Is Maximum Number of Moves in a Grid easy or hard?

Maximum Number of Moves in a Grid is classified as a Medium difficulty problem. The challenge comes from recognizing that it is a dynamic programming problem on a grid and correctly handling the three directional transitions while enforcing the strictly increasing condition.

How to solve Maximum Number of Moves in a Grid in O(m * n)?

Use dynamic programming where dp[r][c] stores the maximum moves starting from cell (r, c). Process columns from right to left and check the three allowed neighbors in column c+1 if their values are greater. Each state is computed once, resulting in O(m * n) time.

What is the best approach for Maximum Number of Moves in a Grid?

Dynamic programming with memoized DFS or bottom-up DP is the most effective approach. Each cell represents a state where you compute the maximum moves reachable from that position. Since every state is evaluated once and each transition checks only three neighbors, the total complexity stays O(m * n).

Is Maximum Number of Moves in a Grid asked at Google/Amazon/Meta?

Grid dynamic programming problems like this appear frequently in interviews at companies such as Amazon, Google, and Meta. Variants involving path transitions, increasing values, or restricted movements are common interview patterns.

What data structure is used in Maximum Number of Moves in a Grid?

The main structure is a 2D dynamic programming table built on top of the input matrix. DFS solutions also use recursion with memoization, while iterative solutions store intermediate results directly in a DP array.

What is the time complexity of Maximum Number of Moves in a Grid?

The optimal solutions run in O(m * n) time where m is the number of rows and n is the number of columns. Each grid cell is processed once, and at most three transitions are evaluated per cell. Space complexity is also O(m * n) for storing memoization or DP results.

Maximum Number of Moves in a Grid Python or Java solution approach?

Both Python and Java implementations typically use DFS with memoization or bottom-up dynamic programming. The algorithm checks three neighbors in the next column and updates the maximum moves for each cell. The complexity remains O(m * n) regardless of language.

Description Hints 2 Solution Video 15:53

2684. Maximum Number of Moves in a Grid

Medium58.6% acceptance2 companies

You are given a 0-indexed m x n matrix grid consisting of positive integers.

You can start at any cell in the first column of the matrix, and traverse the grid in the following way:

From a cell (row, col), you can move to any of the cells: (row - 1, col + 1), (row, col + 1) and (row + 1, col + 1) such that the value of the cell you move to, should be strictly bigger than the value of the current cell.

Return the maximum number of moves that you can perform.

Example 1:

Input: grid = [[2,4,3,5],[5,4,9,3],[3,4,2,11],[10,9,13,15]]
Output: 3
Explanation: We can start at the cell (0, 0) and make the following moves:
- (0, 0) -> (0, 1).
- (0, 1) -> (1, 2).
- (1, 2) -> (2, 3).
It can be shown that it is the maximum number of moves that can be made.

Example 2:


Input: grid = [[3,2,4],[2,1,9],[1,1,7]]
Output: 0
Explanation: Starting from any cell in the first column we cannot perform any moves.

Constraints:

m == grid.length
n == grid[i].length
2 <= m, n <= 1000
4 <= m * n <= 10⁵
1 <= grid[i][j] <= 10⁶

Asked at 2 companies

Accenture

Google

Topics

Hints open one at a time

Hint 1

Consider using dynamic programming to find the maximum number of moves that can be made from each cell.

Hint 2

The final answer will be the maximum value in cells of the first column.

15:53

Still stuck?Read 3 approaches, or watch a walkthrough.

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1class Solution:
2    def maxMoves(self, grid: List[List[int]]) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

[[2,4,3,5],[5,4,9,3],[3,4,2,11],[10,9,13,15]]

Input

[[3,2,4],[2,1,9],[1,1,7]]

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