# Minimum value of maximum absolute difference of all adjacent pairs in an Array

Last Updated : 25 Apr, 2023

Given an array arr, containing non-negative integers and (-1)s, of size N, the task is to replace those (-1)s with a common non-negative integer such that the maximum absolute difference of all adjacent pairs is minimum. Print this minimum possible value of the maximum absolute difference.

Examples:

Input: arr = {-1, -1, 11, -1, 3, -1}
Output:
Replace every -1 element with 7. Now the maximum absolute difference of all adjacent pairs is minimum which is equal to 4

Input: arr = {4, -1}
Output:

Approach:

1. Consider only those non-missing elements that are adjacent to at least one missing element.
2. Find the maximum element and the minimum element among them.
3. We need to find a value that minimizes the maximum absolute difference between the common value and these values.
4. The optimal value is equals to
`(minimum element + maximum element) / 2`

Below is the implementation of the above approach:

## C++

 `// C++ program to find the minimum value` `// of maximum absolute difference of` `// all adjacent pairs in an Array` `#include ` `using` `namespace` `std;`   `// Function to find the minimum possible` `// value of the maximum absolute difference.` `int` `maximumAbsolute(``int` `arr[], ``int` `n)` `{` `    ``// To store minimum and maximum elements` `    ``int` `mn = INT_MAX;` `    ``int` `mx = INT_MIN;`   `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``// If right side element is equals -1` `        ``// and left side is not equals -1` `        ``if` `(i > 0` `            ``&& arr[i] == -1` `            ``&& arr[i - 1] != -1) {` `            ``mn = min(mn, arr[i - 1]);` `            ``mx = max(mx, arr[i - 1]);` `        ``}`   `        ``// If left side element is equals -1` `        ``// and right side is not equals -1` `        ``if` `(i < n - 1` `            ``&& arr[i] == -1` `            ``&& arr[i + 1] != -1) {` `            ``mn = min(mn, arr[i + 1]);` `            ``mx = max(mx, arr[i + 1]);` `        ``}` `    ``}`   `    ``// Calculating the common integer` `    ``// which needs to be replaced with` `    ``int` `common_integer = (mn + mx) / 2;`   `    ``// Replace all -1 elements` `    ``// with the common integer` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``if` `(arr[i] == -1)` `            ``arr[i] = common_integer;` `    ``}`   `    ``int` `max_diff = 0;`   `    ``// Calculating the maximum` `    ``// absolute difference` `    ``for` `(``int` `i = 0; i < n - 1; i++) {` `        ``int` `diff = ``abs``(arr[i] - arr[i + 1]);`   `        ``if` `(diff > max_diff)` `            ``max_diff = diff;` `    ``}`   `    ``// Return the maximum absolute difference` `    ``return` `max_diff;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `arr[] = { -1, -1, 11, -1, 3, -1 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);`   `    ``// Function call` `    ``cout << maximumAbsolute(arr, n);`   `    ``return` `0;` `}`

## Java

 `// Java program to find the minimum value` `// of maximum absolute difference of` `// all adjacent pairs in an Array` `import` `java.util.*;`   `class` `GFG{` ` `  `// Function to find the minimum possible` `// value of the maximum absolute difference.` `static` `int` `maximumAbsolute(``int` `arr[], ``int` `n)` `{` `    ``// To store minimum and maximum elements` `    ``int` `mn = Integer.MAX_VALUE;` `    ``int` `mx = Integer.MIN_VALUE;` ` `  `    ``for` `(``int` `i = ``0``; i < n; i++) {`   `        ``// If right side element is equals -1` `        ``// and left side is not equals -1` `        ``if` `(i > ``0` `            ``&& arr[i] == -``1` `            ``&& arr[i - ``1``] != -``1``) {` `            ``mn = Math.min(mn, arr[i - ``1``]);` `            ``mx = Math.max(mx, arr[i - ``1``]);` `        ``}` ` `  `        ``// If left side element is equals -1` `        ``// and right side is not equals -1` `        ``if` `(i < n - ``1` `            ``&& arr[i] == -``1` `            ``&& arr[i + ``1``] != -``1``) {` `            ``mn = Math.min(mn, arr[i + ``1``]);` `            ``mx = Math.max(mx, arr[i + ``1``]);` `        ``}` `    ``}` ` `  `    ``// Calculating the common integer` `    ``// which needs to be replaced with` `    ``int` `common_integer = (mn + mx) / ``2``;` ` `  `    ``// Replace all -1 elements` `    ``// with the common integer` `    ``for` `(``int` `i = ``0``; i < n; i++) {` `        ``if` `(arr[i] == -``1``)` `            ``arr[i] = common_integer;` `    ``}` ` `  `    ``int` `max_diff = ``0``;` ` `  `    ``// Calculating the maximum` `    ``// absolute difference` `    ``for` `(``int` `i = ``0``; i < n - ``1``; i++) {` `        ``int` `diff = Math.abs(arr[i] - arr[i + ``1``]);` ` `  `        ``if` `(diff > max_diff)` `            ``max_diff = diff;` `    ``}` ` `  `    ``// Return the maximum absolute difference` `    ``return` `max_diff;` `}` ` `  `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    ``int` `arr[] = { -``1``, -``1``, ``11``, -``1``, ``3``, -``1` `};` `    ``int` `n = arr.length;` ` `  `    ``// Function call` `    ``System.out.print(maximumAbsolute(arr, n));` `}` `}`   `// This code is contributed by Rajput-Ji`

