Cumulative Target Index — Problem Statement & Solution Guide
Problem Description
In a distributed telemetry system, sensor nodes emit integer-valued metric readings that must be aggregated to compute a global health score. This score, referred to as the Cumulative Target Index, is defined as the arithmetic sum of all individual readings in the sequence. The computation requires a single pass through the data stream to accumulate the total value.
Given an array of integers representing the sensor readings, calculate the Cumulative Target Index. The result is a single scalar value representing the net sum of all elements in the array.
Your task is to implement a function that takes the array as input and returns the computed index. The solution must handle both positive and negative values, as well as zero, ensuring that the final aggregation accurately reflects the net state of the system.
DSA Pattern Breakdown
DSA Pattern Breakdown
"Cumulative Target Index"
WHY DOES IT MATTER?
The single-pass accumulation pattern is essential because it guarantees linear time complexity and constant auxiliary space, which are the minimal requirements for processing large-scale telemetry streams efficiently. It eliminates the need for nested loops or auxiliary data structures, thereby reducing both CPU and memory overhead.
OPTIMIZATION CHALLENGE
The key insight is recognizing that addition is associative and commutative, allowing us to accumulate incrementally without revisiting previous elements. This reduces the time from O(n^2) in naive nested approaches to O(n) and the space from O(n) to O(1).
REAL-WORLD CONNECTION
In distributed systems like Kafka or Flink, this pattern maps directly to the reduce phase, where each worker computes a partial sum of its partition and the framework merges them. It also mirrors how monitoring dashboards compute rolling totals without storing the entire history of events.
When explaining this to an interviewer, emphasize the importance of streaming-friendly algorithms and how they enable real-time analytics. Highlight that the same pattern scales to distributed environments by simply aggregating partial sums.
COMPLEXITY AT A GLANCE
O(n)O(1)Core Theory — Why This Approach?
The Cumulative Target Index problem is a classic example of a linear-time aggregation task. In its naive form, one might attempt to recompute the sum from scratch for each new element or use nested loops to accumulate partial sums, leading to O(n^2) time complexity and unnecessary memory usage. Such approaches quickly become infeasible as the input size grows into millions or billions of sensor readings, especially in a distributed telemetry context where latency and throughput are critical.
The optimal solution leverages the associative property of addition: the total sum can be obtained by iterating through the array once and maintaining a running accumulator. This single-pass algorithm runs in O(n) time and O(1) auxiliary space, making it ideal for streaming data and real-time dashboards. By avoiding repeated scans or auxiliary data structures, we reduce CPU cycles, cache misses, and memory bandwidth consumption, which are paramount in high-performance telemetry pipelines.
Beyond performance, this pattern also simplifies reasoning about correctness. Since addition is commutative and associative, the order of accumulation does not affect the final result, allowing parallel or distributed implementations to merge partial sums safely. This property underpins many MapReduce and Spark jobs that compute global aggregates over massive datasets.
Interview Questions on This Problem
Q1How would you compute the Cumulative Target Index for a stream of sensor readings that arrives in real-time, and what considerations would you make for memory usage?
I would maintain a single integer variable that holds the running total. Each time a new reading arrives, I add it to this accumulator. This approach uses O(1) additional memory regardless of stream length, which is essential for real-time systems where the data volume can be unbounded.
Q2A fintech platform needs to compute the daily sum of transaction amounts for millions of users. What algorithmic pattern would you recommend and why?
I would recommend a single-pass linear scan with a running sum, which is O(n) time and O(1) space. For distributed processing, we can partition the data, compute partial sums in parallel, and then aggregate them, leveraging the associative property of addition to keep the algorithm scalable and fault-tolerant.
Q3During a high-growth startup interview, you are asked to explain how you would handle potential integer overflow when summing a large array of 32-bit integers. What strategy would you use?
I would use a 64-bit integer type (e.g., long in Java or long long in C++) for the accumulator to accommodate the maximum possible sum. If the language or platform imposes limits, I would also add a check for overflow and either throw an exception or switch to arbitrary-precision arithmetic when necessary.
Examples
Input
nums = [4, -2, 7, 1]
Output
10
Explanation: Initialize sum = 0. Add 4 -> sum = 4. Add -2 -> sum = 2. Add 7 -> sum = 9. Add 1 -> sum = 10. The final Cumulative Target Index is 10.
Input
nums = [-5, -3, -1]
Output
-9
Explanation: Initialize sum = 0. Add -5 -> sum = -5. Add -3 -> sum = -8. Add -1 -> sum = -9. The final Cumulative Target Index is -9.
Input
nums = [0, 0, 0]
Output
0
Explanation: Initialize sum = 0. Add 0 -> sum = 0. Add 0 -> sum = 0. Add 0 -> sum = 0. The final Cumulative Target Index is 0.
Input
nums = [1000000, -1000000, 5]
Output
5
Explanation: Initialize sum = 0. Add 1000000 -> sum = 1000000. Add -1000000 -> sum = 0. Add 5 -> sum = 5. The final Cumulative Target Index is 5.
Constraints
- 1 <= nums.length <= 10^5
- -10^9 <= nums[i] <= 10^9
- The sum of all elements will fit within a 64-bit signed integer.
Optimal Approach & Strategy
The optimal approach iterates through the array once, maintaining a running accumulator. This yields O(n) time and O(1) auxiliary space, making it suitable for large datasets and streaming data.
Brute Force Approach
A naive approach might recompute the sum from scratch for each element or use nested loops to accumulate partial sums, resulting in O(n^2) time complexity and unnecessary memory usage.
Verified Code Solutions
function cumulativeTargetIndex(nums) {
let sum = 0;
for (const v of nums) {
sum += v;
}
return sum;
}
// Example usage
const nums = [4, -2, 7, 1];
console.log(cumulativeTargetIndex(nums)); // Expected output: 10#include <bits/stdc++.h>
using namespace std;
int cumulativeTargetIndex(const vector<int>& nums) {
long long sum = 0; // use long long to avoid overflow
for (int v : nums) {
sum += v;
}
return static_cast<int>(sum);
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
vector<int> nums = {4, -2, 7, 1};
cout << cumulativeTargetIndex(nums) << "\n"; // Expected output: 10
return 0;
}public class Solution {
public int cumulativeTargetIndex(int[] nums) {
long sum = 0L; // use long to prevent overflow
for (int v : nums) {
sum += v;
}
return (int) sum;
}
public static void main(String[] args) {
Solution sol = new Solution();
int[] nums = {4, -2, 7, 1};
System.out.println(sol.cumulativeTargetIndex(nums)); // Expected output: 10
}
}def cumulative_target_index(nums):
"""Return the arithmetic sum of all integers in the list `nums`."""
return sum(nums)
# Example usage
if __name__ == "__main__":
nums = [4, -2, 7, 1]
print(cumulative_target_index(nums)) # Expected output: 10function cumulativeTargetIndex(nums) {
let sum = 0;
for (const v of nums) {
sum += v;
}
return sum;
}
// Example usage
const nums = [4, -2, 7, 1];
console.log(cumulativeTargetIndex(nums)); // Expected output: 10Asked in Top Tech Interviews
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