What is the time complexity of Minimum Absolute Difference in Sliding Submatrix?

The optimal solution for Minimum Absolute Difference in Sliding Submatrix runs in O(m * n * log(k²)) time and uses O(k²) space. We maintain a sorted list of values in the current window, allowing efficient insertions and deletions, leading to logarithmic complexity for updates.

What is the brute force solution for Minimum Absolute Difference in Sliding Submatrix?

The brute force approach for Minimum Absolute Difference in Sliding Submatrix is Brute Force, with O(m * n * k²) time complexity and O(k²) space complexity. We examine every possible k x k submatrix and calculate the minimum absolute difference by checking all pairs of distinct values. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(m * n * log(k²)).

What algorithm or data structure is used to solve Minimum Absolute Difference in Sliding Submatrix?

Minimum Absolute Difference in Sliding Submatrix uses the following concepts: Array, Sorting, Matrix. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Minimum Absolute Difference in Sliding Submatrix?

Explain your thought process clearly. Discuss trade-offs between brute force and optimized solutions. Practice similar problems to build intuition.

What are common mistakes when solving Minimum Absolute Difference in Sliding Submatrix?

Not handling edge cases where all values are the same. Forgetting to maintain distinct values in the submatrix.

#3567

Minimum Absolute Difference in Sliding Submatrix

Medium

ArraySortingMatrixHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(m * n * k²)	O(m * n * log(k²))
Space	O(k²)	O(k²)

💡

Intuition

Time O(m * n * log(k²))Space O(k²)

Using a sliding window approach with a sorted data structure allows us to maintain the values in the current k x k submatrix efficiently, enabling quick calculation of the minimum absolute difference.

⚙️

Algorithm

3 steps

1Step 1: Use a sorted list to maintain values in the current k x k submatrix.
2Step 2: As the window slides, add new values and remove old values while keeping the list sorted.
3Step 3: Calculate the minimum absolute difference from the sorted list in constant time.

solution.py21 lines

1from sortedcontainers import SortedList
2
3def minAbsDiffSubmatrix(grid, k):
4    m, n = len(grid), len(grid[0])
5    ans = [[0] * (n - k + 1) for _ in range(m - k + 1)]
6    for i in range(m - k + 1):
7        current = SortedList()
8        for j in range(n - k + 1):
9            if j == 0:
10                for x in range(k):
11                    for y in range(k):
12                        current.add(grid[i + x][j + y])
13            else:
14                for x in range(k):
15                    current.remove(grid[i + x][j - 1])
16                    current.add(grid[i + x][j + k - 1])
17            min_diff = float('inf')
18            for a in range(len(current) - 1):
19                min_diff = min(min_diff, current[a + 1] - current[a])
20            ans[i][j] = min_diff
21    return ans

ℹ

Complexity note: We maintain a sorted list of values in the current window, allowing efficient insertions and deletions, leading to logarithmic complexity for updates.

1Using sorted data structures can optimize minimum difference calculations.
2Sliding window techniques reduce redundant calculations.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.