Minimum cost to convert str1 to str2 with the given operations

Given two strings of equal lengths str1 and str2 consisting of characters ‘a’ and ‘b’ only. The following operations can be performed on str1:

1. Any character can be changed from ‘a’ to ‘b’ or from ‘b’ to ‘a’ with 1 unit cost.
2. Any two characters str1[i] and str1[j] can be swapped with cost |i – j|.

The task is to find the minimum cost required to convert str1 to str2.

Examples:

Input: str1 = “abb”, str2 = “baa”
Output: 2
Swap(str1[0], str1[1]), str1 = “bab” and cost = 1
Change str1[2] = ‘b’ to ‘a’, str1 = “baa” and cost = 2

Input: str1 = “abab”, str2 = “aabb”
Output: 1

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: It can be observed that swapping will only be performed on consecutive characters because if the characters are not consecutive then the cost of swapping will be ≥ 2 which will give cost greater than or equal to the cost of changing those characters using the operation of the first type. Now, for every two consecutive characters if they are different in both the string then swap these characters incurring 1 unit cost as compares to 2 unit cost when both of them are changed separately. Else change the character which is different in both the strings (either the current or the next). Finally, print the calculated cost.

Below is the implementation of the above approach:

C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the minimum ` `// cost to convert str1 to sr2 ` `int` `minCost(string str1, string str2, ``int` `n) ` `{ ` `    ``int` `cost = 0; ` ` `  `    ``// For every character of str1 ` `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``// If current character is not ` `        ``// equal in both the strings ` `        ``if` `(str1[i] != str2[i]) { ` ` `  `            ``// If the next character is also different in both ` `            ``// the strings then these characters can be swapped ` `            ``if` `(i < n - 1 && str1[i + 1] != str2[i + 1]) { ` `                ``swap(str1[i], str1[i + 1]); ` `                ``cost++; ` `            ``} ` ` `  `            ``// Change the current character ` `            ``else` `{ ` `                ``cost++; ` `            ``} ` `        ``} ` `    ``} ` `    ``return` `cost; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``string str1 = ``"abb"``, str2 = ``"bba"``; ` `    ``int` `n = str1.length(); ` ` `  `    ``cout << minCost(str1, str2, n); ` ` `  `    ``return` `0; ` `} `

Java

 `// Java implementation of the approach ` `import` `java.util.*; ` ` `  `class` `GFG  ` `{ ` ` `  `// Function to return the minimum ` `// cost to convert str1 to sr2 ` `static` `int` `minCost(``char` `[]str1,  ` `                   ``char` `[]str2, ``int` `n) ` `{ ` `    ``int` `cost = ``0``; ` ` `  `    ``// For every character of str1 ` `    ``for` `(``int` `i = ``0``; i < n; i++)  ` `    ``{ ` ` `  `        ``// If current character is not ` `        ``// equal in both the strings ` `        ``if` `(str1[i] != str2[i]) ` `        ``{ ` ` `  `            ``// If the next character is also different in both ` `            ``// the strings then these characters can be swapped ` `            ``if` `(i < n - ``1` `&& str1[i + ``1``] != str2[i + ``1``])  ` `            ``{ ` `                ``swap(str1, i, i + ``1``); ` `                ``cost++; ` `            ``} ` ` `  `            ``// Change the current character ` `            ``else`  `            ``{ ` `                ``cost++; ` `            ``} ` `        ``} ` `    ``} ` `    ``return` `cost; ` `} ` ` `  `static` `void` `swap(``char` `[]arr, ``int` `i, ``int` `j) ` `{ ` `    ``char` `temp = arr[i]; ` `    ``arr[i] = arr[j]; ` `    ``arr[j] = temp; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``String str1 = ``"abb"``, str2 = ``"bba"``; ` `    ``int` `n = str1.length(); ` ` `  `    ``System.out.println(minCost(str1.toCharArray(),  ` `                               ``str2.toCharArray(), n)); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

Python3

 `# Python3 implementation of the approach  ` ` `  `# Function to return the minimum  ` `# cost to convert str1 to sr2  ` `def` `minCost(str1, str2, n):  ` ` `  `    ``cost ``=` `0` ` `  `    ``# For every character of str1 ` `    ``for` `i ``in` `range``(n):  ` ` `  `        ``# If current character is not  ` `        ``# equal in both the strings  ` `        ``if` `(str1[i] !``=` `str2[i]):  ` ` `  `            ``# If the next character is also different in both  ` `            ``# the strings then these characters can be swapped  ` `            ``if` `(i < n ``-` `1` `and` `str1[i ``+` `1``] !``=` `str2[i ``+` `1``]):  ` `                ``swap(str1[i], str1[i ``+` `1``])  ` `                ``cost ``+``=` `1` `             `  `            ``# Change the current character  ` `            ``else``:  ` `                ``cost ``+``=` `1` `             `  `    ``return` `cost  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `'__main__'``:  ` ` `  `    ``str1 ``=` `"abb"` `    ``str2 ``=` `"bba"` `    ``n ``=` `len``(str1)  ` ` `  `    ``print``(minCost(str1, str2, n))  ` ` `  `# This code is contributed by ashutosh450 `

C#

 `// C# implementation of the approach  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `    ``// Function to return the minimum  ` `    ``// cost to convert str1 to sr2  ` `    ``static` `int` `minCost(``string` `str1,  ` `                       ``string` `str2, ``int` `n)  ` `    ``{  ` `        ``int` `cost = 0;  ` `     `  `        ``char``[] array = str1.ToCharArray(); ` `         `  `        ``// For every character of str1  ` `        ``for` `(``int` `i = 0; i < n; i++)  ` `        ``{  ` `     `  `            ``// If current character is not  ` `            ``// equal in both the strings  ` `            ``if` `(str1[i] != str2[i])  ` `            ``{  ` `     `  `                ``// If the next character is also different in both  ` `                ``// the strings then these characters can be swapped  ` `                ``if` `(i < n - 1 && str1[i + 1] != str2[i + 1]) ` `                ``{  ` `                    ``char` `temp = array[i]; ` `                    ``array[i] = array[i + 1]; ` `                    ``array[i + 1] = temp ; ` `                     `  `                    ``cost++;  ` `                ``}  ` `     `  `                ``// Change the current character  ` `                ``else` `                ``{  ` `                    ``cost++;  ` `                ``}  ` `            ``}  ` `        ``}  ` `        ``return` `cost;  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``static` `public` `void` `Main ()  ` `    ``{  ` `        ``string` `str1 = ``"abb"``, str2 = ``"bba"``;  ` `        ``int` `n = str1.Length;  ` `     `  `        ``Console.WriteLine(minCost(str1, str2, n));  ` `    ``}  ` `} ` ` `  `// This code is contributed by AnkitRai01 `

Output:

```2
```

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