Given an array, arr[] of size N and an integer K, the task is to find the minimum number of operations required to make all array elements equal to K by performing the following operations any number of times:
- Convert arr[i] to arr[i] + X, where X is an odd number.
- Convert arr[i] to arr[i] – Y, where Y is an even number.
Examples:
Input: arr[] = {8, 7, 2, 1, 3}, K = 5
Output: 8
Explanation: To make all elements of the given array equal to K(= 5), following operations are required:
arr[0] = arr[0] + X, X = 1
arr[0] = arr[0] – Y, Y = 4
arr[1] = arr[1] – Y, Y = 2
arr[2] = arr[2] + X, X = 3
arr[3] = arr[3] + X, X = 3
arr[3] = arr[3] + X, X = 1
arr[4] = arr[4] + X, X = 1
arr[4] = arr[4] + X, X = 1Input: arr[] = {1, 2, 3, 4, 5, 6, 7}, K = 3
Output: 9
Approach: The problem can be solved using the Greedy technique. Following are the observations:
Even + Even = Even
Even + Odd = Odd
Odd + Odd = Even
Odd + Even = Odd
Follow the steps below to solve the problem:
-
Traverse the given array and check the following conditions.
- If K > arr[i] and (K – arr[i]) % 2 == 0 then add two odd numbers(X) into arr[i]. Therefore, total 2 operations required.
- If K > arr[i] and (K – arr[i]) % 2 != 0 then add one odd numbers(X) into arr[i]. Therefore, total 1 operations required.
- If K < arr[i] and (arr[i] – arr[i]) % 2 == 0 then subtract one even numbers(Y) into arr[i]. Therefore, total 1 operations required.
- If K < arr[i] and (K – arr[i]) % 2 != 0 then add an odd numbers(X) into arr[i] and subtract an even numbers(Y) from arr[i]. Therefore, total 2 operations required.
- Finally, print the total number of operations required to make all the array elements equal to K.
Below is the implementation of the above approach
// C++ program to implement // the above approach #include <bits/stdc++.h> using namespace std;
// Function to find the minimum operations // required to make array elements equal to K int MinOperation( int arr[], int N, int K)
{ // Stores minimum count of operations
int cntOpe = 0;
// Traverse the given array
for ( int i = 0; i < N; i++) {
// If K is greater than arr[i]
if (K > arr[i]) {
// If (K - arr[i]) is even
if ((K - arr[i]) % 2 == 0) {
// Update cntOpe
cntOpe += 2;
}
else {
// Update cntOpe
cntOpe += 1;
}
}
// If K is less than arr[i]
else if (K < arr[i]) {
// If (arr[i] - K) is even
if ((K - arr[i]) % 2 == 0) {
// Update cntOpe
cntOpe += 1;
}
else {
// Update cntOpe
cntOpe += 2;
}
}
}
return cntOpe;
} // Driver Code int main()
{ int arr[] = { 8, 7, 2, 1, 3 };
int K = 5;
int N = sizeof (arr) / sizeof (arr[0]);
cout << MinOperation(arr, N, K);
return 0;
} |
// Java program to implement // the above approach class GFG{
// Function to find the minimum // operations required to make // array elements equal to K public static int MinOperation( int arr[],
int N, int K)
{ // Stores minimum count of
// operations
int cntOpe = 0 ;
// Traverse the given array
for ( int i = 0 ; i < N; i++)
{
// If K is greater than
// arr[i]
if (K > arr[i])
{
// If (K - arr[i]) is even
if ((K - arr[i]) % 2 == 0 )
{
// Update cntOpe
cntOpe += 2 ;
}
else
{
// Update cntOpe
cntOpe += 1 ;
}
}
// If K is less than
// arr[i]
else if (K < arr[i])
{
// If (arr[i] - K) is
// even
if ((K - arr[i]) % 2 == 0 )
{
// Update cntOpe
cntOpe += 1 ;
}
else
{
// Update cntOpe
cntOpe += 2 ;
}
}
}
return cntOpe;
} // Driver code public static void main(String[] args)
{ int arr[] = { 8 , 7 , 2 , 1 , 3 };
int K = 5 ;
int N = arr.length;
System.out.println(
MinOperation(arr, N, K));
} } // This code is contributed by divyeshrabadiya07 |
# Python3 program to implement # the above approach # Function to find the minimum operations # required to make array elements equal to K def MinOperation(arr, N, K):
# Stores minimum count of operations
cntOpe = 0
# Traverse the given array
for i in range (N):
# If K is greater than arr[i]
if (K > arr[i]):
# If (K - arr[i]) is even
if ((K - arr[i]) % 2 = = 0 ):
# Update cntOpe
cntOpe + = 2
else :
# Update cntOpe
cntOpe + = 1
# If K is less than arr[i]
elif (K < arr[i]):
# If (arr[i] - K) is even
if ((K - arr[i]) % 2 = = 0 ):
# Update cntOpe
cntOpe + = 1
else :
# Update cntOpe
cntOpe + = 2
return cntOpe
# Driver Code arr = [ 8 , 7 , 2 , 1 , 3 ]
K = 5
N = len (arr)
print (MinOperation(arr, N, K))
# This code is contributed by sanjoy_62 |
// C# program to implement // the above approach using System;
class GFG{
// Function to find the minimum // operations required to make // array elements equal to K public static int MinOperation( int []arr,
int N, int K)
{ // Stores minimum count of
// operations
int cntOpe = 0;
// Traverse the given array
for ( int i = 0; i < N; i++)
{
// If K is greater than
// arr[i]
if (K > arr[i])
{
// If (K - arr[i]) is even
if ((K - arr[i]) % 2 == 0)
{
// Update cntOpe
cntOpe += 2;
}
else
{
// Update cntOpe
cntOpe += 1;
}
}
// If K is less than
// arr[i]
else if (K < arr[i])
{
// If (arr[i] - K) is
// even
if ((K - arr[i]) % 2 == 0)
{
// Update cntOpe
cntOpe += 1;
}
else
{
// Update cntOpe
cntOpe += 2;
}
}
}
return cntOpe;
} // Driver code public static void Main(String[] args)
{ int []arr = {8, 7, 2, 1, 3};
int K = 5;
int N = arr.Length;
Console.WriteLine(
MinOperation(arr, N, K));
} } // This code is contributed by Amit Katiyar |
<script> // Javascript program to implement // the above approach // Function to find the minimum // operations required to make // array elements equal to K function MinOperation(arr, N, K)
{ // Stores minimum count of
// operations
let cntOpe = 0;
// Traverse the given array
for (let i = 0; i < N; i++)
{
// If K is greater than
// arr[i]
if (K > arr[i])
{
// If (K - arr[i]) is even
if ((K - arr[i]) % 2 == 0)
{
// Update cntOpe
cntOpe += 2;
}
else
{
// Update cntOpe
cntOpe += 1;
}
}
// If K is less than
// arr[i]
else if (K < arr[i])
{
// If (arr[i] - K) is
// even
if ((K - arr[i]) % 2 == 0)
{
// Update cntOpe
cntOpe += 1;
}
else
{
// Update cntOpe
cntOpe += 2;
}
}
}
return cntOpe;
} // Driver Code
let arr = [8, 7, 2, 1, 3];
let K = 5;
let N = arr.length;
document.write(
MinOperation(arr, N, K));
</script> |
8
Time Complexity: O(N)
Auxiliary Space: O(1)