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Maximum adjacent difference in an array in its sorted form
• Difficulty Level : Hard
• Last Updated : 20 Jan, 2021

Given an array, find the maximum difference between its two consecutive elements in its sorted form.
Examples:

```Input: arr[] = {1, 10, 5}
Output: 5
Sorted array would be {1, 5, 10} and
maximum adjacent difference would be
10 - 5 = 5

Input: arr[] = {2, 4, 8, 11}
Output: 4```

Naive Solution:

First sort the array, then traverse it and keep track of the maximum difference between adjacent elements.
The time complexity of this method is O(nlogn).

Efficient Solution:
This solution is based on the idea of Pigeonhole sorting. No need to sort the array, just have to fill the buckets and keep track of the maximum and minimum value of each bucket. If found an empty bucket, The maximum gap would be the difference of maximum value in the previous bucket – minimum value in the next bucket.
Below is the code for the above approach:

C++

 `// CPP program to find maximum adjacent difference``// between two adjacent after sorting.``#include ``using` `namespace` `std;` `int` `maxSortedAdjacentDiff(``int``* arr, ``int` `n)``{``    ``// Find maximum and minimum in arr[]``    ``int` `maxVal = arr[0], minVal = arr[0];``    ``for` `(``int` `i = 1; i < n; i++) {``        ``maxVal = max(maxVal, arr[i]);``        ``minVal = min(minVal, arr[i]);``    ``}` `    ``// Arrays to store maximum and minimum values``    ``// in n-1 buckets of differences.``    ``int` `maxBucket[n - 1];``    ``int` `minBucket[n - 1];``    ``fill_n(maxBucket, n - 1, INT_MIN);``    ``fill_n(minBucket, n - 1, INT_MAX);` `    ``// Expected gap for every bucket.``    ``float` `delta = (``float``)(maxVal - minVal) / (``float``)(n - 1);` `    ``// Traversing through array elements and``    ``// filling in appropriate bucket if bucket``    ``// is empty. Else updating bucket values.``    ``for` `(``int` `i = 0; i < n; i++) {``        ``if` `(arr[i] == maxVal || arr[i] == minVal)``            ``continue``;` `        ``// Finding index of bucket.``        ``int` `index = (``float``)(``floor``(arr[i] - minVal) / delta);` `        ``// Filling/Updating maximum value of bucket``        ``if` `(maxBucket[index] == INT_MIN)``            ``maxBucket[index] = arr[i];``        ``else``            ``maxBucket[index]``                ``= max(maxBucket[index], arr[i]);` `        ``// Filling/Updating minimum value of bucket``        ``if` `(minBucket[index] == INT_MAX)``            ``minBucket[index] = arr[i];``        ``else``            ``minBucket[index]``                ``= min(minBucket[index], arr[i]);``    ``}` `    ``// Finding maximum difference between maximum value``    ``// of previous bucket minus minimum of current bucket.``    ``int` `prev_val = minVal;``    ``int` `max_gap = 0;``    ``for` `(``int` `i = 0; i < n - 1; i++) {``        ``if` `(minBucket[i] == INT_MAX)``            ``continue``;``        ``max_gap = max(max_gap, minBucket[i] - prev_val);``        ``prev_val = maxBucket[i];``    ``}``    ``max_gap = max(max_gap, maxVal - prev_val);` `    ``return` `max_gap;``}` `int` `main()``{``    ``int` `arr[] = { 1, 10, 5 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);``    ``cout << maxSortedAdjacentDiff(arr, n) << endl;``    ``return` `0;``}`

Java

 `// Java program for the above approach``import` `java.util.Arrays;` `// Java program to find maximum adjacent difference``// between two adjacent after sorting.``class` `GFG {` `    ``static` `int` `maxSortedAdjacentDiff(``int``[] arr, ``int` `n)``    ``{``        ``// Find maximum and minimum in arr[]``        ``int` `maxVal = arr[``0``];``        ``int` `minVal = arr[``0``];``        ``for` `(``int` `i = ``1``; i < n; i++) {``            ``maxVal = Math.max(maxVal, arr[i]);``            ``minVal = Math.min(minVal, arr[i]);``        ``}` `        ``// Arrays to store maximum and minimum values``        ``// in n-1 buckets of differences.