Solve Triangle Rows and Top Frequencies

You have 1 hour to solve both coding problems.

Problem 1: Build an Additive Number Triangle

Given an integer numRows, return the first numRows rows of a triangle of numbers with the following rules:

• Row indexing starts at 0.
• The first and last value in every row are 1.
• Each interior value is the sum of the two adjacent values directly above it: triangle[i][j] = triangle[i - 1][j - 1] + triangle[i - 1][j].

Return the triangle as a list of rows.

Example:

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

Problem 2: Return the K Most Frequent Values

Given an integer array nums and an integer k, return any k distinct values that appear most frequently in nums.

If multiple values have the same frequency, any valid set of k values is acceptable. The output may be returned in any order.

Example:

Input: nums = [1,1,1,2,2,3], k = 2
Output: [1,2]

Expected approach: count frequencies and use a size-k min-heap to keep the current k most frequent values.

Part 1: Build an Additive Number Triangle

Given a non-negative integer numRows, build and return the first numRows rows of an additive number triangle.

Rules:

• Row indexing starts at 0.
• The first and last value of every row are 1.
• Each interior value is the sum of the two values directly above it from the previous row.

If numRows is 0, return an empty list.

Constraints

• 0 <= numRows <= 30
• Row 0 is [1]
• Each row i contains exactly i + 1 integers

Examples

Example 1

Input: 0
Output: []

Explanation: Edge case: zero rows means the triangle is empty.

Example 2

Input: 1
Output: [[1]]

Explanation: Only the first row is needed.

Hints

1. Build the triangle one row at a time, starting from row 0.
2. For each new row, set the first and last elements to 1, then fill the middle using the previous row.

Part 2: Return the K Most Frequent Values

Given an integer array nums and an integer k, return k distinct values that appear most frequently in nums.

If multiple values have the same frequency, any valid set of k values is acceptable. The result may be returned in any order.

A strong approach is to count frequencies first, then use a size-k min-heap to keep track of the current top k values.

Constraints

• 1 <= len(nums) <= 100000
• -10^9 <= nums[i] <= 10^9
• 1 <= k <= number of distinct values in nums

Examples

Example 1

Input: ([1, 1, 1, 2, 2, 3], 2)
Output: [1, 2]

Explanation: Value 1 appears 3 times and value 2 appears 2 times, so they are the top 2.

Example 2

Input: ([5], 1)
Output: [5]

Explanation: Edge case: with one element, that element is the most frequent.

Hints

1. Use a hash map or Counter to compute how often each value appears.
2. Keep a min-heap of size k so the least useful candidate can be removed when a better one appears.