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# Smallest number that can replace all -1s in an array such that maximum absolute difference between any pair of adjacent elements is minimum

• Last Updated : 08 Jul, 2021

Given an array arr[] consisting of N positive integers and some elements as -1, the task is to find the smallest number, say K, such that replacing all -1s in the array by K minimizes the maximum absolute difference between any pair of adjacent elements.

Examples:

Input: arr[] = {-1, 10, -1, 12, -1}
Output: 11
Explanation:
Consider the value of K as 11. Now, replacing all array elements having value -1 to the value K(= 11) modifies the array to {11, 10, 11, 12, 11}. The maximum absolute difference among all the adjacent element is 1, which is minimum among all possible value of K.

Input: arr[] = {1, -1, 3, -1}
Output: 2

Naive Approach: The simplest approach to solve the given problem by iterating over all possible values of K from 1 check one by one which value of K gives the minimized maximum absolute difference between any two adjacent elements and print that value K

Time Complexity: O(N*K)
Auxiliary Space: O(1)

Efficient Approach: The above approach can also be optimized based on the following observations:

• If the absolute value of any number, say X is to be minimized from the set of numbers, the average of the minimum and maximum element of the set of is the most optimal value for X that minimizes the absolute value.
• Therefore, the idea is to find the minimum and the maximum value of all the array elements which are adjacent to the element “-1” and print the average of the two number as the resultant value of K.

Follow the steps below to solve the problem:

• Initialize two variables, say maxE as INT_MIN and minE as INT_MAX, to store the maximum and the minimum element among all possible values that are adjacent to “-1” in the array.
• Traverse the given array and perform the following steps:
• If the current element arr[i] is “-1” and the next element is not “-1”, then update the value of maxE to the maximum of maxE and arr[i + 1] and minE to the minimum of minE and arr[i + 1].
• If the current element arr[i] is not “-1” and the next element is “-1”, then update the value of maxE to the maximum of maxE and arr[i] and minE to the minimum of minE and arr[i].
• After completing the above steps, if the value of maxE and minE is unchanged then all array elements are “-1”, therefore, print 0 as the resultant value of K. Otherwise, print the average of minE and maxE as the resultant value of K.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ``using` `namespace` `std;` `// Function to find the value of K to``// minimize the value of maximum absolute``// difference between adjacent elements``void` `findMissingValue(``int` `arr[], ``int` `N)``{` `    ``// Stores the maximum and minimum``    ``// among array elements that are``    ``// adjacent to "-1"``    ``int` `minE = INT_MAX, maxE = INT_MIN;` `    ``// Traverse the given array arr[]``    ``for` `(``int` `i = 0; i < N - 1; i++) {` `        ``// If arr[i] is -1 & arr[i + 1]``        ``// is not -1``        ``if` `(arr[i] == -1``            ``&& arr[i + 1] != -1) {``            ``minE = min(minE, arr[i + 1]);``            ``maxE = max(maxE, arr[i + 1]);``        ``}` `        ``// If arr[i + 1] is -1 & arr[i]``        ``// is not -1``        ``if` `(arr[i] != -1``            ``&& arr[i + 1] == -1) {``            ``minE = min(minE, arr[i]);``            ``maxE = max(maxE, arr[i]);``        ``}``    ``}` `    ``// If all array element is -1``    ``if` `(minE == INT_MAX``        ``and maxE == INT_MIN) {``        ``cout << ``"0"``;``    ``}` `    ``// Otherwise``    ``else` `{``        ``cout << (minE + maxE) / 2;``    ``}``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 1, -1, -1, -1, 5 };``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);``    ``findMissingValue(arr, N);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.io.*;` `class` `GFG{``    ` `// Function to find the value of K to``// minimize the value of maximum absolute``// difference between adjacent elements``public` `static` `void` `findMissingValue(``int` `arr[], ``int` `N)``{``    ` `    ``// Stores the maximum and minimum``    ``// among array elements that are``    ``// adjacent to "-1"``    ``int` `minE = Integer.MAX_VALUE,``        ``maxE = Integer.MIN_VALUE;` `    ``// Traverse the given array arr[]``    ``for``(``int` `i = ``0``; i < N - ``1``; i++)``    ``{``        ` `        ``// If arr[i] is -1 & arr[i + 1]``        ``// is not -1``        ``if` `(arr[i] == -``1` `&& arr[i + ``1``] != -``1``)``        ``{``            ``minE = Math.min(minE, arr[i + ``1``]);``            ``maxE = Math.max(maxE, arr[i + ``1``]);``        ``}` `        ``// If arr[i + 1] is -1 & arr[i]``        ``// is not -1``        ``if` `(arr[i] != -``1` `&& arr[i + ``1``] == -``1``)``        ``{``            ``minE = Math.min(minE, arr[i]);``            ``maxE = Math.max(maxE, arr[i]);``        ``}``    ``}` `    ``// If all array element is -1``    ``if` `(minE == Integer.MAX_VALUE &&``        ``maxE == Integer.MIN_VALUE)``    ``{``        ``System.out.println(``"0"``);``    ``}` `    ``// Otherwise``    ``else``    ``{``        ``System.out.println((minE + maxE) / ``2``);``    ``}``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``1``, -``1``, -``1``, -``1``, ``5` `};``    ``int` `N = arr.length;``    ` `    ``findMissingValue(arr, N);``}``}` `// This code is contributed by Potta Lokesh`

