Maximize the last Array element as per the given conditions

Given an array arr[] consisting of N integers, rearrange the array such that it satisfies the following conditions:

1. arr[0] must be 1.
2. Difference between adjacent array elements should not exceed 1, that is, arr[i] - arr[i-1] ? 1 for all 1 ? i < N.

The permissible operations are as follows:

1. Rearrange the elements in any way.
2. Reduce any element to any number ? 1.

The task is to find the maximum possible value that can be placed at the last index of the array.

Examples:

Input: arr[] = {3, 1, 3, 4} 
Output: 4 
Explanation: 
Subtracting 1 from the first element modifies the array to {2, 1, 3, 4}. 
Swapping the first two elements modifies the array to {1, 2, 3, 4}. 
Therefore, maximum value placed at the last index is 4.
Input: arr[] = {1, 1, 1, 1} 
Output: 1

Approach: 
To solve the given problem, sort the given array and balance it according to the given condition starting from left towards right. Follow the below steps to solve the problem:

• Sort the array in ascending order.
• If the first element is not 1, make it 1.
• Traverse the array over the indices [1, N - 1) and check if every adjacent element has a difference of ? 1.
• If not, decrement the value till the difference becomes ? 1.
• Return the last element of the array.

Below is the implementation of the above problem:

// C++ Program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to find the maximum possible value
// that can be placed at the last index
int maximizeFinalElement(int arr[], int n)
{
    // Sort array in ascending order
    sort(arr, arr + n);

    // If the first element
    // is not equal to 1
    if (arr[0] != 1)
        arr[0] = 1;

    // Traverse the array to make
    // difference between adjacent
    // elements <=1
    for (int i = 1; i < n; i++) {
        if (arr[i] - arr[i - 1] > 1) {
            arr[i] = arr[i - 1] + 1;
        }
    }
    return arr[n - 1];
}

// Driver Code
int main()
{
    int n = 4;
    int arr[] = { 3, 1, 3, 4 };

    int max = maximizeFinalElement(arr, n);
    cout << max;

    return 0;
}

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

class GFG{

// Function to find the maximum possible value
// that can be placed at the last index
public static int maximizeFinalElement(int arr[],
                                       int n)
{
    
    // Sort the array elements
    // in ascending order
    Arrays.sort(arr);

    // If the first element is
    // is not equal to 1
    if (arr[0] != 1)
        arr[0] = 1;

    // Traverse the array to make
    // difference between adjacent
    // elements <=1
    for(int i = 1; i < n; i++) 
    {
        if (arr[i] - arr[i - 1] > 1)
        {
            arr[i] = arr[i - 1] + 1;
        }
    }
    return arr[n - 1];
}

// Driver Code
public static void main (String[] args) 
{ 
    int n = 4; 
    int arr[] = { 3, 1, 3, 4 }; 
  
    int max = maximizeFinalElement(arr, n); 
    System.out.print(max); 
}
}

# Python3 program to implement
# the above approach

# Function to find the maximum possible value
# that can be placed at the last index
def maximizeFinalElement(arr, n):
    
    # Sort the array elements
    # in ascending order
    arr.sort();

    # If the first element is
    # is not equal to 1
    if (arr[0] != 1):
        arr[0] = 1;

    # Traverse the array to make
    # difference between adjacent
    # elements <=1
    for i in range(1, n):
        if (arr[i] - arr[i - 1] > 1):
            arr[i] = arr[i - 1] + 1;

    return arr[n - 1];

# Driver Code
if __name__ == '__main__':
    
    n = 4;
    arr = [3, 1, 3, 4];
    
    max = maximizeFinalElement(arr, n);
    print(max);
    
# This code is contributed by Princi Singh 

// C# Program to implement
// the above approach
using System;
class GFG{

// Function to find the maximum possible value
// that can be placed at the last index
public static int maximizeFinalElement(int []arr,
                                       int n)
{
    // Sort the array elements
    // in ascending order
    Array.Sort(arr);

    // If the first element is
    // is not equal to 1
    if (arr[0] != 1)
        arr[0] = 1;

    // Traverse the array to make
    // difference between adjacent
    // elements <=1
    for (int i = 1; i < n; i++)
    {
        if (arr[i] - arr[i - 1] > 1) 
        {
            arr[i] = arr[i - 1] + 1;
        }
    }

    return arr[n - 1];
}

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

    int max = maximizeFinalElement(arr, n);
    Console.WriteLine(max);
}
}

// This code is contributed by sapnasingh4991

<script>

// JavaScript Program to implement 
// the above approach 

// Function to find the maximum possible value 
// that can be placed at the last index 
function maximizeFinalElement(arr, n) 
{ 
    // Sort array in ascending order 
    arr.sort((a, b) => a - b); 

    // If the first element 
    // is not equal to 1 
    if (arr[0] != 1) 
        arr[0] = 1; 

    // Traverse the array to make 
    // difference between adjacent 
    // elements <=1 
    for (let i = 1; i < n; i++) { 
        if (arr[i] - arr[i - 1] > 1) { 
            arr[i] = arr[i - 1] + 1; 
        } 
    } 
    return arr[n - 1]; 
} 

// Driver Code 

    let n = 4; 
    let arr = [ 3, 1, 3, 4 ]; 

    let max = maximizeFinalElement(arr, n); 
    document.write(max); 


// This code is contributed by Surbhi Tyagi.

</script>

4

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