Minimum Difference Between Highest And Lowest Of K Scores Leetcode [Python]

Welcome to another coding session!

Today, we'll tackle the Minimum Difference Between Highest And Lowest Of K Scores problem, which is an easy one from LeetCode's contest.

We'll provide you with a clear Python solution and dive into the reasoning behind our approach.

Problem Overview

You are given an array nums, where nums[i] represents the score of the ith student.

Additionally, you're given an integer k.

The task is to pick the scores of any k students from the array in such a way that the difference between the highest and lowest of these k scores is minimized.

Your goal is to return the minimum possible difference.

Example 1:

Input: nums = [90], k = 1
Output: 0

Explanation: There is only one way to pick a score of one student, which is [90].

The difference between the highest and lowest score is 90 - 90 = 0.

So, the minimum possible difference is 0. Example 2:

Input: nums = [9, 4, 1, 7], k = 2
Output: 2

Explanation: There are multiple ways to pick scores for two students.

Let's consider them:
– [9, 4]: The difference between the highest and lowest score is 9 - 4 = 5.
– [9, 1]: The difference between the highest and lowest score is 9 - 1 = 8.
– [4, 1]: The difference between the highest and lowest score is 4 - 1 = 3.
– [7, 4]: The difference between the highest and lowest score is 7 - 4 = 3.
– [4, 1]: The difference between the highest and lowest score is 7 - 4 = 3.
– [9, 1]: The difference between the highest and lowest score is 7 - 1 = 6.

The minimum possible difference is 2.

Constraints:

• 1 <= k <= nums.length <= 1000
• 0 <= nums[i] <= 105

Now, let's break down our Python solution.

Efficient Python Code Solution

def minimumDifference(self, nums: List[int], k: int) -> int:
    nums.sort()
    l, r = 0, k - 1
    res = float("inf")

    while r < len(nums):
        res = min(res, nums[r] - nums[l])
        l, r = l + 1, r + 1
    return res

Our solution begins by sorting the input array nums.

Sorting the array is the key to solving this problem efficiently.

Once the array is sorted, we set up a sliding window of size k.

The sliding window technique uses two pointers, l (left) and r (right).

We initialize l to 0 and r to k - 1, ensuring the window size is k.

We also initialize a variable res to positive infinity (float("inf")).

This variable will store the minimum difference we are seeking.

The main part of the algorithm is a loop that continues as long as the right pointer (r) is within the bounds of the array.

Inside the loop, we calculate the difference between the elements at the right and left pointers, which are currently within our sliding window.

We update res with the minimum of its current value and this newly calculated difference.

After that, we increment both l and r by 1 to slide the window to the right and consider the next set of elements.

The loop continues until r goes out of bounds, and we are left with the minimum possible difference stored in res.

This value is then returned as the result.

Time and Space Complexity

Let's analyze the time and space complexity of our solution:

• Time Complexity: The most time-consuming operation is sorting the input array, which has a time complexity of O(n log n).

The sliding window technique itself is linear, so it doesn't dominate the time complexity.

Thus, the overall time complexity is O(n log n), where n is the length of the input array.

• Space Complexity: We use a constant amount of extra space for variables like l, r, and res, so the space complexity is O(1).

Reasoning Behind Our Approach

The key insight for this problem is that sorting the array allows us to easily find the minimum possible difference between the highest and lowest scores.

When the array is sorted, the closest scores are adjacent to each other, making it efficient to pick the smallest difference.

We employ the sliding window technique to maintain a window of size k as we iterate through the sorted array.

This ensures that we consider all possible combinations of k scores and calculate their differences.

By keeping track of the minimum difference, we can efficiently find the answer.

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Conclusion

In this blog post, we've tackled the Minimum Difference Between Highest And Lowest Of K Scores problem from LeetCode.

We provided an efficient Python solution that leverages sorting and the sliding window technique to find the minimum possible difference between scores.

Sorting the array allows us to consider adjacent scores, making the process straightforward.

Remember, understanding the problem and choosing the right approach is key to successful problem-solving.

We hope this guide has been helpful for your coding journey.

If you have any questions, suggestions, or comments, please feel free to share them.

Happy coding!

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