1200-minimum-absolute-difference

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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(Python)

class Solution:
    def minimumAbsDifference(self, arr: List[int]) -> List[List[int]]:
        return self.CountingsortedSolution(arr)
        
        
    # Time Complexity: O(n^2)
    # Space COmplexity: O(1)
    def naiveSolution(self, arr: List[int]) -> List[List[int]]:
        n = len(arr)
        result = []
        min_diff = inf
        for i in range(n):
            pair = (i, i)
            for j in range(i+1, n):
                if i == j:
                    continue
                if arr[j]-arr[i] < min_diff:
                    min_diff = arr[j]-arr[i]
        for i in range(n):
            for j in range(i+1, n):
                if i == j:
                    continue
                if arr[j]-arr[i] == min_diff:  
                    result.append((arr[i], arr[j]))
        return result
    
    # Time Complexity: O(n^logn)
    # Space COmplexity: O(1)
    def sortedSolution(self, arr: List[int]) -> List[List[int]]:
        arr.sort()
        result = []
        mindiff = inf
        n = len(arr)
        for i in range(1, n):
            curdiff =  arr[i] - arr[i-1]

            if curdiff < mindiff:
                mindiff = curdiff
                result = [[arr[i-1], arr[i]]]
            elif curdiff == mindiff:
                result.append([arr[i-1], arr[i]])
        return result
    
    # Time Complexity: O(n+M)
    # Space COmplexity: O(M)
    def CountingsortedSolution(self, arr: List[int]) -> List[List[int]]:
        arr = self.countingSort(arr)
        result = []
        mindiff = inf
        n = len(arr)
        for i in range(1, n):
            curdiff =  arr[i] - arr[i-1]
            
            if curdiff < mindiff:
                mindiff = curdiff
                result = [[arr[i-1], arr[i]]]
            elif curdiff == mindiff:
                result.append([arr[i-1], arr[i]])
        return result
    
    def countingSort(self, nums):
        min_, max_ = min(nums), max(nums)
        count = [0] * (max_-min_+1)
        for num in nums:
            count[num-min_] += 1
        result = []
        for i, c in enumerate(count):
            result.extend([i+min_]*c)
        return result