Hex.*

LC1200MinimumAbsoluteDifference

Posted on In
Leetcode: 148/2658 (59+70+19)

Description

Given an array of distinct integers arr, find all pairs of elements with the minimum absolute difference of any two elements.
Return a list of pairs in ascending order(with respect to pairs), each pair [a, b] follows

  • a, b are from arr
  • a < b
  • b - a equals to the minimum absolute difference of any two elements in arr

Example 1:
Input: arr = [4,2,1,3]
Output: [[1,2],[2,3],[3,4]]
Explanation: The minimum absolute difference is 1. List all pairs with difference equal to 1 in ascending order.

Example 2:
Input: arr = [1,3,6,10,15]
Output: [[1,3]]

Example 3:
Input: arr = [3,8,-10,23,19,-4,-14,27]
Output: [[-14,-10],[19,23],[23,27]]

Constraints:
2 <= arr.length <= 105
-106 <= arr[i] <= 106

Solution

The smallest difference must exist in the difference between two adjacent numbers after sorting

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# O(nlogn) time | O(n) space
class Solution:
    def minimumAbsDifference(self, arr: List[int]) -> List[List[int]]:
        diff = {}
        arr.sort()

        for i in range(1, len(arr)):
            gap = arr[i] - arr[i-1]
            if gap not in diff:
                diff[gap] = [[arr[i-1], arr[i]]]
            else:
                diff[gap].append([arr[i-1], arr[i]])
        minKey = float('inf')
        ans = []
        for key, val in diff.items():
            if key < minKey:
                minKey= key
                ans = val
        return ans

Optimize space complexity

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# O(nlogn) time | O(1) space
class Solution:
    def minimumAbsDifference(self, arr: List[int]) -> List[List[int]]:
        arr.sort()
        minDiff = arr[1] - arr[0]
        ans = [[arr[0], arr[1]]]

        if len(arr) >2:
            for i in range(2, len(arr)):
                diff = arr[i] - arr[i-1]
                if diff < minDiff:
                    minDiff = diff
                    ans = [[arr[i-1], arr[i]]]
                elif diff == minDiff:
                    ans.append([arr[i-1], arr[i]])
        return ans

#Runtime: 335 ms, faster than 99.47% of Python3 online submissions for Minimum Absolute Difference.
#Memory Usage: 28.8 MB, less than 83.82% of Python3 online submissions for Minimum Absolute Difference.