MaximalRectangle.java

package stack;

import java.util.Stack;

/**
 * Created by gouthamvidyapradhan on 29/11/2017.
 *
 * Given a 2D binary matrix filled with 0's and 1's, find the largest rectangle containing only 1's and return its area.

 For example, given the following matrix:

 1 0 1 0 0
 1 0 1 1 1
 1 1 1 1 1
 1 0 0 1 0
 Return 6.

 Solution O(n * m): This problem is similar to LargestRectangleInHistogram.
 Run the largest rectangle in histogram algorithm for each row.
 */
public class MaximalRectangle {

    /**
     * Main method
     * @param args
     * @throws Exception
     */
    public static void main(String[] args) throws Exception{
        char[][] matrix = {{'1','0','1','0','0'}, {'1', '0', '1', '1', '1'}, {'1', '1', '1', '1', '1'},
                {'1', '0', '0', '1', '0'}};
        System.out.println(new MaximalRectangle().maximalRectangle(matrix));
    }

    public int maximalRectangle(char[][] matrix) {
        if(matrix.length == 0 || matrix[0].length == 0) return 0;
        int[] A = new int[matrix[0].length];
        int max = Integer.MIN_VALUE;
        for(int i = 0; i < matrix.length; i ++){
            for(int j = 0; j < matrix[0].length; j++){
                if(matrix[i][j] == '1'){
                    if(i > 0 && matrix[i - 1][j] == '1'){
                        A[j] = A[j] + 1;
                    } else{
                        A[j] = 1;
                    }
                } else {
                    A[j] = 0;
                }
            }
            //calculate max rectangle for this row
            max = Math.max(max, getMaxRectangle(A));
        }
        return max;
    }

    /**
     * Get max rectangle algorithm similar to max rectangle in histogram
     * @param heights
     * @return
     */
    private int getMaxRectangle(int[] heights){
        int maxArea = Integer.MIN_VALUE;
        Stack<Integer> stack = new Stack<>();
        int i = 0;
        for (; i < heights.length; i++) {
            while (!stack.isEmpty() && heights[stack.peek()] >= heights[i]) {
                int top = stack.pop();
                int base = stack.isEmpty() ? i : i - stack.peek() - 1;
                maxArea = Math.max(maxArea, base * heights[top]);
            }
            stack.push(i);
        }
        while (!stack.isEmpty()) {
            int top = stack.pop();
            int base = stack.isEmpty() ? i : i - stack.peek() - 1;
            maxArea = Math.max(maxArea, base * heights[top]);
        }
        return maxArea;
    }
}