Is Sum of Weighted Modes in Subarrays easy or hard?

The problem is generally rated Medium because the brute force idea is straightforward but maintaining the mode efficiently requires combining multiple data structures. Understanding frequency updates and lazy deletion inside a heap is the main challenge.

Sum of Weighted Modes in Subarrays Python/Java solution

Typical implementations maintain a dictionary or HashMap for counts and a heap structure storing (frequency, value) pairs. Python solutions use heapq with negative frequencies, while Java solutions rely on PriorityQueue. C++ often uses priority_queue with lazy deletion checks against the current map.

How to solve Sum of Weighted Modes in Subarrays in O(n)?

An O(n) solution is generally not feasible because the problem requires evaluating properties across all O(n²) subarrays. Most optimized implementations focus on reducing the cost of maintaining the mode using heaps or ordered structures. This leads to an O(n² log n) complexity while keeping each update efficient.

What is the best approach for Sum of Weighted Modes in Subarrays?

The most practical approach uses a hash map for frequency counting combined with a priority queue (max heap) to track the current mode. Each time a value appears in the expanding window, its frequency is updated and pushed into the heap. Lazy deletion removes outdated entries when querying the top. This keeps mode retrieval efficient while processing all subarrays.

Is Sum of Weighted Modes in Subarrays asked at Google/Amazon/Meta?

Problems involving dynamic frequency tracking and mode maintenance appear frequently in interviews at companies like Amazon, Google, and Meta. Variants often test your ability to combine hash maps with heaps or ordered data structures to maintain statistics inside sliding windows or subarrays.

What data structure is used in Sum of Weighted Modes in Subarrays?

The main data structures are a hash map for frequency counting and a priority queue (max heap) for retrieving the element with the highest frequency. Some variations also use ordered sets or balanced trees to keep elements sorted by frequency.

What is the time complexity of Sum of Weighted Modes in Subarrays?

The optimized solution typically runs in O(n² log n) time. There are O(n²) subarrays, and each update to the heap or ordered structure costs O(log n). Space complexity is O(n) due to storing frequency counts and heap entries.

3672. Sum of Weighted Modes in Subarrays - Practice Online

You are given an integer array nums and an integer k.

For every subarray of length k:

The mode is defined as the element with the highest frequency. If there are multiple choices for a mode, the smallest such element is taken.
The weight is defined as mode * frequency(mode).

Return the sum of the weights of all subarrays of length k.

Note:

A subarray is a contiguous non-empty sequence of elements within an array.
The frequency of an element x is the number of times it occurs in the array.

Example 1:

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

Output: 8

Explanation:

Subarrays of length k = 3 are:

Subarray	Frequencies	Mode	Mode Frequency	Weight
[1, 2, 2]	1: 1, 2: 2	2	2	2 × 2 = 4
[2, 2, 3]	2: 2, 3: 1	2	2	2 × 2 = 4

Thus, the sum of weights is 4 + 4 = 8.

Example 2:

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

Output: 3

Explanation:

Subarrays of length k = 2 are:

Subarray	Frequencies	Mode	Mode Frequency	Weight
[1, 2]	1: 1, 2: 1	1	1	1 × 1 = 1
[2, 1]	2: 1, 1: 1	1	1	1 × 1 = 1
[1, 2]	1: 1, 2: 1	1	1	1 × 1 = 1

Thus, the sum of weights is 1 + 1 + 1 = 3.

Example 3:

Input: nums = [4,3,4,3], k = 3

Output: 14

Explanation:

Subarrays of length k = 3 are:

Subarray	Frequencies	Mode	Mode Frequency	Weight
[4, 3, 4]	4: 2, 3: 1	4	2	2 × 4 = 8
[3, 4, 3]	3: 2, 4: 1	3	2	2 × 3 = 6

Thus, the sum of weights is 8 + 6 = 14.

Constraints:

1 <= nums.length <= 10⁵
1 <= nums[i] <= 10⁵
1 <= k <= nums.length