LeetCode 1277: Count Square Submatrices with All Ones Solution

Master LeetCode problem 1277 (Count Square Submatrices with All Ones), a medium 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.

1277. Count Square Submatrices with All Ones

Medium

Array Dynamic Programming Matrix

Problem Explanation

Explanation

To solve this problem, we can use dynamic programming. We create a 2D DP array where each cell (i, j) represents the size of the largest square with all ones with bottom-right corner at (i, j).

For each cell (i, j) in the matrix:

If matrix[i][j] is 0, the largest square with all ones ending at this cell will be 0.
If matrix[i][j] is 1, we look at the values of (i-1, j), (i, j-1), and (i-1, j-1) in the DP array to determine the size of the square ending at (i, j).

The total number of squares with all ones is the sum of all values in the DP array.

Time complexity: O(mn) where m is the number of rows and n is the number of columns in the input matrix. Space complexity: O(mn) for the DP array.

Solution Code

class Solution {
    public int countSquares(int[][] matrix) {
        int m = matrix.length;
        int n = matrix[0].length;
        int[][] dp = new int[m][n];
        int count = 0;

        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (matrix[i][j] == 1) {
                    if (i == 0 || j == 0) {
                        dp[i][j] = 1;
                    } else {
                        dp[i][j] = Math.min(dp[i-1][j], Math.min(dp[i][j-1], dp[i-1][j-1])) + 1;
                    }
                    count += dp[i][j];
                }
            }
        }

        return count;
    }
}

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