Verified Frequency Balance — Problem Statement & Solution Guide
Problem Description
Given an integer array nums, compute its Verified Frequency Balance, defined as the arithmetic sum of all elements in the array. The function should return this sum as a 64‑bit signed integer. The input consists of a single line containing the space‑separated elements of nums. The output is a single integer representing the Verified Frequency Balance.
DSA Pattern Breakdown
DSA Pattern Breakdown
"Verified Frequency Balance"
WHY DOES IT MATTER?
Linear aggregation patterns like sum, min, max, and count are foundational because they appear in virtually every data‑processing pipeline, from analytics dashboards to real‑time monitoring systems. Mastering this pattern ensures you can write code that scales linearly with input size while keeping memory footprints minimal.
OPTIMIZATION CHALLENGE
The key insight is recognizing that addition is both associative and commutative, allowing the problem to be solved with a single accumulator variable. This eliminates the need for auxiliary arrays, nested loops, or hash‑based bookkeeping, collapsing the complexity to O(n) time and O(1) space.
REAL-WORLD CONNECTION
Think of a distributed log aggregation service that continuously sums request latencies to compute total processing time. Each log entry is processed exactly once, and the service maintains a single counter—mirroring the single‑pass sum algorithm.
During an interview, start by stating the O(n) single‑pass solution, then immediately discuss edge cases (empty array, overflow, negative numbers) and how you would use a 64‑bit type to guarantee correctness.
COMPLEXITY AT A GLANCE
O(n)O(1)Core Theory — Why This Approach?
The Verified Frequency Balance problem reduces to computing the arithmetic sum of an integer array, which is a classic example of a linear aggregation operation. In algorithmic terms, this belongs to the "prefix sum" family, where each element contributes exactly once to the final result, allowing a single pass over the data. Naïve approaches that attempt to recompute partial sums repeatedly or use nested loops incur O(n²) time, which quickly becomes infeasible for large inputs (e.g., arrays with millions of elements) due to both time and memory constraints.
The optimal paradigm leverages the associative property of addition: (a + b) + c = a + (b + c). By iterating once through the array and maintaining a running total in a 64‑bit accumulator, we achieve O(n) time and O(1) auxiliary space. This approach also guarantees correct handling of potential integer overflow when the sum exceeds the 32‑bit range, as the accumulator is explicitly defined as a 64‑bit signed integer.
From a hashing perspective, although the problem statement mentions "Hashing," the core operation does not require any hash table; the term emphasizes the need for constant‑time updates, akin to how hash maps provide O(1) access. Understanding this distinction helps candidates avoid over‑engineering solutions with unnecessary data structures.
Interview Questions on This Problem
Q1How would you modify the solution to return the sum modulo 10⁹+7, and why is this a common requirement in coding interviews?
Initialize the accumulator as a 64‑bit integer, and after adding each element, apply "sum = (sum + num) % MOD" where MOD = 1_000_000_007. This prevents overflow and keeps the result within a fixed range, which is useful for problems that require large‑scale combinatorial counts.
Q2If the input stream is infinite (e.g., reading numbers from a socket), how can you compute the Verified Frequency Balance without storing the entire array?
Use a streaming algorithm: maintain a running 64‑bit total and update it for each incoming number. Since only the aggregate is needed, memory usage stays O(1) regardless of stream length.
Q3Explain how you would detect and handle integer overflow when the sum exceeds the limits of a signed 64‑bit integer.
Before adding a new number, check if "sum > Long.MAX_VALUE - num" (or "sum < Long.MIN_VALUE - num" for negatives). If the condition holds, you can either throw an overflow exception or clamp the result, depending on the problem constraints.
Examples
Input
4 7 -2 5
Output
14
Explanation: The array contains four numbers: 4, 7, -2, and 5. Adding them yields 4 + 7 + (-2) + 5 = 14. Hence the Verified Frequency Balance is 14.
Input
-10 0 10 20 -5
Output
15
Explanation: Step 1: List the numbers: -10, 0, 10, 20, -5. Step 2: Compute the cumulative sum: -10 + 0 = -10; -10 + 10 = 0; 0 + 20 = 20; 20 + (-5) = 15. The final sum is 15, which is the Verified Frequency Balance.
Input
1000000000 -1000000000 999999999 -999999999
Output
0
Explanation: The four numbers cancel each other out: (1 000 000 000 + (-1 000 000 000)) + (999 999 999 + (-999 999 999)) = 0. Therefore the Verified Frequency Balance equals 0.
Constraints
- 1 <= nums.length <= 100000
- -10^9 <= nums[i] <= 10^9
- The resulting sum fits within the signed 64‑bit integer range.
Optimal Approach & Strategy
The optimal solution iterates once over the array, maintaining a running 64‑bit total that is updated with each element. This yields O(n) time and O(1) auxiliary space.
Brute Force Approach
A naive method would use a nested loop to add each element to every other element, effectively recomputing partial sums many times. This results in O(n²) time, which is impractical for large arrays.
Verified Code Solutions
// Read input from stdin
const fs = require('fs');
const input = fs.readFileSync(0, 'utf8').trim();
if (input.length === 0) process.exit(0);
const tokens = input.split(/\s+/);
let sum = 0n;
for (const t of tokens) {
sum += BigInt(t);
}
console.log(sum.toString());#include <bits/stdc++.h>
using namespace std;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
string line;
if (!getline(cin, line)) return 0;
stringstream ss(line);
long long x;
long long sum = 0;
while (ss >> x) {
sum += x;
}
cout << sum << "\n";
return 0;
}
import java.io.*;
import java.util.*;
public class Main {
public static void main(String[] args) throws IOException {
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
String line = br.readLine();
if (line == null || line.isEmpty()) {
return;
}
String[] parts = line.trim().split("\\s+");
long sum = 0L;
for (String p : parts) {
sum += Long.parseLong(p);
}
System.out.println(sum);
}
}
import sys
def main():
data = sys.stdin.read().strip()
if not data:
return
nums = map(int, data.split())
total = sum(nums)
print(total)
if __name__ == "__main__":
main()
// Read input from stdin
const fs = require('fs');
const input = fs.readFileSync(0, 'utf8').trim();
if (input.length === 0) process.exit(0);
const tokens = input.split(/\s+/);
let sum = 0n;
for (const t of tokens) {
sum += BigInt(t);
}
console.log(sum.toString());
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