Largest One Submatrix with Column Swaps - Google Top Interview Questions


Problem Statement :


You are given a two-dimensional list of integers matrix containing 1s and 0s. 

Given that you can first rearrange the columns as many times as you want, return the area of the largest submatrix containing all 1s.

Constraints

1 ≤ n * m ≤ 100,000 where n and m are the number of rows and columns in matrix

Example 1

Input

matrix = [

    [0, 0, 1],

    [1, 1, 1],

    [1, 0, 1]

]

Output

4

Explanation

We can rearrange the columns to:



[[0, 1, 0],

 [1, 1, 1],

 [1, 1, 0]]

And then take the bottom 2 x 2 submatrix with all 1s


Solution :



title-img 




                        Solution in C++ :

int solve(vector<vector<int>>& mat) {
    int n = mat.size(), m = mat[0].size(), ret = 0;
    for (int i = 1; i < n; i++) {
        for (int j = 0; j < m; j++) {
            if (mat[i][j]) mat[i][j] += mat[i - 1][j];
        }
    }
    for (auto& row : mat) sort(row.begin(), row.end());
    for (int i = 0; i < n; i++) {
        for (int j = m - 1; j >= 0; j--) {
            ret = max(ret, mat[i][j] * (m - j));
        }
    }
    return ret;
}
                    


                        Solution in Java :

import java.util.*;

class Solution {
    public int solve(int[][] matrix) {
        int m = matrix.length;
        int n = matrix[0].length;

        int[] heights = new int[n];
        int res = 0;

        for (int row = 0; row < m; row++) {
            for (int col = 0; col < n; col++) {
                if (matrix[row][col] == 1) {
                    heights[col]++;
                } else {
                    heights[col] = 0;
                }
            }

            int[] cur_heights = heights.clone();
            Arrays.sort(cur_heights);

            for (int col = 0; col < n; col++) {
                res = Math.max(res, cur_heights[col] * (n - col));
            }
        }
        return res;
    }
}
                    


                        Solution in Python : 
                            
class Solution:
    def solve(self, matrix):
        rows, cols = len(matrix), len(matrix[0])

        # compute histogram
        hist = [[0 for col in range(cols)] for row in range(rows)]
        for col in range(cols):
            hist[0][col] = matrix[0][col]
            for row in range(1, rows):
                if matrix[row][col]:
                    hist[row][col] = hist[row - 1][col] + 1
                else:
                    hist[row][col] = 0

        # counting sort of rows
        for row in range(rows):
            count = [0 for val in range(rows + 1)]
            for col in range(cols):
                count[hist[row][col]] += 1
            col = 0
            for val in range(rows, -1, -1):
                for _ in range(count[val]):
                    hist[row][col] = val
                    col += 1

        # find max rectangle
        max_area = 0
        for row in range(rows):
            for col in range(cols):
                max_area = max(max_area, (col + 1) * hist[row][col])
        return max_area


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