Solution: Pascal’s Triangle
Explore how to generate the first numRows of Pascal’s Triangle using dynamic programming. This lesson guides you through constructing each row iteratively, leveraging previously computed rows to build an efficient solution. Understand the dynamic programming relation that avoids redundant calculations and master a key pattern for coding interviews involving recursive dependencies and optimization.
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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
at the top, and each row expands based on this rule.
Constraints:
1
numRows
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