How can I maximize the sum of rook placements in the Maximum Value Sum by Placing Three Rooks II problem?

The optimal approach involves dynamic programming where you track the top three values in each row and compute state transitions across rows to maximize the sum.

What is the time complexity of solving the Maximum Value Sum by Placing Three Rooks II problem?

The time complexity is O(m * n) due to the dynamic programming approach, where m is the number of rows and n is the number of columns.

Can the Maximum Value Sum by Placing Three Rooks II problem be solved without dynamic programming?

While it's possible to attempt brute force, dynamic programming significantly optimizes the process by reducing repeated computations and minimizing time complexity.

What should I focus on while solving the Maximum Value Sum by Placing Three Rooks II problem in an interview?

Focus on understanding the state transition dynamic programming pattern and optimizing both time and space complexity.

How does GhostInterview help with the Maximum Value Sum by Placing Three Rooks II problem?

GhostInterview assists by providing detailed guidance on solving this problem, highlighting key concepts like dynamic programming, state transitions, and common pitfalls.

#3257

Hard

auto_awesome状态·转移·动态规划

LeetCode 题解工作台

放三个车的价值之和最大 II

给你一个 m x n 的二维整数数组 board ，它表示一个国际象棋棋盘，其中 board[i][j] 表示格子 (i, j) 的价值。处于同一行或者同一列车会互相攻击。你需要在棋盘上放三个车，确保它们两两之间都无法互相攻击。请你返回满足上述条件下，三个车所在格子值之和…

数组动态规划矩阵枚举

题目描述

给你一个 m x n 的二维整数数组 board ，它表示一个国际象棋棋盘，其中 board[i][j] 表示格子 (i, j) 的价值。

处于 同一行 或者 同一列 车会互相攻击。你需要在棋盘上放三个车，确保它们两两之间都 无法互相攻击 。

请你返回满足上述条件下，三个车所在格子值之和最大为多少。

示例 1：

输入：board = [[-3,1,1,1],[-3,1,-3,1],[-3,2,1,1]]

输出：4

解释：

我们可以将车分别放在格子 (0, 2) ，(1, 3) 和 (2, 1) 处，价值之和为 1 + 1 + 2 = 4 。

示例 2：

输入：board = [[1,2,3],[4,5,6],[7,8,9]]

输出：15

解释：

我们可以将车分别放在格子 (0, 0) ，(1, 1) 和 (2, 2) 处，价值之和为 1 + 5 + 9 = 15 。

示例 3：

输入：board = [[1,1,1],[1,1,1],[1,1,1]]

输出：3

解释：

我们可以将车分别放在格子 (0, 2) ，(1, 1) 和 (2, 0) 处，价值之和为 1 + 1 + 1 = 3 。

提示：

3 <= m == board.length <= 500
3 <= n == board[i].length <= 500
-10⁹ <= board[i][j] <= 10⁹

lightbulb

解题思路

方法一

1

2

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
Check if the candidate can identify the dynamic programming nature of this problem.
question_mark
Evaluate the candidate's understanding of row-wise maximization and state transitions.
question_mark
Observe the candidate's ability to optimize space complexity while maintaining efficiency.

warning

常见陷阱

外企场景

error
Failing to track the top three values in each row and revisiting the same values repeatedly.
error
Not handling row and column uniqueness correctly, leading to invalid rook placements.
error
Overcomplicating the solution by attempting brute force instead of utilizing dynamic programming optimizations.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Increasing the number of rooks to be placed, which adds complexity to the dynamic programming approach.
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Considering different board sizes, such as a larger m x n array, to challenge the space and time optimizations.
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Allowing for variable rook placements, where more complex rules determine valid positions, still using dynamic programming.

help

常见问题

外企场景

继续练习

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