# Minimize characters to be changed to make the left and right rotation of a string same

Given a string S of lowercase English alphabets, the task is to find the minimum number of characters to be changed such that the left and right rotation of the string are the same.

Examples:

Input: S = “abcd”
Output: 2
Explanation:
String after the left shift: “bcda”
String after the right shift: “dabc”
Changing the character at position 3 to ‘a’ and character at position 4 to ‘b’, the string is modified to “abab”.
Therefore, both the left and right rotations becomes “baba”.

Input: S = “gfg”
Output: 1
Explanation:
After updating the character at position 1 to ‘g’, the string becomes “ggg”.
Therefore, the left and right rotation are equal.

Approach: The key observation to solve the problem is that when the length of the string is even, then all the characters at even index and characters at odd index must be the same for the left and right rotations to be the same. For strings of odd length, all the characters must be equal. Follow the steps below to solve the problem:

• Check if the length of the string is even, then the minimum number of characters to be changed is the length of the string excluding the frequency of the most occurring element at the even indices and odd indices.
• Otherwise, if the length of the string is odd, then the minimum number of characters to be changed is the length of the string excluding the frequency of the most occurring character in the string.
• Print the final count obtained.

Below is the implementation of the above approach:

## C++

 `// C++ Program of the` `// above approch`   `#include ` `using` `namespace` `std;`   `// Function to find the minimum` `// characters to be removed from` `// the string` `int` `getMinimumRemoval(string str)` `{` `    ``int` `n = str.length();`   `    ``// Initialize answer by N` `    ``int` `ans = n;`   `    ``// If length is even` `    ``if` `(n % 2 == 0) {`   `        ``// Frequency array for odd` `        ``// and even indices` `        ``vector<``int``> freqEven(128);` `        ``vector<``int``> freqOdd(128);`   `        ``// Store the frequency of the` `        ``// characters at even and odd` `        ``// indices` `        ``for` `(``int` `i = 0; i < n; i++) {` `            ``if` `(i % 2 == 0) {` `                ``freqEven[str[i]]++;` `            ``}` `            ``else` `{` `                ``freqOdd[str[i]]++;` `            ``}` `        ``}`   `        ``// Stores the most occuring frequency` `        ``// for even and odd indices` `        ``int` `evenMax = 0, oddMax = 0;`   `        ``for` `(``char` `chr = ``'a'``; chr <= ``'z'``; chr++) {`   `            ``evenMax = max(evenMax, freqEven[chr]);` `            ``oddMax = max(oddMax, freqOdd[chr]);` `        ``}`   `        ``// Update the answer` `        ``ans = ans - evenMax - oddMax;` `    ``}`   `    ``// If length is odd` `    ``else` `{` `        ``// Stores the frequency of the` `        ``// characters of the string` `        ``vector<``int``> freq(128);` `        ``for` `(``int` `i = 0; i < n; i++) {` `            ``freq[str[i]]++;` `        ``}`   `        ``// Stores the most occuring character` `        ``// in the string` `        ``int` `strMax = 0;` `        ``for` `(``char` `chr = ``'a'``; chr <= ``'z'``; chr++) {` `            ``strMax = max(strMax, freq[chr]);` `        ``}`   `        ``// Update the answer` `        ``ans = ans - strMax;` `    ``}`   `    ``return` `ans;` `}`   `// Driver Code` `int` `main()` `{` `    ``string str = ``"geeksgeeks"``;`   `    ``cout << getMinimumRemoval(str);` `}`

