algoadvance

You are given a list of scores of different students, scores, where scores[i] represents the score of the i-th student. You are also given an integer k, which represents the number of students to consider. Your task is to pick k scores from the list scores such that the difference between the highest and lowest scores in this subset is minimized. Return the minimum difference.

Example:

Clarifying Questions

  1. Can we assume that k is always a valid integer (1 ≤ k ≤ len(scores))?
    • Yes, you can assume that k is always valid.
  2. Is the list of scores always non-empty?
    • Yes, the list of scores is always non-empty.
  3. Can the scores have duplicate values?
    • Yes, scores can have duplicate values.
  4. How large can the input list scores be?
    • The length of scores can be up to 10^5.

Strategy

The strategy to solve this problem involves sorting the list of scores and then using a sliding window of size k to find the minimum difference between the highest and lowest scores within any subset of k consecutive scores.

  1. Sort the list of scores.
  2. Initialize the minimum difference to a large number (e.g., infinity).
  3. Slide a window of size k over the sorted list:
    • For each window, compute the difference between the highest and lowest scores (i.e., the difference between the first and the last element in the window).
    • Update the minimum difference.

This approach ensures that we efficiently find the minimum possible difference.

Code

from typing import List

def minimumDifference(scores: List[int], k: int) -> int:
    # Step 1: Sort the scores
    scores.sort()
    
    # Step 2: Initialize the minimum difference with a large value
    min_diff = float('inf')
    
    # Step 3: Slide a window of size k
    for i in range(len(scores) - k + 1):
        # Compute the difference between the current window's highest and lowest scores
        current_diff = scores[i + k - 1] - scores[i]
        # Update the minimum difference
        min_diff = min(min_diff, current_diff)
    
    return min_diff

# Example usage:
scores = [90, 100, 78, 89, 67, 85]
k = 3
print(minimumDifference(scores, k))  # Output: 5

Time Complexity

This solution is efficient and should work within the problem constraints.

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