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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:

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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 <bits/stdc++.h>
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[0]);
    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




<script>
 
// JavaScript program for the above approach
 
// Function to find the value of K to
// minimize the value of maximum absolute
// difference between adjacent elements
function findMissingValue(arr, N)
{
     
    // Stores the maximum and minimum
    // among array elements that are
    // adjacent to "-1"
    let minE = Number.MAX_VALUE,
        maxE = Number.MIN_VALUE;
 
    // Traverse the given array arr[]
    for(let 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 == Number.MAX_VALUE &&
        maxE == Number.MIN_VALUE)
    {
        document.write("0");
    }
 
    // Otherwise
    else
    {
        document.write((minE + maxE) / 2);
    }
}
 
// Driver Code
let arr = [ 1, -1, -1, -1, 5 ];
let N = arr.length;
 
findMissingValue(arr, N);
 
// This code is contributed by Potta Lokesh
 
</script>
Output: 
3

 

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




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