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Maximal Rectangle

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C++ program to find the maximal rectangle in a binary matrix. Given a rows x cols binary matrix filled with 0's and 1's, find the area of the largest rectangle containing only 1's and return its area.

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:
    
      
      
    • The maximal rectangle is shown in the above grid.
      • 
      
    • It forms a 2x3 rectangle of all 1's, which has area = 6.
      • 
    
    
  
    •
Example 2
    
  
  • Input: matrix = [["0"]]
    • 
  
  • Output: 0
    • 
  
  • Explanation:
    
      
      
    • There is no '1' in the matrix, so the max rectangle area is 0.
      • 
    
    
  
    •
Constraints
    
  
  • rows == matrix.length
    • 
  
  • cols == matrix[i].length
    • 
  
  • 1 ≤ rows, cols ≤ 200
    • 
  
  • matrix[i][j] is '0' or '1'
    • 
  
  • Time Complexity: O(rows * cols)
    • 
  
  • Space Complexity: O(cols)
    •
ArraysMicrosoftTCS (Tata Consultancy Services)
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Hint
Solution

Solution Hints

    
  
  • Convert the 2D problem into a series of 1D problems
    • 
  
  • For each row, compute the height of the '1's bar ending at that position
    • 
  
  • For each position in a row, calculate the largest rectangle using the "largest rectangle in histogram" approach
    • 
  
  • Use a stack to track heights in ascending order
    • 
  
  • When a height decreases, calculate areas of rectangles that can be formed
    •

Steps to solve by this approach:

 Step 1: For each row in the matrix, build a histogram where the height at each position represents the number of consecutive '1's above (including the current position).
 Step 2: For each histogram, find the largest rectangle area using the "largest rectangle in histogram" algorithm.
 Step 3: Use a stack to keep track of bars in ascending order of height.
 Step 4: When encountering a bar shorter than the one at the top of the stack, calculate the area of rectangles that must end at the current position.
 Step 5: After processing all rows, return the maximum area found across all histograms.
 Step 6: For the histogram calculation, ensure proper handling of edge cases (empty stack, index calculations).
 Step 7: The final answer is the maximum rectangle area found among all rows.

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