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Minimum number of moves to make a binary array K periodic
• Difficulty Level : Basic
• Last Updated : 05 Apr, 2021

Given a binary array arr[] (containing only 0s and 1s) and an integer K. The task is to find the minimum number of moves to make the array K-periodic.
An array is said to be K-periodic if the sub-arrays [1 to K], [k+1 to 2K], [2k+1 to 3K], … are all exactly same.
In a single move any 1 can be changed to a 0 or any 0 can be changed into a 1.

Examples:

Input: arr[] = {1, 1, 0, 0, 1, 1}, K = 2
Output:
The new array can be {1, 1, 1, 1, 1, 1}

Input: arr[] = {1, 0, 0, 0, 1, 0}, K = 2
Output:
The new array can be {1, 0, 1, 0, 1, 0}

Approach: For an array to be K-periodic. Consider indices i where i % K = X. All these indices must have the same value. So either the 1s can be converted to 0s or vice-versa. In order to reduce the number of moves, we choose the conversion which is minimum.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to return the minimum moves required``int` `minMoves(``int` `n, ``int` `a[], ``int` `k)``{` `    ``int` `ct1[k] = { 0 }, ct0[k] = { 0 }, moves = 0;` `    ``// Count the number of 1s and 2s``    ``// at each X such that i % K = X``    ``for` `(``int` `i = 0; i < n; i++)``        ``if` `(a[i] == 1)``            ``ct1[i % k]++;``        ``else``            ``ct0[i % k]++;` `    ``// Choose the minimum elements to change``    ``for` `(``int` `i = 0; i < k; i++)``        ``moves += min(ct1[i], ct0[i]);` `    ``// Return the minimum moves required``    ``return` `moves;``}` `// Driver code``int` `main()``{``    ``int` `k = 2;``    ``int` `a[] = { 1, 0, 0, 0, 1, 0 };``    ``int` `n = ``sizeof``(a) / ``sizeof``(a[0]);``    ``cout << minMoves(n, a, k);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``import` `java.io.*;` `class` `GFG``{` `// Function to return the minimum``// moves required``static` `int` `minMoves(``int` `n, ``int` `a[], ``int` `k)``{``    ``int` `ct1[] = ``new` `int` `[k];``    ``int` `ct0[] = ``new` `int``[k];``    ``int` `moves = ``0``;` `    ``// Count the number of 1s and 2s``    ``// at each X such that i % K = X``    ``for` `(``int` `i = ``0``; i < n; i++)``        ``if` `(a[i] == ``1``)``            ``ct1[i % k]++;``        ``else``            ``ct0[i % k]++;` `    ``// Choose the minimum elements to change``    ``for` `(``int` `i = ``0``; i < k; i++)``        ``moves += Math.min(ct1[i], ct0[i]);` `    ``// Return the minimum moves required``    ``return` `moves;``}` `// Driver code``public` `static` `void` `main (String[] args)``{``    ``int` `k = ``2``;``    ``int` `a[] = { ``1``, ``0``, ``0``, ``0``, ``1``, ``0` `};``    ``int` `n = a.length;``    ``System.out.println(minMoves(n, a, k));``}``}` `// This is code contributed by inder_verma`

## Python3

 `# Python3 implementation of the approach` `# Function to return the minimum``# moves required``def` `minMoves(n, a, k):``    ``ct1 ``=` `[``0` `for` `i ``in` `range``(k)]``    ``ct0 ``=` `[``0` `for` `i ``in` `range``(k)]``    ``moves ``=` `0` `    ``# Count the number of 1s and 2s``    ``# at each X such that i % K = X``    ``for` `i ``in` `range``(n):``        ``if` `(a[i] ``=``=` `1``):``            ``ct1[i ``%` `k] ``+``=` `1``        ``else``:``            ``ct0[i ``%` `k] ``+``=` `1` `    ``# Choose the minimum elements to change``    ``for` `i ``in` `range``(k):``        ``moves ``+``=` `min``(ct1[i], ct0[i])` `    ``# Return the minimum moves required``    ``return` `moves` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``k ``=` `2``    ``a ``=` `[``1``, ``0``, ``0``, ``0``, ``1``, ``0``]``    ``n ``=` `len``(a)``    ``print``(minMoves(n, a, k))` `# This code is contributed by``# Surendra_Gangwar`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{` `// Function to return the minimum``// moves required``static` `int` `minMoves(``int` `n, ``int``[] a, ``int` `k)``{``    ``int``[] ct1 = ``new` `int` `[k];``    ``int``[] ct0 = ``new` `int``[k];``    ``int` `moves = 0;` `    ``// Count the number of 1s and 2s``    ``// at each X such that i % K = X``    ``for` `(``int` `i = 0; i < n; i++)``        ``if` `(a[i] == 1)``            ``ct1[i % k]++;``        ``else``            ``ct0[i % k]++;` `    ``// Choose the minimum elements to change``    ``for` `(``int` `i = 0; i < k; i++)``        ``moves += Math.Min(ct1[i], ct0[i]);` `    ``// Return the minimum moves required``    ``return` `moves;``}` `// Driver code``public` `static` `void` `Main ()``{``    ``int` `k = 2;``    ``int``[] a = { 1, 0, 0, 0, 1, 0 };``    ``int` `n = a.Length;``    ``Console.WriteLine(minMoves(n, a, k));``}``}` `// This is code contributed by Code_Mech`

## PHP

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## Javascript

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Output:
`1`

Time Complexity: O(N)

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