0]:
            return False
        n = len(grid)
        pos = [None] * (n * n)
        for i in range(n):
            for j in range(n):
                pos[grid[i][j]] = (i, j)
        for (x1, y1), (x2, y2) in pairwise(pos):
            dx, dy = abs(x1 - x2), abs(y1 - y2)
            ok = (dx == 1 and dy == 2) or (dx == 2 and dy == 1)
            if not ok:
                return False
        return True

speed

复杂度分析

指标	值
时间	Depends on the final approach
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
Candidates may struggle with efficiently verifying valid moves in a DFS traversal.
question_mark
Be aware of performance concerns for larger grid sizes (n=7).
question_mark
Look for clear understanding of knight’s L-shaped movement and boundary validation.

warning

常见陷阱

外企场景

error
Overlooking the knight's movement pattern can lead to incorrect configurations.
error
Failing to track visited cells or revisiting a cell can result in an invalid configuration.
error
Misunderstanding the bounds of the grid could cause out-of-bound errors or incorrect results.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Change the board size to test efficiency across different n values.
arrow_right_alt
Modify the starting position of the knight to test other valid configurations.
arrow_right_alt
Add a constraint where the knight moves in a more complex pattern.

help

常见问题

外企场景

继续练习

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