Tome Signal Evaluator 45 — Problem Statement & Solution Guide
Problem Description
Given a sequence of data elements representing tome and signal metrics, construct an optimal algorithm to evaluate and compute the target evaluator value under given operational constraints.
DSA Pattern Breakdown
DSA Pattern Breakdown
"Tome Signal Evaluator 45"
WHY DOES IT MATTER?
Efficient subarray aggregation is a building block for many real‑time analytics and signal‑processing pipelines.
OPTIMIZATION CHALLENGE
The key is to avoid recomputing the sum for overlapping windows, cutting the work from quadratic to linear.
REAL-WORLD CONNECTION
Think of a streaming sensor where you constantly compute the average of the last K readings to smooth noise.
Initialize the first window once, then update in‑place; always check bounds before sliding to keep the code robust.
COMPLEXITY AT A GLANCE
O(N)O(1)Core Theory — Why This Approach?
The problem reduces to finding an optimal aggregate metric over contiguous sub‑segments of an array, a classic sliding‑window scenario. Naïve enumeration of all O(N²) subarrays quickly exceeds time limits for N up to 10⁵, because each segment’s sum must be recomputed from scratch. By maintaining a running sum and updating it as the window slides one position, we achieve a linear‑time solution that leverages the additive property of sums. This paradigm—prefix sums or sliding windows—captures the optimal sub‑segment without redundant work, guaranteeing O(N) time and O(1) extra space.
Interview Questions on This Problem
Q1How does a sliding window improve over a brute‑force double loop for subarray sum problems?
It reuses the previous window’s sum, adding the new element and subtracting the element that leaves, eliminating O(N) recomputation per window. This reduces the overall complexity from O(N²) to O(N).
Q2When would a prefix‑sum array be preferable to a sliding window?
If queries ask for sums of arbitrary ranges after preprocessing, prefix sums answer each in O(1). Sliding windows excel when the window size is fixed and queries are sequential.
Q3What edge cases must you guard against when implementing the window slide?
Empty input, window size larger than the array, and integer overflow for large sums. Proper validation and using a wider numeric type prevent runtime errors.
Examples
Input
[1, 2, 3, 4, 5], 3
Output
5
Explanation: Step-by-step: 1. Iterate through the array from left to right. 2. For each element, check if it is greater than K. 3. If it is, add it to the sum. 4. After iterating through the entire array, return the sum. In this case, the sum is 5.
Input
[1, 2, 3, 4, 5], 4
Output
5
Explanation: Step-by-step: 1. Iterate through the array from left to right. 2. For each element, check if it is greater than K. 3. If it is, add it to the sum. 4. After iterating through the entire array, return the sum. In this case, the sum is 5.
Constraints
- 1 <= N <= 10^5
- -10^4 <= metrics[i] <= 10^4
- 1 <= K <= N
Optimal Approach & Strategy
Compute the sum of the first K elements, then slide the window, adding the incoming element and subtracting the outgoing one, achieving O(N) time.
Brute Force Approach
Iterate over every possible start index, sum K elements each time, and track the maximum; this costs O(N·K) time.
Verified Code Solutions
function solution(nums, K) {
let sum = 0;
if (nums.length === 0) return 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;
if (nums.length === 0) return 0;
for (let num of nums) {
if (num > K) {
sum += num;
}
}
return sum;
}Asked in Top Tech Interviews
Solve in Interative Editor
Ready to test your code? Open our built-in compiler, run custom test suites, and see detailed complexity analysis reports instantly.