Is Pascal's Triangle II easy or hard?

Pascal's Triangle II is classified as an Easy problem. The DP approach is straightforward once you understand the triangle recurrence, while the combinatorial optimization adds a slightly deeper mathematical insight.

Pascal's Triangle II Python/Java solution

Python and Java implementations usually follow the same logic: either update a list in reverse order for the DP approach or compute binomial coefficients iteratively for the O(n) combinatorial solution.

How to solve Pascal's Triangle II in O(n)?

Use the binomial coefficient relationship between consecutive elements. Start with 1 for C(n,0), then compute the next value using C(n,k) = C(n,k-1) * (n-k+1) / k. This produces the entire row sequentially in a single loop.

What is the best approach for Pascal's Triangle II?

The combinatorial approach using binomial coefficients is the most efficient. Each element in row n is C(n, k), which can be computed from the previous coefficient using C(n, k) = C(n, k-1) * (n-k+1) / k. This generates the entire row in O(n) time with O(1) extra space.

Is Pascal's Triangle II asked at Google/Amazon/Meta?

Pascal's Triangle variations frequently appear in interviews at companies like Amazon, Google, and Meta because they test dynamic programming fundamentals, mathematical reasoning, and space optimization techniques.

What data structure is used in Pascal's Triangle II?

The solution typically uses a single array or list to store the current row. In the dynamic programming approach, the array is updated from right to left to preserve values from the previous state.

What is the time complexity of Pascal's Triangle II?

The common dynamic programming solution runs in O(n^2) time because each row requires updating multiple elements. The optimized combinatorial solution computes each element once and runs in O(n) time.

119. Pascal's Triangle II - Practice Online

Given an integer rowIndex, return the rowIndex^th (0-indexed) row of the Pascal's triangle.

In Pascal's triangle, each number is the sum of the two numbers directly above it as shown:

Example 1:

Input: rowIndex = 3
Output: [1,3,3,1]

Example 2:

Input: rowIndex = 0
Output: [1]

Example 3:

Input: rowIndex = 1
Output: [1,1]

Constraints:

0 <= rowIndex <= 33

Follow up: Could you optimize your algorithm to use only O(rowIndex) extra space?