## Python3

 `# Python3 program to find the minimum value` `# of maximum absolute difference of` `# all adjacent pairs in an Array`   `# Function to find the minimum possible` `# value of the maximum absolute difference.` `def` `maximumAbsolute(arr, n):`   `    ``# To store minimum and maximum elements` `    ``mn ``=` `10``*``*``9` `    ``mx ``=` `-``10``*``*``9`   `    ``for` `i ``in` `range``(n):` `    `  `        ``# If right side element is equals -1` `        ``# and left side is not equals -1` `        ``if` `(i > ``0` `            ``and` `arr[i] ``=``=` `-``1` `            ``and` `arr[i ``-` `1``] !``=` `-``1``):` `            ``mn ``=` `min``(mn, arr[i ``-` `1``])` `            ``mx ``=` `max``(mx, arr[i ``-` `1``])`   `        ``# If left side element is equals -1` `        ``# and right side is not equals -1` `        ``if` `(i < n ``-` `1` `            ``and` `arr[i] ``=``=` `-``1` `            ``and` `arr[i ``+` `1``] !``=` `-``1``):` `            ``mn ``=` `min``(mn, arr[i ``+` `1``])` `            ``mx ``=` `max``(mx, arr[i ``+` `1``])`   `    ``# Calculating the common integer` `    ``# which needs to be replaced with` `    ``common_integer ``=` `(mn ``+` `mx) ``/``/` `2`   `    ``# Replace all -1 elements` `    ``# with the common integer` `    ``for` `i ``in` `range``(n):` `        ``if` `(arr[i] ``=``=` `-``1``):` `            ``arr[i] ``=` `common_integer`   `    ``max_diff ``=` `0`   `    ``# Calculating the maximum` `    ``# absolute difference` `    ``for` `i ``in` `range``(n``-``1``):` `        ``diff ``=` `abs``(arr[i] ``-` `arr[i ``+` `1``])`   `        ``if` `(diff > max_diff):` `            ``max_diff ``=` `diff`   `    ``# Return the maximum absolute difference` `    ``return` `max_diff`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    ``arr``=``[``-``1``, ``-``1``, ``11``, ``-``1``, ``3``, ``-``1``]` `    ``n ``=` `len``(arr)`   `    ``# Function call` `    ``print``(maximumAbsolute(arr, n))`   `# This code is contributed by mohit kumar 29`

## C#

 `// C# program to find the minimum value` `// of maximum absolute difference of` `// all adjacent pairs in an Array` `using` `System;`   `class` `GFG{` ` `  `    ``// Function to find the minimum possible` `    ``// value of the maximum absolute difference.` `    ``static` `int` `maximumAbsolute(``int` `[]arr, ``int` `n)` `    ``{` `        ``// To store minimum and maximum elements` `        ``int` `mn = ``int``.MaxValue;` `        ``int` `mx = ``int``.MinValue;` `     `  `        ``for` `(``int` `i = 0; i < n; i++) {` `    `  `            ``// If right side element is equals -1` `            ``// and left side is not equals -1` `            ``if` `(i > 0` `                ``&& arr[i] == -1` `                ``&& arr[i - 1] != -1) {` `                ``mn = Math.Min(mn, arr[i - 1]);` `                ``mx = Math.Max(mx, arr[i - 1]);` `            ``}` `     `  `            ``// If left side element is equals -1` `            ``// and right side is not equals -1` `            ``if` `(i < n - 1` `                ``&& arr[i] == -1` `                ``&& arr[i + 1] != -1) {` `                ``mn = Math.Min(mn, arr[i + 1]);` `                ``mx = Math.Max(mx, arr[i + 1]);` `            ``}` `        ``}` `     `  `        ``// Calculating the common integer` `        ``// which needs to be replaced with` `        ``int` `common_integer = (mn + mx) / 2;` `     `  `        ``// Replace all -1 elements` `        ``// with the common integer` `        ``for` `(``int` `i = 0; i < n; i++) {` `            ``if` `(arr[i] == -1)` `                ``arr[i] = common_integer;` `        ``}` `     `  `        ``int` `max_diff = 0;` `     `  `        ``// Calculating the maximum` `        ``// absolute difference` `        ``for` `(``int` `i = 0; i < n - 1; i++) {` `            ``int` `diff = Math.Abs(arr[i] - arr[i + 1]);` `     `  `            ``if` `(diff > max_diff)` `                ``max_diff = diff;` `        ``}` `     `  `        ``// Return the maximum absolute difference` `        ``return` `max_diff;` `    ``}` `     `  `    ``// Driver Code` `    ``public` `static` `void` `Main(``string``[] args)` `    ``{` `        ``int` `[]arr = { -1, -1, 11, -1, 3, -1 };` `        ``int` `n = arr.Length;` `     `  `        ``// Function call` `        ``Console.Write(maximumAbsolute(arr, n));` `    ``}` `}`   `// This code is contributed by Yash_R`

## Javascript

 ``

Output:

`4`

Time complexity: O(N), The time complexity of the given program is O(n), where n is the size of the input array. This is because the program iterates through the input array twice in two separate for-loops, which have a time complexity of O(n) each.

Auxiliary Space: O(1), The space complexity of the given program is O(1), which means it uses a constant amount of memory regardless of the size of the input array. This is because the program does not create any new data structures that depend on the size of the input array. It only uses a fixed number of integer variables to store the minimum, maximum, and common values, as well as the maximum absolute difference.

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