Change K elements so that (a1^2 + a2^2 + …+ aN^2 ) <= (a1 + a2 +…+ aN) becomes true

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Given an array Arr of size N. The task is to tell whether it is possible to change at most K elements of this sequence to arbitrary positive integers in such a way that the below condition holds.

Examples:

Input:N = 2, Arr[] = {1, 2}, K = 2
Output: Possible
(As A[2] can be change to 1)

Input: N = 2, Arr[] = {5, 6}, K = 1
Output: Not Possible
(As we can only change 1 element to any arbitrary number
and after changing it doesn't satisfy above condition)

Approach:

When all the elements of the array becomes equal to 1 then only the given equation can be satisfied, else not.

Traverse the array and count the number of 1.
If K >= (size of array i.e N – count) then return true, Else return false.

Below is the implementation of the above approach:

C++

// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function that will tell
// whether it is possible or Not
int Series(int Arr[], int N, int K)
{
    int count = 0;
    for (int i = 0; i < N; i++)
        if (Arr[i] == 1)
            count++;
 
    if (K >= (N - count))
        return 1;
    else
        return 0;
}
 
// Driver code
int main()
{
    int Arr[] = { 5, 1, 2 };
    int N = sizeof(Arr) / sizeof(Arr[0]);
    int K = 2;
 
    // Calling function.
    int result = Series(Arr, N, K);
 
    if (result == 1)
        cout << "Possible";
    else
        cout << "Not Possible";
    return 0;
}

Java

//Java  implementation of above approach 
 
import java.io.*;
 
class GFG {
     
// Function that will tell 
// whether it is possible or Not 
static int Series(int Arr[], int N, int K) 
{ 
    int count = 0; 
    for (int i = 0; i < N; i++) 
        if (Arr[i] == 1) 
            count++; 
 
    if (K >= (N - count)) 
        return 1; 
    else
        return 0; 
} 
 
// Driver code 
    public static void main (String[] args) {
    int Arr[] = { 5, 1, 2 }; 
    int N = Arr.length; 
    int K = 2; 
    // Calling function. 
    int result = Series(Arr, N, K); 
    if (result == 1) 
            System.out.println ("Possible"); 
    else
            System.out.println( "Not Possible"); 
         
    }
//This Code is Contributed by ajit    
}

Python3

# Python implementation of 
# above approach
 
# Function that will tell
# whether it is possible or Not
def Series(Arr, N, K):
    count = 0
    for i in range(N):
        if Arr[i] == 1:
            count += 1
    if K >= (N - count):
        return 1
    return 0
 
# Driver code
Arr = [5, 1, 2]
N = len(Arr)
K = 2
 
result = Series(Arr, N, K)
if result == 1:
    print("Possible")
else:
    print("Not Possible")
 
# This code is contributed
# by Shrikant13

C#

//C# implementation of above approach
 
using System;
 
public class GFG{
     
         
// Function that will tell 
// whether it is possible or Not 
static int Series(int []Arr, int N, int K) 
{ 
    int count = 0; 
    for (int i = 0; i < N; i++) 
        if (Arr[i] == 1) 
            count++; 
 
    if (K >= (N - count)) 
        return 1; 
    else
        return 0; 
} 
 
// Driver code 
     
    static public void Main (){
    int []Arr = { 5, 1, 2 }; 
    int N = Arr.Length; 
    int K = 2; 
    // Calling function. 
    int result = Series(Arr, N, K); 
    if (result == 1) 
            Console.WriteLine ("Possible"); 
    else
            Console.WriteLine( "Not Possible"); 
         
    } 
//This Code is Contributed by akt_mit
} 

PHP

<?php
// PHP implementation of above approach 
 
// Function that will tell 
// whether it is possible or Not 
function Series($Arr, $N, $K) 
{ 
    $count = 0; 
    for ($i = 0; $i < $N; $i++) 
        if ($Arr[$i] == 1) 
            $count++; 
 
    if ($K >= ($N - $count)) 
        return 1; 
    else
        return 0; 
} 
 
// Driver code 
$Arr = array( 5, 1, 2 ); 
$N = sizeof($Arr); 
$K = 2; 
 
// Calling function. 
$result = Series($Arr, $N, $K); 
 
if ($result == 1) 
    echo "Possible"; 
else
    echo "Not Possible"; 
 
// This code is contributed
// by Sach_Code
?>

Javascript

<script>
 
// Javascript implementation of above approach
 
// Function that will tell
// whether it is possible or Not
function Series(Arr, N, K)
{
    var count = 0;
    for(var i = 0; i < N; i++)
        if (Arr[i] == 1)
            count++;
 
    if (K >= (N - count))
        return 1;
    else
        return 0;
}
 
// Driver code
var Arr = [ 5, 1, 2 ];
var N = Arr.length;
var K = 2;
 
// Calling function.
var result = Series(Arr, N, K);
 
if (result == 1)
    document.write("Possible");
else
    document.write("Not Possible");
     
// This code is contributed by rutvik_56
 
</script>

Output

Possible

Complexity Analysis:

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

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