Is Maximum Number of Points From Grid Queries easy or hard?

Maximum Number of Points From Grid Queries is categorized as a Hard problem. The challenge comes from recognizing that running a traversal for each query is inefficient and that queries should be processed together using a priority queue and sorted thresholds.

Maximum Number of Points From Grid Queries Python or Java solution

Python solutions typically use heapq for the min-heap and a visited matrix to track explored cells. Java implementations rely on PriorityQueue and arrays for visited tracking. Both versions implement the same BFS expansion logic with sorted queries.

What is the best approach for Maximum Number of Points From Grid Queries?

The best approach uses Breadth-First Search combined with a min-heap (priority queue) and sorted queries. Cells are processed in increasing grid value order, allowing the reachable region to expand gradually as query thresholds increase. Each cell is visited once, giving an efficient O(mn log(mn) + q log q) time complexity.

Is Maximum Number of Points From Grid Queries asked at Google/Amazon/Meta?

Grid traversal problems that combine BFS, heaps, and query processing frequently appear in interviews at companies like Google, Amazon, and Meta. This problem tests your ability to optimize repeated searches and manage expanding frontiers with priority queues.

What data structure is used in Maximum Number of Points From Grid Queries?

The optimal solution uses a min-heap (priority queue) to process cells in ascending value order, a queue-style BFS traversal for neighbors, and a visited matrix to prevent revisiting cells. Sorting is also used to process queries efficiently.

What is the time complexity of Maximum Number of Points From Grid Queries?

The optimal BFS with priority queue solution runs in O(mn log(mn) + q log q) time, where m and n are grid dimensions and q is the number of queries. Each cell is pushed and popped from the heap at most once, while queries are sorted beforehand.

How to solve Maximum Number of Points From Grid Queries in O(mn log(mn)) time?

Sort the queries while tracking their original indices, then perform a BFS from (0,0) using a min-heap ordered by grid value. For each query, pop cells from the heap while their values are smaller than the query threshold and expand to their neighbors. This processes each grid cell once and efficiently builds the reachable region.

Description Hints 3 Solution Video 15:51

2503. Maximum Number of Points From Grid Queries

Hard59.3% acceptance6 companies

You are given an m x n integer matrix grid and an array queries of size k.

Find an array answer of size k such that for each integer queries[i] you start in the top left cell of the matrix and repeat the following process:

If queries[i] is strictly greater than the value of the current cell that you are in, then you get one point if it is your first time visiting this cell, and you can move to any adjacent cell in all 4 directions: up, down, left, and right.
Otherwise, you do not get any points, and you end this process.

After the process, answer[i] is the maximum number of points you can get. Note that for each query you are allowed to visit the same cell multiple times.

Return the resulting array answer.

Example 1:

Input: grid = [[1,2,3],[2,5,7],[3,5,1]], queries = [5,6,2]
Output: [5,8,1]
Explanation: The diagrams above show which cells we visit to get points for each query.

Example 2:

Input: grid = [[5,2,1],[1,1,2]], queries = [3]
Output: [0]
Explanation: We can not get any points because the value of the top left cell is already greater than or equal to 3.

Constraints:

m == grid.length
n == grid[i].length
2 <= m, n <= 1000
4 <= m * n <= 10⁵
k == queries.length
1 <= k <= 10⁴
1 <= grid[i][j], queries[i] <= 10⁶

Asked at 6 companies

JPMorgan Chase Uber

Google Amazon Meta Bloomberg

Topics

Array Breadth-First Search Heap (Priority Queue)Matrix Sorting Two Pointers Union Find

Hints open one at a time

Hint 1

The queries are all given to you beforehand so you can answer them in any order you want.

Hint 2

Sort the queries knowing their original order to be able to build the answer array.

Hint 3

Run a BFS on the graph and answer the queries in increasing order.

15:51

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