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 4Input: arr = {4, -1}
Output: 0
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; } |
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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 |
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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 |
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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 |
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Output:
4
Time complexity: O(N)
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