What is the primary approach to solve the 'Count Paths With the Given XOR Value' problem?

The problem is solved using dynamic programming with a 3D DP table to track the number of paths to each grid cell with a specific XOR value.

What is the time complexity of solving the 'Count Paths With the Given XOR Value' problem?

The time complexity is O(m * n * 16), where m and n are the dimensions of the grid, and 16 represents the number of possible XOR values.

Can you explain the state transition for this problem?

State transitions occur by considering paths from adjacent cells (top and left) and updating the XOR value at each step, using a dynamic programming approach.

How can I handle large grids efficiently in the 'Count Paths With the Given XOR Value' problem?

By using a 3D DP table, the problem remains manageable even for larger grids, but optimizations like rolling arrays or space compression can help reduce memory usage.

What are the common pitfalls when solving this problem?

Common mistakes include failing to manage boundary conditions, not properly tracking the XOR state, and inefficient space usage in the DP table.

#3393

Medium

auto_awesome状态·转移·动态规划

LeetCode 题解工作台

统计异或值为给定值的路径数目

给你一个大小为 m x n 的二维整数数组 grid 和一个整数 k 。你的任务是统计满足以下条件且从左上格子 (0, 0) 出发到达右下格子 (m - 1, n - 1) 的路径数目：每一步你可以向右或者向下走，也就是如果格子存在的话，可以从格子 (i, j) 走到格子 (i, j + 1…

数组动态规划位运算矩阵

题目描述

给你一个大小为 m x n 的二维整数数组 grid 和一个整数 k 。

你的任务是统计满足以下条件且从左上格子 (0, 0) 出发到达右下格子 (m - 1, n - 1) 的路径数目：

每一步你可以向右或者向下走，也就是如果格子存在的话，可以从格子 (i, j) 走到格子 (i, j + 1) 或者格子 (i + 1, j) 。
路径上经过的所有数字 XOR 异或值必须等于 k 。

请你返回满足上述条件的路径总数。

由于答案可能很大，请你将答案对 10⁹ + 7 取余后返回。

示例 1：

输入：grid = [[2, 1, 5], [7, 10, 0], [12, 6, 4]], k = 11

输出：3

解释：

3 条路径分别为：

(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2)
(0, 0) → (1, 0) → (1, 1) → (1, 2) → (2, 2)
(0, 0) → (0, 1) → (1, 1) → (2, 1) → (2, 2)

示例 2：

输入：grid = [[1, 3, 3, 3], [0, 3, 3, 2], [3, 0, 1, 1]], k = 2

输出：5

解释：

5 条路径分别为：

(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2) → (2, 3)
(0, 0) → (1, 0) → (1, 1) → (2, 1) → (2, 2) → (2, 3)
(0, 0) → (1, 0) → (1, 1) → (1, 2) → (1, 3) → (2, 3)
(0, 0) → (0, 1) → (1, 1) → (1, 2) → (2, 2) → (2, 3)
(0, 0) → (0, 1) → (0, 2) → (1, 2) → (2, 2) → (2, 3)

示例 3：

输入：grid = [[1, 1, 1, 2], [3, 0, 3, 2], [3, 0, 2, 2]], k = 10

输出：0

提示：

1 <= m == grid.length <= 300
1 <= n == grid[r].length <= 300
0 <= grid[r][c] < 16
0 <= k < 16

lightbulb

解题思路

方法一

1

2

speed

复杂度分析

指标	值
时间	complexity depends on the number of cells `m * n` and the number of possible XOR values (16), resulting in a time complexity of O(m * n * 16). Space complexity is similarly O(m * n * 16) due to the DP table size.
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
Look for a candidate's ability to apply dynamic programming to state transitions effectively.
question_mark
Assess whether the candidate understands the necessity of tracking XOR states in paths.
question_mark
Check if the candidate handles the grid traversal and transition properly, avoiding unnecessary recomputation.

warning

常见陷阱

外企场景

error
Candidates may forget to handle boundary conditions when transitioning from cells that are not top or left.
error
Some may struggle with the memory management of the 3D DP table, especially when the grid size is large.
error
Not considering the XOR of previous steps correctly may lead to incorrect path calculations.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Variant where grid size increases but the XOR value remains small.
arrow_right_alt
Grid with higher values of `k` where optimization strategies like bitmasking could help.
arrow_right_alt
Variant involving negative or different range of values in the grid.

help

常见问题

外企场景

继续练习

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