Is Count Submatrices With Equal Frequency of X and Y easy or hard?

The problem is generally rated Medium because it requires recognizing the transformation from equal frequencies to a zero-sum problem. The tricky part is reducing the 2D submatrix search into repeated 1D prefix sum checks. Once that insight is clear, the implementation becomes straightforward.

Count Submatrices With Equal Frequency of X and Y Python/Java solution

Most implementations convert the grid values to +1 and -1, iterate over row pairs, and apply a prefix sum with a hash map across columns. Python typically uses a dictionary for prefix counts, while Java uses HashMap . Both implementations achieve O(m^2 * n) time complexity.

How to solve Count Submatrices With Equal Frequency of X and Y in O(n)?

The 2D problem cannot be solved in pure O(n) for the entire matrix because multiple row pairs must be examined. However, once rows are compressed into a 1D array, counting balanced segments can be done in O(n) using prefix sums and a hash map. This O(n) subarray step is repeated for each row pair.

What is the best approach for Count Submatrices With Equal Frequency of X and Y?

The most efficient approach uses prefix sums with a hash map. Convert X to +1 and Y to -1 so that any balanced submatrix has total sum zero. Fix two row boundaries, compress the rows into a 1D array of column sums, and count zero-sum subarrays using a hash map. This runs in O(m^2 * n) time.

Is Count Submatrices With Equal Frequency of X and Y asked at Google/Amazon/Meta?

Balanced submatrix and prefix-sum rectangle problems frequently appear in interviews at large tech companies such as Google, Amazon, and Meta. Variations include counting submatrices with target sums or equal frequencies of elements. These problems test prefix sum reasoning and hash map optimization.

What data structure is used in Count Submatrices With Equal Frequency of X and Y?

The main data structures are prefix sum arrays and a hash map. Prefix sums track cumulative differences between X and Y, while the hash map stores how often each prefix sum appears to quickly count balanced subarrays.

What is the time complexity of Count Submatrices With Equal Frequency of X and Y?

The optimal solution runs in O(m^2 * n) time for a matrix with m rows and n columns. Two rows are fixed as boundaries and columns are scanned while tracking prefix sums. Space complexity is typically O(n) for the hash map storing prefix frequencies.

Description Hints 3 Solution Video 16:48

3212. Count Submatrices With Equal Frequency of X and Y

Medium69.5% acceptance2 companies

Given a 2D character matrix grid, where grid[i][j] is either 'X', 'Y', or '.', return the number of submatrices that contain:

grid[0][0]
an equal frequency of 'X' and 'Y'.
at least one 'X'.

Example 1:

Input: grid = [["X","Y","."],["Y",".","."]]

Output: 3

Explanation:

Example 2:

Input: grid = [["X","X"],["X","Y"]]

Output: 0

Explanation:

No submatrix has an equal frequency of 'X' and 'Y'.

Example 3:

Input: grid = [[".","."],[".","."]]

Output: 0

Explanation:

No submatrix has at least one 'X'.

Constraints:

1 <= grid.length, grid[i].length <= 1000
grid[i][j] is either 'X', 'Y', or '.'.

Asked at 2 companies

Microsoft Amazon

Topics

Hints open one at a time

Hint 1

Replace ’X’ with 1, ’Y’ with -1 and ’.’ with 0.

Hint 2

You need to find how many submatrices grid[0..x][0..y] have a sum of 0 and at least one ’X’.

Hint 3

Use prefix sum to calculate submatrices sum.

16:48

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3212. Count Submatrices With Equal Frequency of X and Y

Asked at 2 companies

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