Neutralizing Elements in a Sorted Sequence

🎯 Level: Easy ⭐ Score: 30 ⏱️ Estimated Time: 30 mins
📜 Problem Description

You are a Quality Assurance Engineer at a cutting-edge pharmaceutical company, "Zoblik International". Your team is developing a new class of compounds, and a critical stability check involves analyzing the 'reactivity indices' of components within a batch. For a batch to be considered stable and proceed to further testing, there must exist at least two distinct components whose reactivity indices sum up to exactly zero. These indices can be positive, negative, or zero.

You are given a list of reactivity indices for a batch of components. This list is always provided in sorted non-decreasing order. Your task is to quickly determine if any pair of components within this sorted list has reactivity indices that perfectly neutralize each other (i.e., their sum is zero).

If such a pair exists, report "true". Otherwise, report "false".

Input Format

The first line contains an integer 'T' denoting the number of test cases.

For each test case:

  • The first line contains an integer 'n' denoting the number of components (length of the array).
  • The second line contains 'n' space-separated integers, Ai, representing the sorted reactivity indices of the components in the batch.

Output Format

For each test case, output "true" if a neutralizing pair exists, and "false" otherwise. Each output should be on a new line.

Constraints

  • 1 <= T <= 100
  • 2 <= n <= 104
  • -107 <= Ai <= 107
  • The input array A will always be sorted in non-decreasing order.
📌 Constraints
1 <= T <= 100; 2 <= n <= 10^4; -10^7<= Ai<= 10^7
📝 Sample Input/Output
Sample Input 1:
2
4
-3 1 3 4
4
-2 1 3 4
Expected Output 1:
true
false
Explanation for Sample Input 1:
Test Case 1:
Input array: [-3, 1, 3, 4]
We are looking for two numbers that sum to zero.
  • Start with pointers at the beginning (-3) and end (4). Sum = -3 + 4 = 1. Since 1 > 0, we need a smaller sum. Move the right pointer left.
  • Pointers are now at -3 and 3. Sum = -3 + 3 = 0.
  • Since the sum is 0, a neutralizing pair is found! The output is "true".
Test Case 2:
Input array: [-2, 1, 3, 4]
We are looking for two numbers that sum to zero.
  • Start with pointers at the beginning (-2) and end (4). Sum = -2 + 4 = 2. Since 2 > 0, move the right pointer left.
  • Pointers are now at -2 and 3. Sum = -2 + 3 = 1. Since 1 > 0, move the right pointer left.
  • Pointers are now at -2 and 1. Sum = -2 + 1 = -1. Since -1 < 0, we need a larger sum. Move the left pointer right.
  • The left pointer (at -2) would move to 1. Now left and right pointers would both be at index 1 (value 1). Since left < right condition fails, the loop terminates.
  • No pair was found that sums to zero. The output is "false".
💡 Hints
  • 💡 Since the input array is sorted, consider using a two-pointer approach to efficiently search for the pair.
  • 💡 Initialize one pointer at the beginning of the array (left) and another at the end (right). Adjust their positions based on whether their current sum is greater than, less than, or equal to zero.
  • 💡 Pay attention to edge cases such as arrays with only two elements, all positive numbers, all negative numbers, or arrays containing zeros. Remember that the problem requires two *distinct* components, meaning the pointers must not point to the same index (i.e., `left < right`).
📚 Topics

Two Pointers

😕 No submissions found

Start coding and your submissions will appear here.