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Maximal Rectangle

Certification: Advanced Level Accuracy: 100% Submissions: 1 Points: 15

Write a Java program to find the largest rectangle containing only 1's in a binary matrix. The rectangle can be formed by any set of adjacent cells containing '1's. Return the area of the largest such rectangle.

Example 1
    
  
  • Input: matrix = [

     ["1","0","1","0","0"],

     ["1","0","1","1","1"],

     ["1","1","1","1","1"],

     ["1","0","0","1","0"]
]
    • 
  
  • Output: 6
    • 
  
  • Explanation: In the third row, from column 1 to 4, we have consecutive 1's forming a rectangle of height 1 and width 4 with area 4. However, if we consider columns 2-4, we can extend this to the second row, forming a 2x3 rectangle with area 6.
    •
Example 2
    
  
  • Input: matrix = [

     ["0","1","1","0"],

     ["1","1","1","1"],

     ["1","1","1","1"],

     ["0","1","0","0"]
]
    • 
  
  • Output: 8
    • 
  
  • Explanation: In rows 1 and 2, columns 0-3, we have a 2x4 rectangle of 1's with area 8. There are other rectangles of 1's, but none with area greater than 8.
    •
Constraints
    
  
  • rows == matrix.length, cols == matrix[i].length
    • 
  
  • 0 ≤ rows, cols ≤ 200
    • 
  
  • matrix[i][j] is '0' or '1'
    • 
  
  • Time Complexity: O(rows * cols)
    • 
  
  • Space Complexity: O(cols)
    •
MatrixAccentureAdobe
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Hint
Solution

Solution Hints

    
  
  • Use a histogram-based approach to solve this problem
    • 
  
  • For each row, calculate the heights of the "bars" in the histogram
    • 
  
  • Then, for each row, find the largest rectangle in the histogram
    • 
  
  • Use a stack-based approach to find the largest rectangle in each histogram
    • 
  
  • Keep track of the maximum area found so far
    • 
  
  • When a cell is '0', reset the height of that column to 0
    •

Steps to solve by this approach:

 Step 1: Convert the 2D problem into a series of 1D problems using histograms.

 Step 2: For each row, calculate the height of the histogram at each position by counting consecutive '1's above (including the current row).

 Step 3: Implement a function to find the largest rectangle in each histogram.
 Step 4: For each histogram, use a stack-based approach to find the largest rectangle area.

 Step 5: Use two arrays to record the left and right boundaries for each bar in the histogram.

 Step 6: Calculate the area for each bar using its height and width (right boundary - left boundary - 1).

 Step 7: Return the maximum area found across all row histograms.

Submitted Code :