Given a continuous stream of integers, implement an algorithm to optimize the inversion count in the stream, where an inversion is defined as a pair of indices (i, j) such that i stream[j]. Your solution should efficiently handle the streaming input and output the inversion count in real-time, ensuring optimal performance in terms of time and space complexity.

In this problem, we need to count the number of inversions in a continuous stream of integers. An inversion is defined as a pair of indices (i, j) such that i stream[j]. Given the nature of a streaming input, we can't store all the values in memory at once, and we need a solution that counts inversions efficiently as new integers arrive. The optimal approach to tackle this problem is to utilize a modified version of the Merge Sort algorithm, which is known to count inversions in O(n log n) time. This approach can be adapted to handle streaming data while maintaining a manageable memory footprint. 1. **Data Structure**: Use a balanced Binary Search Tree (BST) or a Fenwick Tree (also known as a Binary Indexed Tree) to maintain the current state of the integers seen so far in the stream. This allows us to efficiently query and update counts of elements. 2. **Inversion Count Logic**: For each new integer `num` added to the stream: - Query the tree to count how many of the existing integers are greater than `num`. This gives the number of inversions involving `num`. - Insert `num` into the tree, updating the counts accordingly. 3. **Real-Time Updates**: Each time a new integer arrives, update the inversion count and the tree structure in real-time. 4. **Example**: If the stream is [3, 1, 4, 2]: - When `3` arrives, count = 0. - When `1` arrives, count = 1 (3 > 1). - When `4` arrives, count = 1 (still 1 inversion). - When `2` arrives, count = 3 (3 > 2 and 4 > 2). Total inversions = 3. Here is a Python implementation using a Fenwick Tree for inversion counting: ```python class FenwickTree: def __init__(self, size): self.size = size self.tree = [0] * (size + 1) def update(self, index, value): while index 0: sum += self.tree[index] index -= index & -index return sum class InversionCounter: def __init__(self): self.fenwick_tree = FenwickTree(100000) self.inversions = 0 def add_number(self, num): # Count inversions count_greater = self.fenwick_tree.query(100000) - self.fenwick_tree.query(num) self.inversions += count_greater # Insert current number into Fenwick Tree self.fenwick_tree.update(num, 1) return self.inversions ``` The time complexity of this solution is O(log n) for both updating the Fenwick Tree and querying it, where n is the number of integers processed so far. Given that we are processing each integer in the stream, the overall time complexity for processing all integers in the stream is O(m log n), where m is the total number of integers in the stream. The space complexity is O(n) due to the storage of the Fenwick Tree, which can hold counts for the range of input integers. 1. **Empty Stream**: If no integers are provided in the stream, the inversion count should be 0. 2. **Single Element**: If a single integer is streamed, the inversion count remains 0. 3. **All Elements Equal**: If all streamed integers are the same, there should be no inversions, returning 0. 4. **Large Range of Integers**: If the integers have a large range, ensure that the Fenwick Tree is initialized to accommodate the maximum possible integer value. 5. **Negative Numbers**: If the stream includes negative numbers, adjust the Fenwick Tree to handle negative indexing or offset the values to fit within non-negative indices.

Optimize inversion for streaming input | Elastic Software Engineer Interview

Optimize inversion for streaming input

Last updated: October 15, 2025

Quick Overview

Given a continuous stream of integers, implement an algorithm to optimize the inversion count in the stream, where an inversion is defined as a pair of indices (i, j) such that i < j and stream[i] > stream[j]. Your solution should efficiently handle the streaming input and output the inversion count in real-time, ensuring optimal performance in terms of time and space complexity.

Elastic

Coding & Algorithms

Software Engineer

Elastic

October 15, 2025

Software Engineer

Technical Screen

Coding & Algorithms

Hard

118

1,981 solved

This coding problem is frequently asked during Technical Screen at Elastic. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. Elastic expects candidates to write production-quality code, not just solve the puzzle.

What the Interviewer Expects

Quickly identify the optimal approach and its theoretical basis
Handle complex algorithm design with multiple interacting components
Write concise, elegant code under time pressure
Prove correctness of your approach and discuss alternative solutions
Optimize beyond the obvious: discuss constant factor improvements
Address follow-up variations and explain how the solution generalizes

Key Topics to Cover

Graph algorithms and traversal

Common algorithm patterns (sliding window, two pointers, BFS/DFS)

Hash maps and frequency counting

Tree structures and recursion

How to Approach This

Clarify input constraints and edge cases before writing code.
Walk through your approach verbally and confirm with the interviewer before coding.
Start with a brute force solution, then optimize. Mention time and space complexity.
Test your solution with examples, including edge cases like empty input or duplicates.
Consider common patterns: sliding window, two pointers, hash map, BFS/DFS, dynamic programming.

Possible Follow-up Questions

How would you modify your solution to handle streaming input?
What if the input doesn't fit in memory?
How would you parallelize this solution?

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Problem Analysis

In this problem, we need to count the number of inversions in a continuous stream of integers. An inversion is defined as a pair of indices (i, j) such that i < j and stream[i] > stream[j]. Given the ...

Approach

Data Structure: Use a balanced Binary Search Tree (BST) or a Fenwick Tree (also known as a Binary Indexed Tree) to maintain the current state of the integers seen so far in the stream. This all...

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Optimize inversion for streaming input

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What the Interviewer Expects

Key Topics to Cover

How to Approach This

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