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

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: 4
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: 0

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

Consider only those non-missing elements that are adjacent to at least one missing element.
Find the maximum element and the minimum element among them.
We need to find a value that minimizes the maximum absolute difference between the common value and these values.
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 <bits/stdc++.h> 
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 

Output:

Time complexity: O(N)

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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

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