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Pascal's Triangle

Certification: Basic Level Accuracy: 0% Submissions: 0 Points: 5

Given a non-negative integer numRows, generate the first numRows of Pascal's triangle. In Pascal's triangle, each number is the sum of the two numbers directly above it.

Example 1
    
  
  • Input: numRows = 5
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  • Output: [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]
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  • Explanation:

     Step 1: Row 0: [1]

     Step 2: Row 1: [1,1]

     Step 3: Row 2: [1,2,1] (2 = 1+1)

     Step 4: Row 3: [1,3,3,1] (3 = 1+2, 3 = 2+1)

     Step 5: Row 4: [1,4,6,4,1] (4 = 1+3, 6 = 3+3, 4 = 3+1)
    •
Example 2
    
  
  • Input: numRows = 1
    • 
  
  • Output: [[1]]
    • 
  
  • Explanation:

     Step 1: Only 1 row is requested

     Step 2: Row 0: [1]
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Constraints
    
  
  • 1 <= numRows <= 30
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  • Each row contains exactly i+1 elements where i is the row index (0-indexed)
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  • The values in Pascal's triangle won't exceed 2^31 - 1
    • 
  
  • Time Complexity: O(numRows^2)
    • 
  
  • Space Complexity: O(numRows^2) to store the triangle
    •
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Hint
Solution

Solution Hints

    
  
  • Initialize the triangle with the first row as [1]
    • 
  
  • For each subsequent row, start and end with 1
    • 
  
  • For the middle elements, compute each value as the sum of the two numbers above it
    • 
  
  • Use the previous row to calculate values for the current row
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  • Continue this process until all numRows are generated
    •

Steps to solve by this approach:

 Step 1: Allocate memory for storing the triangle - an array of pointers for each row.

 Step 2: Allocate memory for tracking the size of each row - each row i has i+1 elements.

 Step 3: For each row, start by setting the first and last elements to 1, as these are always 1 in Pascal's triangle.

 Step 4: For middle elements (j from 1 to i-1), calculate the value by adding the two elements above it: triangle[i-1][j-1] + triangle[i-1][j].

 Step 5: Continue this process for all rows from 0 to numRows-1.

 Step 6: Set the returnSize to numRows to indicate the number of rows generated.

 Step 7: Return the resulting triangle array.

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