Reverse Pairs

JCSU Unit 1 Problem Set 2 (Click for link to problem statements)

Problem Highlights

• 💡 Difficulty: Easy
• ⏰ Time to complete: 15 mins
• 🛠️ Topics: Array Manipulation, Reordering

1: U-nderstand

Understand what the interviewer is asking for by using test cases and questions about the problem.

• Established a set (2-3) of test cases to verify their own solution later.
• Established a set (1-2) of edge cases to verify their solution handles complexities.
• Have fully understood the problem and have no clarifying questions.
• Have you verified any Time/Space Constraints for this problem?

• What is the goal of the problem?
  • The goal is to reorder a list of 2n elements where the first half contains xi elements and the second half contains yi elements, such that the result alternates as [y1, x1, y2, x2, ..., yn, xn].
• What are the constraints on input?
  • The input will always contain an even number of elements.

HAPPY CASE Input: pairs = [1, 2, 3, 4, 5, 6] Output: [2, 1, 4, 3, 6, 5] Explanation: The pairs are reversed as [2, 1], [4, 3], [6, 5].

EDGE CASE Input: pairs = [] Output: [] Explanation: An empty list results in an empty output.

2: M-atch

Match what this problem looks like to known categories of problems, e.g. Linked List or Dynamic Programming, and strategies or patterns in those categories.

For array reordering problems, we want to consider the following approaches:

• Iterative Traversal: Use two pointers or indices to traverse both halves of the array and construct the result by appending elements alternately.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea:
Split the array into two halves. Iterate through both halves simultaneously, appending elements from the second half followed by the first half into a new list.

Steps:

1. Determine the midpoint n of the list, which is len(pairs) // 2.
2. Initialize an empty list result.
3. Iterate through indices i from 0 to n - 1:
   • Append the i-th element from the second half of pairs to result.
   • Append the i-th element from the first half of pairs to result.
4. Return the result.

4: I-mplement

Implement the code to solve the algorithm.

def reverse_pairs(pairs):
    n = len(pairs) // 2  # Determine the number of pairs (half the list length)
    result = []
    for i in range(n):
        result.append(pairs[n + i])  # Add the 'yi' element from the second half
        result.append(pairs[i])     # Add the corresponding 'xi' element from the first half
    return result  # Return the reordered list with reversed pairs

5: R-eview

Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.

Example 1:

• Input: pairs = [1, 2, 3, 4, 5, 6]
• Expected Output: [2, 1, 4, 3, 6, 5]
• Observed Output: [2, 1, 4, 3, 6, 5]

Example 2:

• Input: pairs = ['Batman', 'Robin', 'The Joker', 'Harley Quinn']
• Expected Output: ['Robin', 'Batman', 'Harley Quinn', 'The Joker']
• Observed Output: ['Robin', 'Batman', 'Harley Quinn', 'The Joker']

6: E-valuate

Evaluate the performance of your algorithm and state any strong/weak or future potential work.

Assume n is half the size of the input list.

• Time Complexity: O(n) because we traverse half the elements of the list.
• Space Complexity: O(n) because we construct a new result list.