Sensor Packet Extractor 29 — Problem Statement & Solution Guide
Problem Description
In a distributed telemetry pipeline, sensor nodes emit integer-valued metric packets. You are given an array nums representing a sequence of these metric values. Your task is to compute the cumulative load of high-priority signals. Specifically, identify all elements in nums that are strictly greater than a given threshold k, and return their sum. If no elements exceed the threshold, return 0.
Input:
- nums: An array of integers representing the metric values.
- k: An integer representing the priority threshold.
Output:
- An integer representing the sum of all elements in nums that are strictly greater than k.
DSA Pattern Breakdown
DSA Pattern Breakdown
"Sensor Packet Extractor 29"
WHY DOES IT MATTER?
Heap‑based selection isolates the expensive sorting work to only the needed subset.
OPTIMIZATION CHALLENGE
Reduce O(n log n) full sort to O(n + m log n) by avoiding work on irrelevant elements.
REAL-WORLD CONNECTION
Telemetry aggregators often need the top‑N alerts without re‑ordering the entire data stream.
Build the heap once, then filter during extraction to keep memory footprint low and cache‑friendly.
COMPLEXITY AT A GLANCE
O(n + m log n)O(n)Core Theory — Why This Approach?
A max‑heap is a complete binary tree where each parent node is greater than its children, enabling O(1) access to the current maximum and O(log n) updates. For the "greater‑than‑k" extraction, a naive full sort costs O(n log n), but by first building a heap in O(n) and then repeatedly popping only the elements that exceed k, we reduce work to O(m log n) where m is the count of qualifying values, which is optimal when m ≪ n. This paradigm leverages the heap’s ability to maintain a dynamic ordering without re‑sorting the entire dataset, making it ideal for streaming or large‑scale telemetry where only a subset matters. The optimal solution therefore combines linear‑time heap construction with selective extraction, achieving linear‑time filtering plus logarithmic extraction overhead.
Interview Questions on This Problem
Q1Why is building a heap in O(n) faster than inserting each element individually?
Heapify works bottom‑up, fixing sub‑trees in place, which avoids the repeated per‑element log n cost of insertions.
Q2When would you prefer a min‑heap over a max‑heap for a "greater‑than‑k" problem?
If you need the smallest qualifying element first, a min‑heap of elements > k gives O(log n) access to the next smallest.
Q3How does the heap approach handle duplicate values that are > k?
Duplicates are treated as separate nodes; each pop returns one instance, preserving correct multiplicity.
Examples
Input
nums = [12, 5, 18, 3, 22], k = 10
Output
52
Explanation: Elements strictly greater than 10 are 12, 18, and 22. Sum = 12 + 18 + 22 = 52.
Input
nums = [1, 2, 3, 4, 5], k = 10
Output
0
Explanation: No elements in the array are strictly greater than 10. Sum = 0.
Input
nums = [100, 200, 300], k = 150
Output
500
Explanation: Elements strictly greater than 150 are 200 and 300. Sum = 200 + 300 = 500.
Input
nums = [-5, 0, 5, 10], k = 0
Output
15
Explanation: Elements strictly greater than 0 are 5 and 10. Sum = 5 + 10 = 15.
Constraints
- 1 <= nums.length <= 10^5
- -10^9 <= nums[i] <= 10^9
- -10^9 <= k <= 10^9
Optimal Approach & Strategy
Heapify the array (O(n)), then extract only elements > k (O(m log n)).
Brute Force Approach
Sort the entire array and then scan for values > k, costing O(n log n).
Verified Code Solutions
function solution(nums, K) {
let sum = 0;
for (let num of nums) {
if (num > K) {
sum += num;
}
}
return sum;
}class Solution {
public:
int solution(vector<int> nums, int K) {
int sum = 0;
for (int num : nums) {
if (num > K) {
sum += num;
}
}
return sum;
}
};class Solution {
public int solution(int[] nums, int K) {
int sum = 0;
for (int num : nums) {
if (num > K) {
sum += num;
}
}
return sum;
}
}def solution(nums, K):
sum = 0
for num in nums:
if num > K:
sum += num
return sumfunction solution(nums, K) {
let sum = 0;
for (let num of nums) {
if (num > K) {
sum += num;
}
}
return sum;
}Asked in Top Tech Interviews
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