Pair Up Animals for Shelter

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TIP102 Unit 3 Session 1 Advanced (Click for link to problem statements)

U-nderstand

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

• Q: What is the input to the problem?
  • A: The input is a list comfort_levels representing the comfort levels of n animals, where n is an even number.
• Q: What is the output?
  • A: The output is the minimized maximum comfort level after optimally pairing up the animals.
• Q: How do you minimize the maximum comfort level?
  • A: Pair the animals such that the highest possible comfort level among the pairs is as small as possible.

P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Sort the list of comfort levels and use a two-pointer approach to pair the smallest and largest remaining comfort levels. This strategy minimizes the maximum comfort level among all possible pairs.

1. Sort the `comfort_levels` list in ascending order.
2. Initialize two pointers: `left` at the start of the list and `right` at the end of the list.
3. Initialize a variable `max_comfort_level` to keep track of the maximum comfort level encountered during the pairing process.
4. While `left` is less than `right`:
   1. Pair the animal at the `left` pointer with the animal at the `right` pointer.
   2. Calculate the comfort level for this pair and update `max_comfort_level` if this pair's comfort level is higher than the current `max_comfort_level`.
   3. Move the `left` pointer one step to the right and the `right` pointer one step to the left.
5. Return the `max_comfort_level`, which will be the minimized maximum comfort level for the optimal pairing.

⚠️ Common Mistakes

• Forgetting to sort the comfort_levels list before pairing.
• Not updating the max_comfort_level correctly, leading to incorrect results.
• Misplacing the pointers, resulting in incorrect pairings.

I-mplement

def pair_up_animals(comfort_levels):
    # Step 1: Sort the comfort levels
    comfort_levels.sort()
    
    # Step 2: Initialize two pointers
    left = 0
    right = len(comfort_levels) - 1
    
    # Step 3: Initialize a variable to track the maximum pair comfort level
    max_comfort_level = 0
    
    # Step 4: Pair animals using the two-pointer approach
    while left < right:
        pair_comfort_level = comfort_levels[left] + comfort_levels[right]
        # Update the maximum comfort level encountered
        max_comfort_level = max(max_comfort_level, pair_comfort_level)
        # Move the pointers
        left += 1
        right -= 1
    
    # Step 5: Return the minimized maximum comfort level
    return max_comfort_level

# Example usage
print(pair_up_animals([3,5,2,3]))  # Output: 7
print(pair_up_animals([3,5,4,2,4,6]))  # Output: 8