Leetcode #2596: Check Knight Tour Configuration
In this guide, we solve Leetcode #2596 Check Knight Tour Configuration in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
There is a knight on an n x n chessboard. In a valid configuration, the knight starts at the top-left cell of the board and visits every cell on the board exactly once.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Depth-First Search, Breadth-First Search, Array, Matrix, Simulation
Intuition
We need to explore a structure deeply before backing up, which suits DFS.
DFS keeps local context on the call stack and is easy to implement recursively.
Approach
Define a recursive DFS that carries the necessary state.
Combine child results as the recursion unwinds.
Steps:
- Define a recursive DFS with state.
- Visit children and combine results.
- Return the final aggregation.
Example
Input: 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]]
Output: true
Explanation: The above diagram represents the grid. It can be shown that it is a valid configuration.
Python Solution
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
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.