Rearrange the Array to maximize the elements which is smaller than both its adjacent elements

Given an array arr[] consisting of N distinct integers, the task is to rearrange the array elements such that the count of elements that are smaller than their adjacent elements is maximum. 

Note: The elements left of index 0 and right of index N-1 are considered as -INF.

Examples:

Input: arr[] = {1, 2, 3, 4}
Output: 2 1 3 4
Explanation:
One possible way to rearrange is as {2, 1, 3, 4}. 

1. For arr[0](= 2), is greater than the elements on both sides of it.
2. For arr[1](= 1), is less than the elements on both sides of it.
3. For arr[2](= 3), is less than the elements on its right and greater than the elements on its left.
4. For arr[4](= 1), is greater than the elements on both sides of it.

Therefore, there is a total of 1 array element satisfying the condition in the above arrangement. And it is the maximum possible.

Input: arr[] = {2, 7}
Output: 2 7

Approach: The given problem can be solved based on the following observations:

1. Consider the maximum number of indices that can satisfy the conditions being X.
2. Then, at least (X + 1) larger elements are required to make it possible as each element requires 2 greater elements.
3. Therefore, the maximum number of elements that is smaller than their adjacent is given by (N - 1)/2.

Follow the steps below to solve the problem:

• Initialize an array, say temp[] of size N, that stores the rearranged array.
• Sort the given array arr[] in the increasing order.
• Choose the first (N - 1)/2 elements from the array arr[] and place them at the odd indices in the array temp[].
• Choose the rest of the (N + 1)/2 elements from the array arr[] and place them in the remaining indices in the array temp[].
• Finally, after completing the above steps, print the array temp[] as the resultant array.

Below is the implementation of the above approach:

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to rearrange array such that
// count of element that are smaller than
// their adjacent elements is maximum
void maximumIndices(int arr[], int N)
{
    // Stores the rearranged array
    int temp[N] = { 0 };

    // Stores the maximum count of
    // elements
    int maxIndices = (N - 1) / 2;

    // Sort the given array
    sort(arr, arr + N);

    // Place the smallest (N - 1)/2
    // elements at odd indices
    for (int i = 0; i < maxIndices; i++) {
        temp[2 * i + 1] = arr[i];
    }

    // Placing the rest of the elements
    // at remaining indices
    int j = 0;

    for (int i = maxIndices; i < N;) {

        // If no element of the array
        // has been placed here
        if (temp[j] == 0) {
            temp[j] = arr[i];
            i++;
        }
        j++;
    }

    // Print the resultant array
    for (int i = 0; i < N; i++) {
        cout << temp[i] << " ";
    }
}

// Driver Code
int main()
{
    // Input
    int arr[] = { 1, 2, 3, 4 };
    int N = sizeof(arr) / sizeof(arr[0]);

    // Function call
    maximumIndices(arr, N);

    return 0;
}

// Java program for the above approach
import java.io.*;
import java.util.*;

class GFG {

    // Function to rearrange array such that
    // count of element that are smaller than
    // their adjacent elements is maximum
    public static void maximumIndices(int arr[], int N)
    {
        // Stores the rearranged array
        int[] temp = new int[N];

        // Stores the maximum count of
        // elements
        int maxIndices = (N - 1) / 2;

        // Sort the given array
        Arrays.sort(arr);

        // Place the smallest (N - 1)/2
        // elements at odd indices
        for (int i = 0; i < maxIndices; i++) {
            temp[2 * i + 1] = arr[i];
        }

        // Placing the rest of the elements
        // at remaining indices
        int j = 0;

        for (int i = maxIndices; i < N;) {

            // If no element of the array
            // has been placed here
            if (temp[j] == 0) {
                temp[j] = arr[i];
                i++;
            }
            j++;
        }

        // Print the resultant array
        for (int i = 0; i < N; i++) {
            System.out.print(temp[i] + " ");
        }
    }

    // Driver Code
    public static void main(String[] args)
    {
        // Input
        int arr[] = { 1, 2, 3, 4 };
        int N = 4;

        // Function call
        maximumIndices(arr, N);
    }
}

// This code is contributed by RohitOberoi.

# Python program for the above approach

# Function to rearrange array such that
# count of element that are smaller than
# their adjacent elements is maximum
def maximumIndices(arr, N):
    # Stores the rearranged array
    temp = [0] * N

    # Stores the maximum count of
    # elements
    maxIndices = (N - 1) // 2

    # Sort the given array
    arr.sort()

    # Place the smallest (N - 1)/2
    # elements at odd indices
    for i in range(maxIndices):
        temp[2 * i + 1] = arr[i]

    # Placing the rest of the elements
    # at remaining indices
    j = 0
    i = maxIndices

    while(i < N):

        # If no element of the array
        # has been placed here
        if (temp[j] == 0):
            temp[j] = arr[i]
            i += 1

        j += 1

    # Print the resultant array
    for i in range(N):
        print(temp[i], end=" ")


# Driver Code

# Input
arr = [1, 2, 3, 4]
N = len(arr)

# Function call
maximumIndices(arr, N)

# This code is contributed by gfgking

// C# program for the above approach
using System;

class GFG{

// Function to rearrange array such that
// count of element that are smaller than
// their adjacent elements is maximum
public static void maximumIndices(int []arr, int N)
{
    
    // Stores the rearranged array
    int[] temp = new int[N];

    // Stores the maximum count of
    // elements
    int maxIndices = (N - 1) / 2;

    // Sort the given array
    Array.Sort(arr);

    // Place the smallest (N - 1)/2
    // elements at odd indices
    for(int i = 0; i < maxIndices; i++)
    {
        temp[2 * i + 1] = arr[i];
    }

    // Placing the rest of the elements
    // at remaining indices
    int j = 0;

    for(int i = maxIndices; i < N;) 
    {
        
        // If no element of the array
        // has been placed here
        if (temp[j] == 0) 
        {
            temp[j] = arr[i];
            i++;
        }
        j++;
    }

    // Print the resultant array
    for(int i = 0; i < N; i++) 
    {
        Console.Write(temp[i] + " ");
    }
}

// Driver Code
public static void Main(String[] args)
{
    
    // Input
    int []arr = { 1, 2, 3, 4 };
    int N = 4;

    // Function call
    maximumIndices(arr, N);
}
}

// This code is contributed by shivanisinghss2110

   <script>
   
        // JavaScript program for the above approach


        // Function to rearrange array such that
        // count of element that are smaller than
        // their adjacent elements is maximum
        function maximumIndices(arr, N) {
            // Stores the rearranged array
            let temp = new Array(N).fill(0);

            // Stores the maximum count of
            // elements
            let maxIndices = parseInt((N - 1) / 2);

            // Sort the given array
            arr.sort(function (a, b) { return a - b; })

            // Place the smallest (N - 1)/2
            // elements at odd indices
            for (let i = 0; i < maxIndices; i++) {
                temp[2 * i + 1] = arr[i];
            }

            // Placing the rest of the elements
            // at remaining indices
            let j = 0;

            for (let i = maxIndices; i < N;) {

                // If no element of the array
                // has been placed here
                if (temp[j] == 0) {
                    temp[j] = arr[i];
                    i++;
                }
                j++;
            }

            // Print the resultant array
            for (let i = 0; i < N; i++) {
                document.write(temp[i] + " ");
            }
        }

        // Driver Code

        // Input
        let arr = [1, 2, 3, 4];
        let N = arr.length;

        // Function call
        maximumIndices(arr, N);

    // This code is contributed by Potta Lokesh
    
    </script>

2 1 3 4 

Time  Complexity: O(N*log(N))
Auxiliary Space: O(N)