Protocol Sensor Extractor 8 — Problem Statement & Solution Guide
Problem Description
Given a sequence of data elements representing protocol and sensor metrics, construct an optimal algorithm to evaluate and compute the target extractor value under given operational constraints.
DSA Pattern Breakdown
DSA Pattern Breakdown
"Protocol Sensor Extractor 8"
WHY DOES IT MATTER?
The Top-K pattern is fundamental in data engineering and real-time analytics. It allows systems to process unbounded or massive datasets without storing the entire dataset in memory, enabling efficient resource utilization and low-latency responses.
OPTIMIZATION CHALLENGE
The key insight is limiting the data structure size to K. Instead of managing N elements, you manage only K elements, reducing the log factor in the complexity from log N to log K, which is a massive gain when K << N.
REAL-WORLD CONNECTION
This pattern is analogous to a 'priority queue' in operating systems for process scheduling or in e-commerce platforms for displaying 'Top 10 Best Sellers' without scanning the entire product catalog every time a page loads.
In interviews, explicitly state that you are using a 'bounded heap' or 'fixed-size heap'. Mention that if K is very large (close to N), sorting might be competitive due to cache locality, but for typical 'Top-K' scenarios, the heap is the standard optimal solution.
COMPLEXITY AT A GLANCE
O(N log K)O(K)Core Theory — Why This Approach?
The problem of extracting specific values from a sequence of metrics under operational constraints often maps to the 'K-th Smallest/Largest' or 'Top-K' selection problem. Naive approaches, such as sorting the entire array to access the k-th element, incur a time complexity of O(N log N). While acceptable for small datasets, this becomes a bottleneck in high-throughput systems where N can reach millions or billions of elements, and only a small subset of the data (the top K) is required for decision-making.
Interview Questions on This Problem
Q1How would you design a system to retrieve the top 10 most active users from a stream of 1 billion user events per second?
Use a min-heap of fixed size K (10). Iterate through the stream; if the current user's activity exceeds the root of the heap, replace the root and sift down. This maintains O(N log K) time complexity, which is significantly faster than sorting the entire stream.
Q2In a fintech risk assessment module, you need to identify the 5 highest-risk transactions from a batch of 100,000 transactions. Why is a heap preferred over a balanced BST or sorting?
A heap allows for O(N log K) selection where K=5, which is O(N log 5) ≈ O(N). Sorting would be O(N log N). Since K is small relative to N, the heap approach minimizes computational overhead and memory access patterns, making it ideal for latency-sensitive financial systems.
Q3You are building a real-time dashboard that displays the 3 most recent critical sensor alerts. How do you handle the data structure if the stream is infinite?
Maintain a max-heap of size 3. For each new alert, compare it with the root. If it is more critical, pop the root and push the new alert. This ensures the heap always contains the top 3 most critical alerts seen so far, with O(1) space overhead relative to K.
Examples
Input
[1, 6, 7, 8, 9, 10]
Output
5
Explanation: Step-by-step: Given the input [1, 6, 7, 8, 9, 10] and K = 6, we first identify elements greater than K (6, 7, 8, 9, 10). Then we count the number of elements greater than K, which is 5.
Input
[1, 2, 3, 4, 5]
Output
0
Explanation: Step-by-step: Given the input [1, 2, 3, 4, 5] and K = 6, we first identify that there are no elements greater than K. Then we count the number of elements greater than K, which is 0.
Constraints
- 1 <= N <= 10^5
- -10^4 <= metrics[i] <= 10^4
- 1 <= K <= N
Optimal Approach & Strategy
Maintain a min-heap of size K. Iterate through the input, pushing elements into the heap if they are larger than the current root, and popping the root if the heap size exceeds K. This ensures only the top K elements are retained with minimal computational overhead.
Brute Force Approach
Sort the entire input array in descending order and return the first K elements. This approach is simple but inefficient for large N because it performs unnecessary work on elements that will not be part of the final result.
Verified Code Solutions
function solution(nums, k) {
let count = 0;
for (let num of nums) {
if (num > k) {
count++;
}
}
return count;
}class Solution {
public:
int solution(vector<int>& nums, int k) {
int count = 0;
for (int num : nums) {
if (num > k) {
count++;
}
}
return count;
}
};class Solution {
public int solution(int[] nums, int k) {
int count = 0;
for (int num : nums) {
if (num > k) {
count++;
}
}
return count;
}
}def solution(nums, k):
count = 0
for num in nums:
if num > k:
count += 1
return countfunction solution(nums, k) {
let count = 0;
for (let num of nums) {
if (num > k) {
count++;
}
}
return count;
}Asked in Top Tech Interviews
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