``        ``int` `maxBucket[] = ``new` `int``[n - ``1``];``        ``int` `minBucket[] = ``new` `int``[n - ``1``];``        ``Arrays.fill(maxBucket, ``0``, n - ``1``, Integer.MIN_VALUE);``        ``Arrays.fill(minBucket, ``0``, n - ``1``, Integer.MAX_VALUE);` `        ``// Expected gap for every bucket.``        ``float` `delta``            ``= (``float``)(maxVal - minVal) / (``float``)(n - ``1``);` `        ``// Traversing through array elements and``        ``// filling in appropriate bucket if bucket``        ``// is empty. Else updating bucket values.``        ``for` `(``int` `i = ``0``; i < n; i++) {``            ``if` `(arr[i] == maxVal || arr[i] == minVal) {``                ``continue``;``            ``}` `            ``// Finding index of bucket.``            ``int` `index = (``int``)(Math.round((arr[i] - minVal)``                                         ``/ delta));` `            ``// Filling/Updating maximum value of bucket``            ``if` `(maxBucket[index] == Integer.MIN_VALUE) {``                ``maxBucket[index] = arr[i];``            ``}``            ``else` `{``                ``maxBucket[index]``                    ``= Math.max(maxBucket[index], arr[i]);``            ``}` `            ``// Filling/Updating minimum value of bucket``            ``if` `(minBucket[index] == Integer.MAX_VALUE) {``                ``minBucket[index] = arr[i];``            ``}``            ``else` `{``                ``minBucket[index]``                    ``= Math.min(minBucket[index], arr[i]);``            ``}``        ``}` `        ``// Finding maximum difference between maximum value``        ``// of previous bucket minus minimum of current``        ``// bucket.``        ``int` `prev_val = minVal;``        ``int` `max_gap = ``0``;``        ``for` `(``int` `i = ``0``; i < n - ``1``; i++) {``            ``if` `(minBucket[i] == Integer.MAX_VALUE) {``                ``continue``;``            ``}``            ``max_gap = Math.max(max_gap,``                               ``minBucket[i] - prev_val);``            ``prev_val = maxBucket[i];``        ``}``        ``max_gap = Math.max(max_gap, maxVal - prev_val);` `        ``return` `max_gap;``    ``}` `    ``// Driver program to run the case``    ``public` `static` `void` `main(String[] args)``    ``{` `        ``int` `arr[] = { ``1``, ``10``, ``5` `};``        ``int` `n = arr.length;``        ``System.out.println(maxSortedAdjacentDiff(arr, n));``    ``}``}`

Python3

 `# Python3 program to find maximum adjacent``# difference between two adjacent after sorting.` `def` `maxSortedAdjacentDiff(arr, n):` `    ``# Find maximum and minimum in arr[]``    ``maxVal, minVal ``=` `arr[``0``], arr[``0``]``    ``for` `i ``in` `range``(``1``, n):``        ``maxVal ``=` `max``(maxVal, arr[i])``        ``minVal ``=` `min``(minVal, arr[i])` `    ``# Arrays to store maximum and minimum``    ``# values in n-1 buckets of differences.``    ``maxBucket ``=` `[INT_MIN] ``*` `(n ``-` `1``)``    ``minBucket ``=` `[INT_MAX] ``*` `(n ``-` `1``)``    ` `    ``# Expected gap for every bucket.``    ``delta ``=` `(maxVal ``-` `minVal) ``/``/` `(n ``-` `1``)` `    ``# Traversing through array elements and``    ``# filling in appropriate bucket if bucket``    ``# is empty. Else updating bucket values.``    ``for` `i ``in` `range``(``0``, n):``        ``if` `arr[i] ``=``=` `maxVal ``or` `arr[i] ``=``=` `minVal:``            ``continue` `        ``# Finding index of bucket.``        ``index ``=` `(arr[i] ``-` `minVal) ``/``/` `delta` `        ``# Filling/Updating maximum value``        ``# of bucket``        ``if` `maxBucket[index] ``=``=` `INT_MIN:``            ``maxBucket[index] ``=` `arr[i]``        ``else``:``            ``maxBucket[index] ``=` `max``(maxBucket[index],``                                             ``arr[i])` `        ``# Filling/Updating minimum value of bucket``        ``if` `minBucket[index] ``=``=` `INT_MAX:``            ``minBucket[index] ``=` `arr[i]``        ``else``:``            ``minBucket[index] ``=` `min``(minBucket[index],``                                             ``arr[i])``    ` `    ``# Finding maximum difference between ``    ``# maximum value of previous bucket``    ``# minus minimum of current bucket.