# Minimize count of given operations required to make two given strings permutations of each other

Given two strings str1 and str2, the task is to count the minimum number of operations of the following three types on one of the two strings that are required to make str1 and str2 permutations of each other:

1. Insert a character into the string.
2. Remove a character from the string.
3. Replace a character by another character from the string.

Note: All the above operations are of equal cost.

Examples:

Input: str1 = “geeksforgeeks”, str2 = “geeksforcoder”
Output: 4
Explanation: Rearrange the string str2 to “geeksforcedor”
Replace the value of str1[8] to ‘c’.
Replace the value of str1[10] to ‘d’.
Replace the value of str1[11] to ‘o’.
Replace the value of str1[12] to ‘r’.
Therefore, the required output is 4.

Input: str1 = “geeks”, str2 = “keeg”
Output: 1

Approach: The problem can be solved using Hashing to store the frequency of each character of both the string. Below are the observations to solve the problem:

X = Number of characters which are present in both string, str1 and str2.
N1 – X = Number of characters present only in str1.
N2 – X = Number of characters present only in str2.
Total number of replacement operations = min(N1 – X, N2 – X)
Total number of insert/rRemove operations = max(N1 – X, N2 – X) – min(N1 – X, N2 – X).
Therefore, total number of operations = max(N1 – X, N2 – X),

Follow the steps below to solve the problem:

1. Initialize two arrays, say freq1[] and freq2[] to store the frequency of all the characters of str1 and str2 respectively.
2. Traverse both the strings and store the frequency of each character of both the strings in arrays freq1[] and freq2[] respectively.
3. Traverse both the arrays freq1[] and freq2[].
4. For every ith character, if freq1[i] exceeds freq2[i], then replace freq1[i] to freq1[i] – freq2[i] and set freq2[i] = 0 and vice-versa.
5. Finally, calculate the sum of the arrays freq1[] and freq2[], and print the maximum between them as the answer

Below is the implement the above approach:

 `// C++ program to implement` `// the above approach`   `#include ` `using` `namespace` `std;`   `// Function to minimize the count of` `// operations to make str1 and str2` `// permutations of each other` `int` `ctMinEdits(string str1, string str2)` `{` `    ``int` `N1 = str1.length();` `    ``int` `N2 = str2.length();`   `    ``// Store the frequency of` `    ``// each character of str1` `    ``int` `freq1[256] = { 0 };` `    ``for` `(``int` `i = 0; i < N1; i++) {` `        ``freq1[str1[i]]++;` `    ``}`   `    ``// Store the frequency of` `    ``// each character of str2` `    ``int` `freq2[256] = { 0 };` `    ``for` `(``int` `i = 0; i < N2; i++) {` `        ``freq2[str2[i]]++;` `    ``}`   `    ``// Traverse the freq1[] and freq2[]` `    ``for` `(``int` `i = 0; i < 256; i++) {`   `        ``// If frequency of character in` `        ``// str1 is greater than str2` `        ``if` `(freq1[i] > freq2[i]) {` `            ``freq1[i] = freq1[i]` `                       ``- freq2[i];` `            ``freq2[i] = 0;` `        ``}`   `        ``// Otherwise` `        ``else` `{` `            ``freq2[i] = freq2[i]` `                       ``- freq1[i];` `            ``freq1[i] = 0;` `        ``}` `    ``}`   `    ``// Store sum of freq1[]` `    ``int` `sum1 = 0;`   `    ``// Store sum of freq2[]` `    ``int` `sum2 = 0;`   `    ``for` `(``int` `i = 0; i < 256; i++) {` `        ``sum1 += freq1[i];` `        ``sum2 += freq2[i];` `    ``}`   `    ``return` `max(sum1, sum2);` `}`   `// Driver Code` `int` `main()` `{` `    ``string str1 = ``"geeksforgeeks"``;` `    ``string str2 = ``"geeksforcoder"``;` `    ``cout << ctMinEdits(str1, str2);` `}`

 `// Java program to implement ` `// the above approach ` `import` `java.util.*;` `import` `java.io.*;` `import` `java.lang.Math;`   `class` `GFG{` `    `  `// Function to minimize the count of ` `// operations to make str1 and str2 ` `// permutations of each other ` `static` `int` `ctMinEdits(String str1, String str2) ` `{ ` `    ``int` `N1 = str1.length(); ` `    ``int` `N2 = str2.length(); ` `  `  `    ``// Store the frequency of ` `    ``// each character of str1 ` `    ``int` `freq1[] = ``new` `int``[``256``];` `    ``Arrays.fill(freq1, ``0``);` `    `  `    ``for``(``int` `i = ``0``; i < N1; i++)` `    ``{ ` `        ``freq1[str1.charAt(i)]++; ` `    ``} ` `  `  `    ``// Store the frequency of ` `    ``// each character of str2 ` `    ``int` `freq2[] = ``new` `int``[``256``];` `    ``Arrays.fill(freq2, ``0``);` `    `  `    ``for``(``int` `i = ``0``; i < N2; i++)` `    ``{ ` `        ``freq2[str2.charAt(i)]++; ` `    ``} ` `  `  `    ``// Traverse the freq1[] and freq2[] ` `    ``for``(``int` `i = ``0``; i < ``256``; i++)` `    ``{ ` `        `  `        ``// If frequency of character in ` `        ``// str1 is greater than str2 ` `        ``if` `(freq1[i] > freq2[i]) ` `        ``{ ` `            ``freq1[i] = freq1[i] - freq2[i]; ` `            ``freq2[i] = ``0``; ` `        ``} ` `  `  `        ``// Otherwise ` `        ``else` `        ``{ ` `            ``freq2[i] = freq2[i] - freq1[i]; ` `            ``freq1[i] = ``0``; ` `        ``} ` `    ``} ` `  `  `    ``// Store sum of freq1[] ` `    ``int` `sum1 = ``0``; ` `  `  `    ``// Store sum of freq2[] ` `    ``int` `sum2 = ``0``; ` `  `  `    ``for``(``int` `i = ``0``; i < ``256``; i++)` `    ``{ ` `        ``sum1 += freq1[i]; ` `        ``sum2 += freq2[i]; ` `    ``} ` `  `  `    ``return` `Math.max(sum1, sum2); ` `} `   `// Driver Code` `public` `static` `void` `main(``final` `String[] args) ` `{` `    ``String str1 = ``"geeksforgeeks"``; ` `    ``String str2 = ``"geeksforcoder"``; ` `    `  `    ``System.out.println(ctMinEdits(str1, str2)); ` `}` `}`   `// This code is contributed by bikram2001jha`

