Vault Buffer Extractor 42 — Problem Statement & Solution Guide
Problem Description
You are tasked with optimizing the data retrieval process for a high-security vault system. The vault stores a sequence of integer-encoded buffer states. A security protocol requires identifying all buffer states that exceed a specific cryptographic threshold K. Your objective is to compute the aggregate sum of all buffer states strictly greater than K. If no buffer state exceeds the threshold, the result must be zero.
Given an array of integers representing the buffer states and an integer K representing the threshold, return the sum of all elements in the array that are strictly greater than K. The solution must efficiently process the sequence to ensure minimal latency in the vault's access control mechanism.
Input: An array of integers 'buffer' and an integer 'K'.
Output: An integer representing the sum of all elements in 'buffer' that are strictly greater than 'K'.
DSA Pattern Breakdown
DSA Pattern Breakdown
"Vault Buffer Extractor 42"
WHY DOES IT MATTER?
Filtering and aggregating large numeric streams is a core pattern in high‑throughput systems.
OPTIMIZATION CHALLENGE
The key is to cut branch mispredictions and memory stalls by using bitwise masks and vectorized operations.
REAL-WORLD CONNECTION
Think of network packet counters that only sum packets exceeding a size threshold for billing purposes.
Profile the hot loop, align data to cache lines, and use compiler intrinsics for SIMD to extract maximum throughput.
COMPLEXITY AT A GLANCE
O(N)O(1)Core Theory — Why This Approach?
The problem reduces to scanning a massive integer stream and aggregating values that exceed a threshold K. A naïve solution that checks each element with a simple > comparison and adds it runs in O(N) time but can become a bottleneck when N reaches 10^8 or when the integers are 64‑bit, because each addition may overflow and the I/O cost dominates. The optimal paradigm leverages bit‑level tricks: using unsigned 64‑bit arithmetic to detect overflow, applying SIMD‑friendly masks to batch‑process 8 or 16 numbers at a time, and employing a running sum stored in a wider type (e.g., __int128) to guarantee correctness. This approach preserves linear time while dramatically reducing constant factors, making it suitable for hard‑level constraints where memory bandwidth and CPU cycles are at a premium.
Interview Questions on This Problem
Q1How can you safely sum 64‑bit integers that may overflow the signed 64‑bit range?
Promote the accumulator to a wider type such as unsigned __int128 before each addition. This prevents overflow and lets you cast back only after the final result is computed.
Q2Explain how SIMD can accelerate the >K filter in this problem.
Load multiple integers into a vector register, compare them against a broadcasted K, and generate a mask that selects only the qualifying elements for a masked add. This reduces the number of scalar branches and leverages data‑parallelism.
Q3Why is a single pass O(N) algorithm still considered optimal here despite the problem’s ‘hard’ label?
Because any algorithm must inspect each element at least once to decide if it contributes to the sum, establishing a lower bound of Ω(N). The challenge lies in minimizing the hidden constants, not in asymptotic improvement.
Examples
Input
buffer = [12, 45, 7, 89, 3], K = 20
Output
134
Explanation: Iterate through the buffer: 12 <= 20 (skip), 45 > 20 (add 45), 7 <= 20 (skip), 89 > 20 (add 89), 3 <= 20 (skip). Sum = 45 + 89 = 134.
Input
buffer = [5, 10, 15, 20], K = 25
Output
0
Explanation: Iterate through the buffer: 5 <= 25 (skip), 10 <= 25 (skip), 15 <= 25 (skip), 20 <= 25 (skip). No elements exceed the threshold. Sum = 0.
Input
buffer = [-10, -5, 0, 5, 10], K = -3
Output
15
Explanation: Iterate through the buffer: -10 <= -3 (skip), -5 <= -3 (skip), 0 > -3 (add 0), 5 > -3 (add 5), 10 > -3 (add 10). Sum = 0 + 5 + 10 = 15.
Input
buffer = [100, 200, 300], K = 150
Output
500
Explanation: Iterate through the buffer: 100 <= 150 (skip), 200 > 150 (add 200), 300 > 150 (add 300). Sum = 200 + 300 = 500.
Constraints
- 1 <= buffer.length <= 10^5
- -10^9 <= buffer[i] <= 10^9
- -10^9 <= K <= 10^9
Optimal Approach & Strategy
Use SIMD to compare blocks of numbers against K, generate a mask, and perform a masked horizontal add in a wider accumulator type, still O(N) but with far lower constant factors.
Brute Force Approach
Iterate over the array, if a[i] > K add it to a 64‑bit sum; O(N) time, O(1) extra space.
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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