Minimum number of elements to add to make median equals x
Last Updated :
13 Dec, 2024
A median in an array with the length of n is an element which occupies position number (n+1)/2 after we sort the elements in the non-decreasing order (the array elements are numbered starting with 1). A median of an array (2, 6, 1, 2, 3) is the number 2, and a median of array (0, 96, 17, 23) — the number 17.
Examples :
Input : 3 10
10 20 30
Output : 1
In the first sample we can add number 9
to array (10, 20, 30). The resulting array
(9, 10, 20, 30) will have a median in
position (4+1)/2 = 2, that is, 10
Input : 3 4
1 2 3
Output : 4
In the second sample you should add numbers
4, 5, 5, 5. The resulting array has median
equal to 4.
First Approach:- The approach is to add one more number x to the array until the median of the array equals to x. Below is the implementation of the above approach:-
C++
// C++ program to find minimum number
// of elements needs to add to the
// array so that its median equals x.
#include <bits/stdc++.h>
using namespace std;
// Returns count of elements to be
// added to make median x. This function
// assumes that a[] has enough extra space.
int minNumber(int a[], int n, int x)
{
// to sort the array in increasing order.
sort(a, a + n);
int k;
for (k = 0; a[(n - 1) / 2] != x; k++) {
a[n++] = x;
sort(a, a + n);
}
return k;
}
// Driver code
main()
{
int x = 10;
int a[6] = { 10, 20, 30 };
int n = 3;
cout << minNumber(a, n, x) << endl;
return 0;
}
// Java program to find minimum number
// of elements needs to add to the
// array so that its median equals x.
import java.util.Arrays;
class GFG
{
// Returns count of elements to be
// added to make median x. This function
// assumes that a[] has enough extra space.
static int minNumber(int a[], int n, int x)
{
// to sort the array in increasing order.
Arrays.sort(a);
int k;
for (k = 0; a[(n) / 2] != x; k++)
{
a[n++] = x;
Arrays.sort(a);
}
return k;
}
// Driver code
public static void main(String[] args)
{
int x = 10;
int a[] = { 10, 20, 30 };
int n = 3;
System.out.println(minNumber(a, n-1, x));
}
}
// This code has been contributed by 29AjayKumar
# Python3 program to find minimum number
# of elements needs to add to the
# array so that its median equals x.
# Returns count of elements to be added
# to make median x. This function
# assumes that a[] has enough extra space.
def minNumber(a, n, x):
# to sort the array in increasing order.
a.sort(reverse = False)
k = 0
while(a[int((n - 1) / 2)] != x):
a[n - 1] = x
n += 1
a.sort(reverse = False)
k += 1
return k
# Driver code
if __name__ == '__main__':
x = 10
a = [10, 20, 30]
n = 3
print(minNumber(a, n, x))
# This code is contributed by
# Surendra_Gangwar
// C# program to find minimum number
// of elements needs to add to the
// array so that its median equals x.
using System;
class GFG
{
// Returns count of elements to be
// added to make median x. This function
// assumes that a[] has enough extra space.
static int minNumber(int []a, int n, int x)
{
// to sort the array in increasing order.
Array.Sort(a);
int k;
for (k = 0; a[(n) / 2] != x; k++)
{
a[n++] = x;
Array.Sort(a);
}
return k;
}
// Driver code
public static void Main(String[] args)
{
int x = 10;
int []a = { 10, 20, 30 };
int n = 3;
Console.WriteLine(minNumber(a, n-1, x));
}
}
// This code contributed by Rajput-Ji
<?php
// PHP program to find minimum
// number of elements needs to
// add to the array so that its
// median equals x.
// Returns count of elements
// to be added to make median
// x. This function assumes
// that a[] has enough extra space.
function minNumber($a, $n, $x)
{
// to sort the array in
// increasing order.
sort($a);
$k;
for ($k = 0;
$a[($n - 1) / 2] != $x; $k++)
{
$a[$n++] = $x;
sort($a);
}
return $k;
}
// Driver code
$x = 10;
$a = array (10, 20, 30);
$n = 3;
echo minNumber($a, $n, $x),"\n";
// This code is contributed by ajit
?>
<script>
// Javascript program to find minimum number
// of elements needs to add to the
// array so that its median equals x.
// Returns count of elements to be
// added to make median x. This function
// assumes that a[] has enough extra space.
function minNumber(a, n, x)
{
// to sort the array in increasing order.
a.sort();
let k;
for (k = 0; a[parseInt((n - 1) / 2, 10)] != x; k++) {
a[n++] = x;
a.sort();
}
return k;
}
let x = 10;
let a = [ 10, 20, 30 ];
let n = 3;
document.write(minNumber(a, n, x));
// This code is contributed by mukesh07.
</script>
Output :
1
Time complexity : O(k n Logn)
Auxiliary Space: O(1)
Second Approach:- Better approach is to count all the elements equal to x(that is e), greater than x(that is h) and smaller than x(that is l). And then -
if l is greater than h then, the ans will be (l - h) + 1 - e;
And if h is greater than l then, ans will be (h - l - 1) + 1 - e;
We can use Hoare's partition scheme to count smaller, equal and greater elements.
Below is the implementation of the above approach:
C++
// C++ program to find minimum number of
// elements to add so that its median
// equals x.