## Python3

 `# Python 3 program for the above approach``import` `sys` `# Function to find the value of K to``# minimize the value of maximum absolute``# difference between adjacent elements``def` `findMissingValue(arr, N):``  ` `    ``# Stores the maximum and minimum``    ``# among array elements that are``    ``# adjacent to "-1"``    ``minE ``=` `sys.maxsize``    ``maxE ``=` `-``sys.maxsize ``-` `1` `    ``# Traverse the given array arr[]``    ``for` `i ``in` `range``(N ``-` `1``):``      ` `        ``# If arr[i] is -1 & arr[i + 1]``        ``# is not -1``        ``if` `(arr[i] ``=``=` `-``1` `and` `arr[i ``+` `1``] !``=` `-``1``):``            ``minE ``=` `min``(minE, arr[i ``+` `1``])``            ``maxE ``=` `max``(maxE, arr[i ``+` `1``])` `        ``# If arr[i + 1] is -1 & arr[i]``        ``# is not -1``        ``if` `(arr[i] !``=` `-``1` `and` `arr[i ``+` `1``] ``=``=` `-``1``):``            ``minE ``=` `min``(minE, arr[i])``            ``maxE ``=` `max``(maxE, arr[i])` `    ``# If all array element is -1``    ``if` `(minE ``=``=` `sys.maxsize ``and` `maxE ``=``=` `-``sys.maxsize``-``1``):``        ``print``(``"0"``)` `    ``# Otherwise``    ``else``:``        ``print``((minE ``+` `maxE) ``/``/` `2``)` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ``arr ``=` `[``1``, ``-``1``, ``-``1``, ``-``1``, ``5``]``    ``N ``=` `len``(arr)``    ``findMissingValue(arr, N)``    ` `    ``# This code is contributed by SURENDRA_GANGWAR.`

## C#

 `// C# program for the above approach``using` `System;` `class` `GFG{` `// Function to find the value of K to``// minimize the value of maximum absolute``// difference between adjacent elements``public` `static` `void` `findMissingValue(``int``[] arr, ``int` `N)``{``    ` `    ``// Stores the maximum and minimum``    ``// among array elements that are``    ``// adjacent to "-1"``    ``int` `minE = Int32.MaxValue,``        ``maxE = Int32.MinValue;` `    ``// Traverse the given array arr[]``    ``for``(``int` `i = 0; i < N - 1; i++)``    ``{``        ` `        ``// If arr[i] is -1 & arr[i + 1]``        ``// is not -1``        ``if` `(arr[i] == -1 && arr[i + 1] != -1)``        ``{``            ``minE = Math.Min(minE, arr[i + 1]);``            ``maxE = Math.Max(maxE, arr[i + 1]);``        ``}` `        ``// If arr[i + 1] is -1 & arr[i]``        ``// is not -1``        ``if` `(arr[i] != -1 && arr[i + 1] == -1)``        ``{``            ``minE = Math.Min(minE, arr[i]);``            ``maxE = Math.Max(maxE, arr[i]);``        ``}``    ``}` `    ``// If all array element is -1``    ``if` `(minE == Int32.MaxValue &&``        ``maxE == Int32.MinValue)``    ``{``        ``Console.WriteLine(``"0"``);``    ``}` `    ``// Otherwise``    ``else``    ``{``        ``Console.WriteLine((minE + maxE) / 2);``    ``}``}` `// Driver Code``public` `static` `void` `Main()``{``    ``int``[] arr = { 1, -1, -1, -1, 5 };``    ``int` `N = arr.Length;` `    ``findMissingValue(arr, N);``}``}` `// This code is contributed by rishavmahato348`

## Javascript

 ``
Output:
`3`

Time Complexity: O(N)
Auxiliary Space: O(1)

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