``    ``prev_val, max_gap ``=` `minVal, ``0``    ` `    ``for` `i ``in` `range``(``0``, n ``-` `1``):``        ``if` `minBucket[i] ``=``=` `INT_MAX:``            ``continue``            ` `        ``max_gap ``=` `max``(max_gap,``                      ``minBucket[i] ``-` `prev_val)``        ``prev_val ``=` `maxBucket[i]``    ` `    ``max_gap ``=` `max``(max_gap, maxVal ``-` `prev_val)` `    ``return` `max_gap` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:` `    ``arr ``=` `[``1``, ``10``, ``5``]``    ``n ``=` `len``(arr)``    ``INT_MIN, INT_MAX ``=` `float``(``'-inf'``), ``float``(``'inf'``)``    ` `    ``print``(maxSortedAdjacentDiff(arr, n))` `# This code is contributed by Rituraj Jain`

C#

 `// C# program to find maximum``// adjacent difference between``// two adjacent after sorting.``using` `System;``using` `System.Linq;` `class` `GFG``{``static` `int` `maxSortedAdjacentDiff(``int``[] arr,    ``                                 ``int` `n)``{``    ``// Find maximum and minimum in arr[]``    ``int` `maxVal = arr[0];``    ``int` `minVal = arr[0];``    ``for` `(``int` `i = 1; i < n; i++)``    ``{``        ``maxVal = Math.Max(maxVal, arr[i]);``        ``minVal = Math.Min(minVal, arr[i]);``    ``}` `    ``// Arrays to store maximum and``    ``// minimum values in n-1 buckets``    ``// of differences.``    ``int` `[]maxBucket = ``new` `int``[n - 1];``    ``int` `[]minBucket = ``new` `int``[n - 1];``    ``maxBucket = maxBucket.Select(i => ``int``.MinValue).ToArray();``    ``minBucket = minBucket.Select(i => ``int``.MaxValue).ToArray();``    ` `    ``// maxBucket.Fill(int.MinValue);``    ``// Arrays.fill(minBucket, 0, n - 1, Integer.MAX_VALUE);` `    ``// Expected gap for every bucket.``    ``float` `delta = (``float``) (maxVal - minVal) /``                  ``(``float``) (n - 1);` `    ``// Traversing through array elements and``    ``// filling in appropriate bucket if bucket``    ``// is empty. Else updating bucket values.``    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``if` `(arr[i] == maxVal || arr[i] == minVal)``        ``{``            ``continue``;``        ``}` `        ``// Finding index of bucket.``        ``int` `index = (``int``) (Math.Round((arr[i] -``                             ``minVal) / delta));` `        ``// Filling/Updating maximum value of bucket``        ``if` `(maxBucket[index] == ``int``.MinValue)``        ``{``            ``maxBucket[index] = arr[i];``        ``}``        ``else``        ``{``            ``maxBucket[index] = Math.Max(maxBucket[index],``                                                  ``arr[i]);``        ``}` `        ``// Filling/Updating minimum value of bucket``        ``if` `(minBucket[index] == ``int``.MaxValue)``        ``{``            ``minBucket[index] = arr[i];``        ``}``        ``else``        ``{``            ``minBucket[index] = Math.Min(minBucket[index],``                                                  ``arr[i]);``        ``}``    ``}` `    ``// Finding maximum difference between``    ``// maximum value of previous bucket``    ``// minus minimum of current bucket.``    ``int` `prev_val = minVal;``    ``int` `max_gap = 0;``    ``for` `(``int` `i = 0; i < n - 1; i++)``    ``{``        ``if` `(minBucket[i] == ``int``.MaxValue)``        ``{``            ``continue``;``        ``}``        ``max_gap = Math.Max(max_gap, minBucket[i] -``                                    ``prev_val);``        ``prev_val = maxBucket[i];``    ``}``    ``max_gap = Math.Max(max_gap, maxVal -``                                ``prev_val);` `    ``return` `max_gap;``}` `// Driver Code``public` `static` `void` `Main()``{``    ``int` `[]arr = {1, 10, 5};``    ``int` `n = arr.Length;``    ``Console.Write(maxSortedAdjacentDiff(arr, n));``}``}` `// This code contributed by 29AjayKumar`
Output:
`5`

Time complexity: O(n)
Auxiliary Space: O(n)

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