Given an array of length N + K. Also given the average avg of all the elements of the array. If an element that appears exactly K time got removed from the array (all the occurrences) and the resultant array is given, the task is to find the element X. Note that if X is not an integer then print -1.
Examples:
Input: arr[] = {2, 7, 3}, K = 3, avg = 4
Output: 4
The original array was {2, 7, 3, 4, 4, 4}
where 4 which occurred thrice was deleted.
(2 + 7 + 3 + 4 + 4 + 4) / 6 = 4Input: arr[] = {5, 2, 3}, K = 4, avg = 7;
Output: -1
The required element is 9.75 which is not an integer.
Approach:
- Find the sum of the array elements and store it in a variable sum.
- Since X appeared K times then the sum of the original array will be sumOrg = sum + (X * K).
- And the average is given to be avg i.e. avg = sumOrg / (N + K).
- Now, X can be easily calculated as X = ((avg * (N + K)) – sum) / K
Below is the implementation of the above approach:
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std;
// Function to return the missing element int findMissing( int arr[], int n, int k, int avg)
{ // Find the sum of the array elements
int sum = 0;
for ( int i = 0; i < n; i++) {
sum += arr[i];
}
// The numerator and the denominator
// of the equation
int num = (avg * (n + k)) - sum;
int den = k;
// If not divisible then X is
// not an integer
// it is a floating point number
if (num % den != 0)
return -1;
// Return X
return (num / den);
} // Driver code int main()
{ int k = 3, avg = 4;
int arr[] = { 2, 7, 3 };
int n = sizeof (arr) / sizeof ( int );
cout << findMissing(arr, n, k, avg);
return 0;
} |
// Java implementation of the approach class GFG
{ // Function to return the missing element
static int findMissing( int arr[], int n,
int k, int avg)
{
// Find the sum of the array elements
int sum = 0 ;
for ( int i = 0 ; i < n; i++)
{
sum += arr[i];
}
// The numerator and the denominator
// of the equation
int num = (avg * (n + k)) - sum;
int den = k;
// If not divisible then X is
// not an integer
// it is a floating point number
if (num % den != 0 )
return - 1 ;
// Return X
return ( int )(num / den);
}
// Driver code
public static void main (String[] args)
{
int k = 3 , avg = 4 ;
int arr[] = { 2 , 7 , 3 };
int n = arr.length;
System.out.println(findMissing(arr, n, k, avg));
}
} // This code is contributed by AnkitRai01 |
# Python3 implementation of the approach # Function to return the missing element def findMissing(arr, n, k, avg):
# Find the sum of the array elements
sum = 0 ;
for i in range (n):
sum + = arr[i];
# The numerator and the denominator
# of the equation
num = (avg * (n + k)) - sum ;
den = k;
# If not divisible then X is
# not an integer
# it is a floating point number
if (num % den ! = 0 ):
return - 1 ;
# Return X
return ( int )(num / den);
# Driver code k = 3 ; avg = 4 ;
arr = [ 2 , 7 , 3 ] ;
n = len (arr);
print (findMissing(arr, n, k, avg));
# This code is contributed by 29AjayKumar |
// C# implementation of above approach using System;
class GFG
{ // Function to return the missing element
static int findMissing( int []arr, int n,
int k, int avg)
{
// Find the sum of the array elements
int sum = 0;
for ( int i = 0; i < n; i++)
{
sum += arr[i];
}
// The numerator and the denominator
// of the equation
int num = (avg * (n + k)) - sum;
int den = k;
// If not divisible then X is
// not an integer
// it is a floating point number
if (num % den != 0)
return -1;
// Return X
return ( int )(num / den);
}
// Driver code
public static void Main (String[] args)
{
int k = 3, avg = 4;
int []arr = { 2, 7, 3 };
int n = arr.Length;
Console.WriteLine(findMissing(arr, n, k, avg));
}
} // This code is contributed by Rajput-Ji |
<script> // Javascript implementation of the // above approach // Function to return the missing element function findMissing(arr, n, k, avg)
{ // Find the sum of the array elements
var sum = 0;
for ( var i = 0; i < n; i++) {
sum += arr[i];
}
// The numerator and the denominator
// of the equation
var num = (avg * (n + k)) - sum;
var den = k;
// If not divisible then X is
// not an integer
// it is a floating point number
if (num % den != 0)
return -1;
// Return X
return (Math.floor(num / den));
} // Driver code var k = 3;
var avg = 4;
var arr = [ 2, 7, 3 ];
var n = arr.length;
document.write(findMissing(arr, n, k, avg)); // This code is contributed by ShubhamSingh10 </script> |
4
Time Complexity: O(n), where n is the size of the given array.
Auxiliary Space: O(1)