Solution: Pascal’s Triangle

Statement

Given an integer, numRows, generate the first numRows of Pascal’s triangle.

In Pascal’s triangle, each element is formed by adding the two numbers directly above it from the previous row. The triangle starts with a single $1$ at the top, and each row expands based on this rule.

Constraints:

• 1 $\leq$ numRows $\leq$ $30$

Solution

The core intuition behind the solution is to apply a dynamic programming pattern to construct Pascal’s triangle row by row. Instead of recalculating values independently, each row reuses results from the row above, ensuring efficient computation. This recursive property makes Pascal’s triangle a natural fit for dynamic programming, because each state (row element) depends only on previously computed states. The challenge is to compute the interior values correctly while ensuring the boundary values (first and last elements) remain $1$ ...