# Minimum flips required to convert given string into concatenation of equal substrings of length K

• Last Updated : 28 May, 2021

Given a binary string S and an integer K, the task is to find the minimum number of flips required to convert the given string into a concatenation of K-length equal sub-strings. It is given that the given string can be split into K-length substrings.

Examples:

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Input: S = “101100101”, K = 3
Output:
Explanation:
Flip the ‘0’ from index 5 to ‘1’.
The resultant string is S = “101101101”.
It is the concatenation of substring “101”.
Hence, the minimum number of flips required is 1.

Input: S = “10110111”, K = 4
Output:
Explanation:
Flip the ‘0’ and ‘1’ at indexes 4 and 5 respectively.
The resultant string is S = “10111011”.
It is the concatenation of the substring “1011”.
Hence, the minimum number of flips required is 2.

Approach:
The problem can be solved using Greedy Approach

• Iterate the given string with increments of K indices from each index and keep a count of the 0s and 1s.
• The character which occurs the minimum number of times must be flipped and keep incrementing that count.
• Perform the above steps for all the indices from 0 to K-1 to obtain the minimum number of flips required.

Below is the implementation of the above approach:

## C++

 `// C++ Program to implement``// the above approach``#include ``using` `namespace` `std;` `// Function that returns the minimum``// number of flips to convert``// the s into a concatenation``// of K-length sub-string``int` `minOperations(string S, ``int` `K)``{``    ``// Stores the result``    ``int` `ans = 0;` `    ``// Iterate through string index``    ``for` `(``int` `i = 0; i < K; i++) {` `        ``// Stores count of 0s & 1s``        ``int` `zero = 0, one = 0;` `        ``// Iterate making K jumps``        ``for` `(``int` `j = i;``             ``j < S.size(); j += K) {` `            ``// Count 0's``            ``if` `(S[j] == ``'0'``)``                ``zero++;` `            ``// Count 1's``            ``else``                ``one++;``        ``}` `        ``// Add minimum flips``        ``// for index i``        ``ans += min(zero, one);``    ``}` `    ``// Return minimum number``    ``// of flips``    ``return` `ans;``}` `// Driver Code``int` `main()``{``    ``string S = ``"110100101"``;` `    ``int` `K = 3;` `    ``cout << minOperations(S, K);` `    ``return` `0;``}`

## Java

 `// Java program to implement``// the above approach``import` `java.io.*;` `class` `GFG{` `// Function that returns the minimum``// number of flips to convert``// the s into a concatenation``// of K-length sub-string``public` `static` `int` `minOperations(String S, ``int` `K)``{``    ` `    ``// Stores the result``    ``int` `ans = ``0``;` `    ``// Iterate through string index``    ``for``(``int` `i = ``0``; i < K; i++)``    ``{` `        ``// Stores count of 0s & 1s``        ``int` `zero = ``0``, one = ``0``;` `        ``// Iterate making K jumps``        ``for``(``int` `j = i; j < S.length(); j += K)``        ``{``            ` `            ``// Count 0's``            ``if` `(S.charAt(j) == ``'0'``)``                ``zero++;` `            ``// Count 1's``            ``else``                ``one++;``        ``}` `        ``// Add minimum flips``        ``// for index i``        ``ans += Math.min(zero, one);``    ``}` `    ``// Return minimum number``    ``// of flips``    ``return` `ans;``}` `// Driver Code``public` `static` `void` `main(String args[])``{``    ``String S = ``"110100101"``;` `    ``int` `K = ``3``;` `    ``System.out.println(minOperations(S, K));``}``}` `// This code is contributed by grand_master`

## Python3

 `# Python3 program to implement``# the above approach` `# Function that returns the minimum``# number of flips to convert the s``# into a concatenation of K-length``# sub-string``def` `minOperations(S, K):` `    ``# Stores the result``    ``ans ``=` `0` `    ``# Iterate through string index``    ``for` `i ``in` `range``(K):` `        ``# Stores count of 0s & 1s``        ``zero, one ``=` `0``, ``0` `        ``# Iterate making K jumps``        ``for` `j ``in` `range``(i, ``len``(S), K):` `            ``# Count 0's``            ``if``(S[j] ``=``=` `'0'``):``                ``zero ``+``=` `1` `            ``# Count 1's``            ``else``:``                ``one ``+``=` `1` `        ``# Add minimum flips``        ``# for index i``        ``ans ``+``=` `min``(zero, one)` `    ``# Return minimum number``    ``# of flips``    ``return` `ans` `# Driver code``if` `__name__ ``=``=` `'__main__'``:` `    ``s ``=` `"110100101"``    ``K ``=` `3` `    ``print``(minOperations(s, K))` `# This code is contributed by Shivam Singh`

## C#

 `// C# program to implement``// the above approach``using` `System;` `class` `GFG{` `// Function that returns the minimum``// number of flips to convert``// the s into a concatenation``// of K-length sub-string``public` `static` `int` `minOperations(String S, ``int` `K)``{``    ` `    ``// Stores the result``    ``int` `ans = 0;` `    ``// Iterate through string index``    ``for``(``int` `i = 0; i < K; i++)``    ``{` `        ``// Stores count of 0s & 1s``        ``int` `zero = 0, one = 0;` `        ``// Iterate making K jumps``        ``for``(``int` `j = i; j < S.Length; j += K)``        ``{``            ` `            ``// Count 0's``            ``if` `(S[j] == ``'0'``)``                ``zero++;` `            ``// Count 1's``            ``else``                ``one++;``        ``}` `        ``// Add minimum flips``        ``// for index i``        ``ans += Math.Min(zero, one);``    ``}` `    ``// Return minimum number``    ``// of flips``    ``return` `ans;``}` `// Driver Code``public` `static` `void` `Main(String []args)``{``    ``String S = ``"110100101"``;` `    ``int` `K = 3;` `    ``Console.WriteLine(minOperations(S, K));``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``
Output:
`2`

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

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