## Java

 `// Java program of the ` `// above approch ` `class` `GFG{` `    `  `// Function to find the minimum ` `// characters to be removed from ` `// the string ` `public` `static` `int` `getMinimumRemoval(String str) ` `{ ` `    ``int` `n = str.length(); `   `    ``// Initialize answer by N ` `    ``int` `ans = n; `   `    ``// If length is even ` `    ``if` `(n % ``2` `== ``0``)` `    ``{ `   `        ``// Frequency array for odd ` `        ``// and even indices ` `        ``int``[] freqEven = ``new` `int``[``128``];` `        ``int``[] freqOdd = ``new` `int``[``128``];`   `        ``// Store the frequency of the ` `        ``// characters at even and odd ` `        ``// indices ` `        ``for``(``int` `i = ``0``; i < n; i++) ` `        ``{ ` `            ``if` `(i % ``2` `== ``0``)` `            ``{ ` `                ``freqEven[str.charAt(i)]++; ` `            ``} ` `            ``else` `            ``{ ` `                ``freqOdd[str.charAt(i)]++; ` `            ``} ` `        ``} `   `        ``// Stores the most occuring frequency ` `        ``// for even and odd indices ` `        ``int` `evenMax = ``0``, oddMax = ``0``; `   `        ``for``(``char` `chr = ``'a'``; chr <= ``'z'``; chr++)` `        ``{ ` `            ``evenMax = Math.max(evenMax, ` `                               ``freqEven[chr]); ` `            ``oddMax = Math.max(oddMax,` `                              ``freqOdd[chr]); ` `        ``} `   `        ``// Update the answer ` `        ``ans = ans - evenMax - oddMax; ` `    ``} `   `    ``// If length is odd ` `    ``else` `    ``{` `        `  `        ``// Stores the frequency of the ` `        ``// characters of the string ` `        ``int``[] freq = ``new` `int``[``128``];` `        ``for``(``int` `i = ``0``; i < n; i++)` `        ``{ ` `            ``freq[str.charAt(i)]++; ` `        ``} `   `        ``// Stores the most occuring character ` `        ``// in the string ` `        ``int` `strMax = ``0``; ` `        ``for``(``char` `chr = ``'a'``; chr <= ``'z'``; chr++) ` `        ``{ ` `            ``strMax = Math.max(strMax, freq[chr]); ` `        ``} ` `        `  `        ``// Update the answer ` `        ``ans = ans - strMax; ` `    ``} ` `    ``return` `ans; ` `} `   `// Driver code` `public` `static` `void` `main(String[] args) ` `{` `    ``String str = ``"geeksgeeks"``; ` `    `  `    ``System.out.print(getMinimumRemoval(str));` `}` `}`   `// This code is contributed by divyeshrabadiya07`

## Python3

 `# Python3 Program of the` `# above approch`   `# Function to find the minimum` `# characters to be removed from` `# the string` `def` `getMinimumRemoval(``str``):` `  `  `    ``n ``=` `len``(``str``)`   `    ``# Initialize answer by N` `    ``ans ``=` `n`   `    ``# If length is even` `    ``if``(n ``%` `2` `=``=` `0``):`   `        ``# Frequency array for odd` `        ``# and even indices` `        ``freqEven ``=` `{}` `        ``freqOdd ``=` `{}` `        ``for` `ch ``in` `range``(``ord``(``'a'``), ` `                        ``ord``(``'z'``) ``+` `1``):` `            ``freqEven[``chr``(ch)] ``=` `0` `            ``freqOdd[``chr``(ch)] ``=` `0`   `        ``# Store the frequency of the` `        ``# characters at even and odd` `        ``# indices` `        ``for` `i ``in` `range``(n):` `            ``if``(i ``%` `2` `=``=` `0``):` `                ``if` `str``[i] ``in` `freqEven:` `                    ``freqEven[``str``[i]] ``+``=` `1` `            ``else``:` `                ``if` `str``[i] ``in` `freqOdd:` `                    ``freqOdd[``str``[i]] ``+``=` `1`   `        ``# Stores the most occuring ` `        ``# frequency for even and ` `        ``# odd indices` `        ``evenMax ``=` `0` `        ``oddMax ``=` `0`   `        ``for` `ch ``in` `range``(``ord``(``'a'``), ` `                        ``ord``(``'z'``) ``+` `1``):` `            ``evenMax ``=` `max``(evenMax, ` `                      ``freqEven[``chr``(ch)])` `            ``oddMax ``=` `max``(oddMax, ` `                     ``freqOdd[``chr``(ch)])`   `        ``# Update the answer` `        ``ans ``=` `ans ``-` `evenMax ``-` `oddMax`   `    ``# If length is odd` `    ``else``:`   `        ``# Stores the frequency of the` `        ``# characters of the string` `        ``freq ``=` `{}` `        `  `        ``for` `ch ``in` `range``(``'a'``,``'z'``):` `            ``freq[``chr``(ch)] ``=` `0` `        ``for` `i ``in` `range``(n):` `            ``if` `str``[i] ``in` `freq:` `                ``freq[``str``[i]] ``+``=` `1`   `        ``# Stores the most occuring ` `        ``# characterin the string` `        ``strMax ``=` `0` `        `  `        ``for` `ch ``in` `range``(``'a'``,``'z'``):` `            ``strMax ``=` `max``(strMax, ` `                     ``freq[``chr``(ch)])`   `        ``# Update the answer` `        ``ans ``=` `ans ``-` `strMax`   `    ``return` `ans`   `# Driver Code` `str` `=` `"geeksgeeks"` `print``(getMinimumRemoval(``str``))`   `# This code is contributed by avanitrachhadiya2155`

