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Maximal Rectangle

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

Write a C program to find the largest rectangle containing only 1's in a binary matrix. Given a rows x cols binary matrix filled with 0's and 1's, find 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"]]
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  • Output: 6
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  • Explanation: 
    • The matrix has several rectangles of 1's. 
    • The maximal rectangle is at positions forming a 2x3 rectangle. 
    • This rectangle has area = 2 * 3 = 6. 
    • Therefore, maximal rectangle area = 6.
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Example 2
    
      
  • Input: matrix = [["0"]]
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  • Output: 0
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  • Explanation: 
    • The matrix contains only one element which is "0". 
    • No rectangle of 1's can be formed. 
    • Therefore, maximal rectangle area = 0.
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Constraints
    
      
  • rows == matrix.length
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  • cols == matrix[i].length
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  • 1 ≤ row, cols ≤ 200
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  • matrix[i][j] is '0' or '1'
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  • Time Complexity: O(rows * cols)
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  • Space Complexity: O(cols)
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MatrixDropboxD. E. Shaw
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Hint
Solution

Solution Hints

    
      
  • Use the concept of largest rectangle in histogram for each row
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  • For each row, calculate heights of consecutive 1's ending at that row
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  • Apply largest rectangle in histogram algorithm on these heights
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  • Use stack-based approach to find maximum rectangle efficiently
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  • Update heights array: if current cell is '0', height becomes 0, else increment
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Steps to solve by this approach:

 Step 1: Initialize a heights array to track consecutive 1's ending at each column for current row.
 Step 2: For each row in the matrix, update the heights array based on current row values.
 Step 3: If current cell is '1', increment the corresponding height, otherwise reset height to 0.
 Step 4: Apply largest rectangle in histogram algorithm on the updated heights array.
 Step 5: Use stack-based approach to efficiently find maximum rectangle area in the histogram.
 Step 6: Keep track of maximum area found across all rows.
 Step 7: Return the maximum rectangle area found in the entire matrix.

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