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Pascal's Triangle

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

Write a JavaScript program to generate Pascal's Triangle with a given number of rows. Pascal's Triangle is a triangular array where each number is the sum of the two numbers directly above it, with 1s at the edges.

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: 
    • Row 0 contains [1]. Row 1 contains [1, 1] where edges are 1. 
    • Row 2 contains [1, 2, 1] where middle element 2 = 1 + 1. 
    • Row 3 contains [1, 3, 3, 1] where 3 = 1 + 2 and 3 = 2 + 1. 
    • Row 4 contains [1, 4, 6, 4, 1] where elements are sum of above two.
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Example 2
    
  
  • Input: numRows = 1
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  • Output: [[1]]
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  • Explanation: 
    • With only 1 row, Pascal's Triangle contains just [1]. 
    • This is the base case of Pascal's Triangle.
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Constraints
    
  
  • 1 ≤ numRows ≤ 30
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  • Each row starts and ends with 1
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  • Time Complexity: O(numRows^2)
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  • Space Complexity: O(numRows^2) for storing the result
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ArraysHCL TechnologiesApple
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Hint
Solution

Solution Hints

    
  
  • Initialize the result array to store all rows of Pascal's Triangle
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  • The first row always contains [1]
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  • For each subsequent row, start and end with 1
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  • Calculate middle elements by adding corresponding elements from the previous row
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  • For row i, element at position j equals prevRow[j-1] + prevRow[j]
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  • Each row has one more element than its row number (row i has i+1 elements)
    •

Steps to solve by this approach:

 Step 1: Initialize an empty result array to store all rows of Pascal's Triangle.
 Step 2: Use an outer loop to iterate through each row from 0 to numRows-1.
 Step 3: For each row i, create a new array to store i+1 elements.
 Step 4: Use an inner loop to calculate each element in the current row.
 Step 5: Set first and last elements of each row to 1 (boundary condition).
 Step 6: For middle elements, sum the corresponding elements from the previous row: result[i-1][j-1] + result[i-1][j].
 Step 7: Add the completed row to the result array and return the final Pascal's Triangle.

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