Is Max Sum of Rectangle No Larger Than K easy or hard?

Max Sum of Rectangle No Larger Than K is classified as a Hard problem. It combines multiple concepts including 2D prefix sums, subarray optimization, and ordered sets, and requires reducing a matrix problem to repeated 1D searches.

Max Sum of Rectangle No Larger Than K Python or Java solution?

Python implementations typically use the bisect module with a sorted list to simulate an ordered set, while Java solutions commonly use TreeSet. Both maintain sorted prefix sums so binary search can find valid subarray sums in O(log n) time.

How to solve Max Sum of Rectangle No Larger Than K efficiently?

Convert the 2D rectangle problem into multiple 1D subarray problems. For every pair of columns, compute cumulative row sums and maintain prefix sums in a sorted structure. Use binary search to find the smallest prefix ≥ currentSum - k, which gives the best valid subarray ending at the current position.

What is the best approach for Max Sum of Rectangle No Larger Than K?

The most efficient approach uses prefix sums combined with an ordered set (such as a balanced BST). Fix two column boundaries, compress the rows into a 1D array, and then find the maximum subarray sum ≤ k using prefix sums and binary search. This reduces the problem to O(cols^2 * rows log rows) time and O(rows) space.

What data structure is used in Max Sum of Rectangle No Larger Than K?

The optimal solution uses an ordered set or balanced binary search tree to maintain prefix sums in sorted order. This structure enables efficient binary search to find the smallest prefix greater than or equal to currentSum - k while scanning the compressed array.

What is the time complexity of Max Sum of Rectangle No Larger Than K?

The optimal solution runs in O(cols^2 * rows log rows). Two columns are fixed to define the rectangle width, rows are compressed into a 1D array, and an ordered set is used to search prefix sums in O(log rows). Brute-force prefix-sum approaches can take O(m^2 * n^2).

Is Max Sum of Rectangle No Larger Than K asked at Google, Amazon, or Meta?

Max Sum of Rectangle No Larger Than K is a well-known hard matrix problem frequently associated with Google-style interviews. It tests prefix sums, binary search, and advanced data structures like ordered sets, which are common in high-level algorithm interviews.

Description Solution Video 18:50

363. Max Sum of Rectangle No Larger Than K

Hard46.0% acceptance3 companies

Given an m x n matrix matrix and an integer k, return the max sum of a rectangle in the matrix such that its sum is no larger than k.

It is guaranteed that there will be a rectangle with a sum no larger than k.

Example 1:

Input: matrix = [[1,0,1],[0,-2,3]], k = 2
Output: 2
Explanation: Because the sum of the blue rectangle [[0, 1], [-2, 3]] is 2, and 2 is the max number no larger than k (k = 2).

Example 2:

Input: matrix = [[2,2,-1]], k = 3
Output: 3

Constraints:

m == matrix.length
n == matrix[i].length
1 <= m, n <= 100
-100 <= matrix[i][j] <= 100
-10⁵ <= k <= 10⁵

Follow up: What if the number of rows is much larger than the number of columns?

Asked at 3 companies

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Topics

18:50

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1class Solution:
2    def maxSumSubmatrix(self, matrix: List[List[int]], k: int) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

[[1,0,1],[0,-2,3]]
2

Input

[[2,2,-1]]
3

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