#include <bits/stdc++.h>
using namespace std;
int minNumber(int a[], int n, int x)
{
int l = 0, h = 0, e = 0;
for (int i = 0; i < n; i++) {
// no. of elements equals to x,
// that is, e.
if (a[i] == x)
e++;
// no. of elements greater than x,
// that is, h.
else if (a[i] > x)
h++;
// no. of elements smaller than x,
// that is, l.
else if (a[i] < x)
l++;
}
int ans = 0;
if (l > h)
ans = l - h;
else if (l < h)
ans = h - l - 1;
// subtract the no. of elements
// that are equal to x.
return ans + 1 - e;
}
// Driver code
int main()
{
int x = 10;
int a[] = { 10, 20, 30 };
int n = sizeof(a) / sizeof(a[0]);
cout << minNumber(a, n, x) << endl;
return 0;
}
// Java program to find minimum number
// of elements to add so that its
// median equals x.
import java.util.*;
import java.lang.*;
class GFG {
public static int minNumber(int a[],
int n, int x)
{
int l = 0, h = 0, e = 0;
for (int i = 0; i < n; i++)
{
// no. of elements equals to
// x, that is, e.
if (a[i] == x)
e++;
// no. of elements greater
// than x, that is, h.
else if (a[i] > x)
h++;
// no. of elements smaller
// than x, that is, l.
else if (a[i] < x)
l++;
}
int ans = 0;
if (l > h)
ans = l - h;
else if (l < h)
ans = h - l - 1;
// subtract the no. of elements
// that are equal to x.
return ans + 1 - e;
}
// Driven Program
public static void main(String[] args)
{
int x = 10;
int a[] = { 10, 20, 30 };
int n = a.length;
System.out.println(
minNumber(a, n, x));
}
}
// This code is contributed by
// Prasad Kshirsagar
# Python3 program to find minimum number
# of elements to add so that its median
# equals x.
def minNumber (a, n, x):
l = 0
h = 0
e = 0
for i in range(n):
# no. of elements equals to x,
# that is, e.
if a[i] == x:
e+=1
# no. of elements greater than x,
# that is, h.
elif a[i] > x:
h+=1
# no. of elements smaller than x,
# that is, l.
elif a[i] < x:
l+=1
ans = 0;
if l > h:
ans = l - h
elif l < h:
ans = h - l - 1;
# subtract the no. of elements
# that are equal to x.
return ans + 1 - e
# Driver code
x = 10
a = [10, 20, 30]
n = len(a)
print(minNumber(a, n, x))
# This code is contributed
# by "Abhishek Sharma 44"
// C# program to find minimum
// number of elements to add
// so that its median equals x.
using System;
class GFG
{
public static int minNumber(int []a,
int n,
int x)
{
int l = 0, h = 0, e = 0;
for (int i = 0; i < n; i++)
{
// no. of elements
// equals to x,
// that is, e.
if (a[i] == x)
e++;
// no. of elements
// greater than x,
// that is, h.
else if (a[i] > x)
h++;
// no. of elements smaller
// than x, that is, l.
else if (a[i] < x)
l++;
}
int ans = 0;
if (l > h)
ans = l - h;
else if (l < h)
ans = h - l - 1;
// subtract the no.
// of elements that
// are equal to x.
return ans + 1 - e;
}
// Driver Code
public static void Main()
{
int x = 10;
int []a = {10, 20, 30};
int n = a.Length;
Console.WriteLine(
minNumber(a, n, x));
}
}
// This code is contributed
// by anuj_67.
<?php
// PHP program to find minimum
// number of elements to add so
// that its median equals x.
function minNumber($a, $n, $x)
{
$l = 0; $h = 0; $e = 0;
for ($i = 0; $i < $n; $i++)
{
// no. of elements equals
// to x, that is, e.
if ($a[$i] == $x)
$e++;
// no. of elements greater
// than x, that is, h.
else if ($a[$i] > $x)
$h++;
// no. of elements smaller
// than x, that is, l.
else if ($a[$i] < $x)
$l++;
}
$ans = 0;
if ($l > $h)
$ans = $l - $h;
else if ($l < $h)
$ans = $h - $l - 1;
// subtract the no. of elements
// that are equal to x.
return $ans + 1 - $e;
}
// Driver code
$x = 10;
$a = array (10, 20, 30);
$n = sizeof($a) ;
echo minNumber($a, $n, $x), "\n";
// This code is contributed by jit_t
?>
<script>
// Javascript program to find minimum number
// of elements to add so that its median
// equals x.
function minNumber(a, n, x)
{
let l = 0, h = 0, e = 0;
for(let i = 0; i < n; i++)
{
// No. of elements equals to x,
// that is, e.
if (a[i] == x)
e++;
// No. of elements greater than x,
// that is, h.
else if (a[i] > x)
h++;
// No. of elements smaller than x,
// that is, l.
else if (a[i] < x)
l++;
}
let ans = 0;
if (l > h)
ans = l - h;
else if (l < h)
ans = h - l - 1;
// Subtract the no. of elements
// that are equal to x.
return ans + 1 - e;
}
// Driver code
let x = 10;
let a = [ 10, 20, 30 ];
let n = a.length;
document.write(minNumber(a, n, x));
// This code is contributed by suresh07
</script>
Output :
1
Time complexity : O(n)
Auxiliary Space: O(1)
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