## C#

 `// C# program of the ` `// above approch ` `using` `System;` `class` `GFG{` `    `  `// Function to find the minimum ` `// characters to be removed from ` `// the string ` `public` `static` `int` `getMinimumRemoval(String str) ` `{ ` `  ``int` `n = str.Length; `   `  ``// Initialize answer by N ` `  ``int` `ans = n; `   `  ``// If length is even ` `  ``if` `(n % 2 == 0)` `  ``{ ` `    ``// Frequency array for odd ` `    ``// and even indices ` `    ``int``[] freqEven = ``new` `int``;` `    ``int``[] freqOdd = ``new` `int``;`   `    ``// Store the frequency of the ` `    ``// characters at even and odd ` `    ``// indices ` `    ``for``(``int` `i = 0; i < n; i++) ` `    ``{ ` `      ``if` `(i % 2 == 0)` `      ``{ ` `        ``freqEven[str[i]]++; ` `      ``} ` `      ``else` `      ``{ ` `        ``freqOdd[str[i]]++; ` `      ``} ` `    ``} `   `    ``// Stores the most occuring frequency ` `    ``// for even and odd indices ` `    ``int` `evenMax = 0, oddMax = 0; `   `    ``for``(``char` `chr = ``'a'``; chr <= ``'z'``; chr++)` `    ``{ ` `      ``evenMax = Math.Max(evenMax, ` `                         ``freqEven[chr]); ` `      ``oddMax = Math.Max(oddMax,` `                        ``freqOdd[chr]); ` `    ``} `   `    ``// Update the answer ` `    ``ans = ans - evenMax - oddMax; ` `  ``} `   `  ``// If length is odd ` `  ``else` `  ``{` `    ``// Stores the frequency of the ` `    ``// characters of the string ` `    ``int``[] freq = ``new` `int``;` `    ``for``(``int` `i = 0; i < n; i++)` `    ``{ ` `      ``freq[str[i]]++; ` `    ``} `   `    ``// Stores the most occuring character ` `    ``// in the string ` `    ``int` `strMax = 0; ` `    ``for``(``char` `chr = ``'a'``; chr <= ``'z'``; chr++) ` `    ``{ ` `      ``strMax = Math.Max(strMax, freq[chr]); ` `    ``} `   `    ``// Update the answer ` `    ``ans = ans - strMax; ` `  ``} ` `  ``return` `ans; ` `} `   `// Driver code` `public` `static` `void` `Main(String[] args) ` `{` `  ``String str = ``"geeksgeeks"``; ` `  ``Console.Write(getMinimumRemoval(str));` `}` `}`   `// This code is contributed by Rajput-Ji`

Output:

```6

```

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

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