How do I maximize the value sum when placing three rooks on the board?

You need to use dynamic programming to keep track of the largest values in each row and column while ensuring no rooks attack each other. The solution should explore optimal placements that maximize the sum of the selected cells.

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

The time complexity typically depends on the dynamic programming approach used, often O(m * n) where m is the number of rows and n is the number of columns in the board.

Can I place more than three rooks on the board?

Yes, this problem can be extended to place more than three rooks. However, the dynamic programming approach would need to account for additional rooks and the corresponding constraints.

What is the best way to handle negative values on the chessboard?

You should still apply dynamic programming, but ensure your solution accounts for the possibility of negative values when selecting rook placements to maximize the sum.

How does dynamic programming help in solving the problem?

Dynamic programming helps by storing intermediate results and state transitions, reducing redundant calculations and efficiently finding the best rook placements.

#3256

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 I

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 <= 100
3 <= n == board[i].length <= 100
-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
Assess the candidate's understanding of dynamic programming and state transitions in grid-based problems.
question_mark
Evaluate the ability to manage constraints like row and column restrictions when placing objects on a grid.
question_mark
Look for clear reasoning behind optimizing the search for the best rook placements using pre-calculated values.

warning

常见陷阱

外企场景

error
Failing to properly handle row and column restrictions, leading to incorrect placements.
error
Overlooking edge cases, such as negative values in the board or having too few rows and columns.
error
Not optimizing by storing the largest values, leading to unnecessary recalculations and inefficiencies.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Instead of three rooks, consider placing a different number of rooks, adjusting the dynamic programming approach accordingly.
arrow_right_alt
Extend the problem to larger boards with more rows and columns, requiring more sophisticated optimizations.
arrow_right_alt
Introduce varying rook values or constraints to test the algorithm's adaptability to different scenarios.

help

常见问题

外企场景

继续练习

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