 `# Python3 program to implement` `# the above approach` ` `  `# Function to minimize the count of` `# operations to make str1 and str2` `# permutations of each other` `def` `ctMinEdits(str1, str2):` `    `  `    ``N1 ``=` `len``(str1)` `    ``N2 ``=` `len``(str2)` ` `  `    ``# Store the frequency of` `    ``# each character of str1` `    ``freq1 ``=`  `[``0``] ``*` `256` `    ``for` `i ``in` `range``(N1):` `        ``freq1[``ord``(str1[i])] ``+``=` `1` `    `  `    ``# Store the frequency of` `    ``# each character of str2` `    ``freq2 ``=` `[``0``] ``*` `256` `    ``for` `i ``in` `range``(N2):` `        ``freq2[``ord``(str2[i])] ``+``=` `1` `    `  `    ``# Traverse the freq1[] and freq2[]` `    ``for` `i ``in` `range``(``256``):` ` `  `        ``# If frequency of character in` `        ``# str1 is greater than str2` `        ``if` `(freq1[i] > freq2[i]):` `            ``freq1[i] ``=` `freq1[i] ``-` `freq2[i]` `            ``freq2[i] ``=` `0` ` `  `        ``# Otherwise` `        ``else``:` `            ``freq2[i] ``=` `freq2[i] ``-` `freq1[i]` `            ``freq1[i] ``=` `0` `        `  `    ``# Store sum of freq1[]` `    ``sum1 ``=` `0` ` `  `    ``# Store sum of freq2[]` `    ``sum2 ``=` `0` ` `  `    ``for` `i ``in` `range``(``256``):` `        ``sum1 ``+``=` `freq1[i]` `        ``sum2 ``+``=` `freq2[i]` `    `  `    ``return` `max``(sum1, sum2)`   `# Driver Code` `str1 ``=` `"geeksforgeeks"` `str2 ``=` `"geeksforcoder"`   `print``(ctMinEdits(str1, str2))`   `# This code is contributed by code_hunt`

 `// C# program to implement` `// the above approach` `using` `System;`   `class` `GFG{` `     `  `// Function to minimize the count of ` `// operations to make str1 and str2 ` `// permutations of each other ` `static` `int` `ctMinEdits(``string` `str1, ``string` `str2) ` `{ ` `    ``int` `N1 = str1.Length; ` `    ``int` `N2 = str2.Length; ` `   `  `    ``// Store the frequency of ` `    ``// each character of str1 ` `    ``int``[] freq1 = ``new` `int``[256];` `    ``freq1[0] = str1[0]; ` `     `  `    ``for``(``int` `i = 0; i < N1; i++)` `    ``{ ` `        ``freq1[str1[i]]++; ` `    ``} ` `   `  `    ``// Store the frequency of ` `    ``// each character of str2 ` `    ``int``[] freq2 = ``new` `int``[256];` `    ``freq2[0] = str2[0]; ` `     `  `    ``for``(``int` `i = 0; i < N2; i++)` `    ``{ ` `        ``freq2[str2[i]]++; ` `    ``} ` `   `  `    ``// Traverse the freq1[] and freq2[] ` `    ``for``(``int` `i = 0; i < 256; i++)` `    ``{ ` `        `  `        ``// If frequency of character in ` `        ``// str1 is greater than str2 ` `        ``if` `(freq1[i] > freq2[i]) ` `        ``{ ` `            ``freq1[i] = freq1[i] - freq2[i]; ` `            ``freq2[i] = 0; ` `        ``} ` `   `  `        ``// Otherwise ` `        ``else` `        ``{ ` `            ``freq2[i] = freq2[i] - freq1[i]; ` `            ``freq1[i] = 0; ` `        ``} ` `    ``} ` `   `  `    ``// Store sum of freq1[] ` `    ``int` `sum1 = 0; ` `   `  `    ``// Store sum of freq2[] ` `    ``int` `sum2 = 0; ` `   `  `    ``for``(``int` `i = 0; i < 256; i++)` `    ``{ ` `        ``sum1 += freq1[i]; ` `        ``sum2 += freq2[i]; ` `    ``} ` `    ``return` `Math.Max(sum1, sum2); ` `} ` ` `  `// Driver Code` `public` `static` `void` `Main() ` `{` `    ``string` `str1 = ``"geeksforgeeks"``; ` `    ``string` `str2 = ``"geeksforcoder"``; ` `     `  `    ``Console.WriteLine(ctMinEdits(str1, str2)); ` `}` `}`   `// This code is contributed by code_hunt`

Output:
```4

```

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

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Improved By : bikram2001jha, code_hunt

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