LeetCode 3359: Find Sorted Submatrices With Maximum Element at Most K Solution

Master LeetCode problem 3359 (Find Sorted Submatrices With Maximum Element at Most K), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

3359. Find Sorted Submatrices With Maximum Element at Most K

Hard

Array Stack Matrix Monotonic Stack

Problem Explanation

Explanation:

To solve this problem, we can utilize the concept of dynamic programming and binary search. We will iterate over all possible columns pairs and maintain a 1D array representing the sum of elements in these columns. Then, for each pair of rows, we will find the subarray with the maximum sum that is less than or equal to k using binary search. By doing this for all possible pairs of rows and columns, we can find the count of submatrices with the maximum element at most k.

Algorithm:

Initialize a variable result to store the count of submatrices with the maximum element at most k.
Iterate over all possible pairs of columns c1 and c2.
For each pair of columns, initialize a 1D array colSum to store the sum of elements between these columns for each row.
Iterate over all pairs of rows r1 and r2.
Compute the sum of elements between columns c1 and c2 for each row between r1 and r2 and store it in the colSum array.
For each row pair, find the subarray with the maximum sum that is less than or equal to k using binary search.
Increment the result by the number of valid submatrices found in step 6.
Return the result.

Time Complexity:

The time complexity of this approach is O(n^2 * m * log(m)), where n is the number of rows and m is the number of columns in the input matrix.

Space Complexity:

The space complexity is O(m) for storing the colSum array.

: :

Solution Code

class Solution {
    public int numSubmatrixSumTarget(int[][] matrix, int k) {
        int n = matrix.length;
        int m = matrix[0].length;
        int result = 0;
        
        for (int c1 = 0; c1 < m; c1++) {
            int[] colSum = new int[n];
            for (int c2 = c1; c2 < m; c2++) {
                for (int r = 0; r < n; r++) {
                    colSum[r] += matrix[r][c2];
                }
                TreeSet<Integer> set = new TreeSet<>();
                set.add(0);
                int prefixSum = 0;
                for (int sum : colSum) {
                    prefixSum += sum;
                    Integer target = set.ceiling(prefixSum - k);
                    if (target != null) {
                        result += set.subSet(target, prefixSum).size();
                    }
                    set.add(prefixSum);
                }
            }
        }
        
        return result;
    }
}

Try It Yourself

Loading code editor...

Frequently Asked Questions

How to solve LeetCode 3359 (Find Sorted Submatrices With Maximum Element at Most K)?

This page provides optimized solutions for LeetCode problem 3359 (Find Sorted Submatrices With Maximum Element at Most K) in Java, C++, and Python, along with a detailed explanation and an interactive code editor to test your code.

What is the time complexity of LeetCode 3359 (Find Sorted Submatrices With Maximum Element at Most K)?

The time complexity for LeetCode 3359 (Find Sorted Submatrices With Maximum Element at Most K) varies by solution. Check the detailed explanation section for specific complexities in Java, C++, and Python implementations.

Can I run code for LeetCode 3359 on DevExCode?

Yes, DevExCode provides an interactive code editor where you can write, test, and run your code for LeetCode 3359 in Java, C++, or Python.

Back to LeetCode Solutions