# Minimize Cost to sort a String in Increasing Order of Frequencies of Characters

Given a string S, the task is to calculate the minimum cost to sort the string in increasing order of their frequencies by swapping a block of repeated characters with another block of different repeated characters. The cost of each operation is the absolute difference of the two blocks.
Examples:

Input: S = “aabbcccdeffffggghhhhhii”
Output: 5
Explanation

• Swap ‘d’ with ‘aa’. The Cost of this Operation is 1
• Swap ‘e’ with ‘bb’. The Cost of this Operation is 1
• Swap ‘ii’ with ‘ccc’. The Cost of this Operation is cost is 1
• Swap ‘ccc’ with ‘ffff’. The Cost of this Operation is 1
• Swap ‘ffff’ with ‘hhhhh’. The Cost of this Operation is 1

Input : S = “aaaa”
Output : 0

Approach:
Follow the steps below to solve the problem:

• Store the frequency of each character present in the String.
• Sort the frequencies.
• Calculate the difference between each frequency in the sorted and original sequence.
• Half of the total sum of all the differences is the required answer. This is because, for each swap, the difference is calculated twice in the above step.

Below is the implementation of the above approach:

## C++

 `#include  ` `using` `namespace` `std; `   `int` `sortString(string S) ` `{ `   `    ``vector sorted, original; `   `    ``bool` `insert = ``false``; `   `    ``// For a single character ` `    ``if` `(S.length() == 1) { ` `        ``cout << 0 << endl; ` `    ``} `   `    ``// Stores count of repetitions ` `    ``// of a character ` `    ``int` `curr = 1; `   `    ``for` `(``int` `i = 0; i < (S.length() - 1); i++) { ` `        ``// If repeating character ` `        ``if` `(S[i] == S[i + 1]) { ` `            ``curr += 1; ` `            ``insert = ``false``; ` `        ``} `   `        ``// Otherwise ` `        ``else` `{ ` `            ``// Store frequency ` `            ``sorted.push_back(curr); ` `            ``original.push_back(curr); `   `            ``// Reset count ` `            ``curr = 1; ` `            ``insert = ``true``; ` `        ``} ` `    ``} ` `    ``// Insert the last character block ` `    ``if` `((S[(S.length() - 1)] != S[(S.length() - 2)]) ` `        ``|| insert == ``false``) { ` `        ``sorted.push_back(curr); ` `        ``original.push_back(curr); ` `    ``} `   `    ``// Sort the frequencies ` `    ``sort(sorted.begin(), sorted.end()); `   `    ``// Stores the minimum cost of all operations ` `    ``int` `t_cost = 0; `   `    ``for` `(``int` `i = 0; i < sorted.size(); i++) { ` `        ``// Store the absolute difference of ` `        ``// i-th frequencies of ordered and ` `        ``// unordered sequences ` `        ``t_cost += ``abs``(sorted[i] - original[i]); ` `    ``} `   `    ``// Return the minimum cost ` `    ``return` `(t_cost / 2); ` `} `   `// Driver Code ` `int` `main() ` `{ ` `    ``string S = ``"aabbcccdeffffggghhhhhii"``; ` `    ``cout << sortString(S); `   `    ``return` `0; ` `} `

## Java

 `// Java program to implement ` `// above approach` `import` `java.util.*;` `class` `GFG{` `    `  `public` `static` `int` `sortString(String S) ` `{ `   `    ``Vector sorted = ``new` `Vector();` `    ``Vector original = ``new` `Vector(); `   `    ``boolean` `insert = ``false``; `   `    ``// For a single character ` `    ``if` `(S.length() == ``1``) ` `    ``{ ` `        ``System.out.println(``0``);` `    ``} `   `    ``// Stores count of repetitions ` `    ``// of a character ` `    ``int` `curr = ``1``; `   `    ``for``(``int` `i = ``0``; i < (S.length() - ``1``); i++)` `    ``{` `        `  `        ``// If repeating character ` `        ``if` `(S.charAt(i) == S.charAt(i + ``1``))` `        ``{ ` `            ``curr += ``1``; ` `            ``insert = ``false``; ` `        ``} `   `        ``// Otherwise ` `        ``else` `        ``{` `            `  `            ``// Store frequency ` `            ``sorted.add(curr); ` `            ``original.add(curr); `   `            ``// Reset count ` `            ``curr = ``1``; ` `            ``insert = ``true``; ` `        ``} ` `    ``} ` `    ``// Insert the last character block ` `    ``if` `((S.charAt(S.length() - ``1``) != ` `         ``S.charAt(S.length() - ``2``)) || ` `         ``insert == ``false``) ` `    ``{ ` `        ``sorted.add(curr); ` `        ``original.add(curr); ` `    ``} `   `    ``// Sort the frequencies ` `    ``Collections.sort(sorted); `   `    ``// Stores the minimum cost of all operations ` `    ``int` `t_cost = ``0``; `   `    ``for``(``int` `i = ``0``; i < sorted.size(); i++)` `    ``{` `        `  `        ``// Store the absolute difference of ` `        ``// i-th frequencies of ordered and ` `        ``// unordered sequences ` `        ``t_cost += Math.abs(sorted.get(i) - ` `                         ``original.get(i)); ` `    ``} `   `    ``// Return the minimum cost ` `    ``return` `(t_cost / ``2``); ` `} `   `// Driver code` `public` `static` `void` `main(String[] args)` `{` `    ``String S = ``"aabbcccdeffffggghhhhhii"``; ` `    ``System.out.print(sortString(S));` `}` `}`   `// This code is contributed by divyeshrabadiya07`

## Python3

 `# Python program to implement` `# the above approach` `def` `sortString(S):` `    ``sorted1 ``=` `[]` `    ``original ``=` `[]` `    ``insert ``=` `False`   `    ``# For a single character` `    ``if` `(``len``(S) ``=``=` `1``):` `        ``print``(``0``)`   `    ``# Stores count of repetitions` `    ``# of a character` `    ``curr ``=` `1`   `    ``for` `i ``in` `range``(``len``(S) ``-` `1``):` `        ``# If repeating character` `        ``if` `(S[i] ``=``=` `S[i ``+` `1``]):` `            ``curr ``+``=` `1` `            ``insert ``=` `False`   `        ``# Otherwise` `        ``else``:` `            ``# Store frequency` `            ``sorted1.append(curr)` `            ``original.append(curr)`   `            ``# Reset count` `            ``curr ``=` `1` `            ``insert ``=` `True`   `    ``# Insert the last character block` `    ``if` `((S[(``len``(S) ``-` `1``)] !``=` `S[(``len``(S) ``-` `2``)]) ``or` `         ``insert ``=``=` `False``):` `        ``sorted1.append(curr)` `        ``original.append(curr)`   `    ``# Sort the frequencies` `    ``sorted1.sort()`   `    ``# Stores the minimum cost of all operations` `    ``t_cost ``=` `0`   `    ``for` `i ``in` `range``(``len``(sorted1)):` `      `  `        ``# Store the absolute difference of` `        ``# i-th frequencies of ordered and` `        ``# unordered sequences` `        ``t_cost ``+``=` `abs``(sorted1[i] ``-` `original[i])`   `    ``# Return the minimum cost` `    ``return` `(t_cost ``/``/` `2``)`   `# Driver Code` `if` `__name__ ``=``=` `"__main__"``:` `    ``S ``=` `"aabbcccdeffffggghhhhhii"` `    ``print``(sortString(S))`   `# This code is contributed by Chitranayal`

Output:

```5

```

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

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