# Shortest string possible after removal of all pairs of similar adjacent characters

Given a string S, the task is to find the resultant smallest string possible, formed by repeatedly removing pairs of adjacent characters which are equal.

Examples:

Input: S = “aaabccddd”
Output: abd
Explanation: Following sequence of removal of pairs of adjacent characters minimizes the length of the string:
aaabccddd ? abccddd ? abddd ? abd.

Input: S = aa
Output: Empty String
Explanation: Following sequence of removal of pairs of adjacent characters minimizes the length of the string:
aa ? “”.

Approach: The main idea to solve the given problem is to recursively delete all pairs of adjacent characters which are equal, one by one. Follow the steps to solve the given problem:

• Initialize an empty string, say ans, to store the string of minimum length after deleting all pairs of equal adjacent characters.
• Initialize a string, say pre, to store the updated string after every removal of equal adjacent characters.
• Now, iterate until the string ans and pre are unequal and perform the following steps:
• Update the value of the string ans by removing the first adjacent same character using the function removeAdjacent().
• If the value of the string ans is the same as the string pre, then break out of the loop. Otherwise, update the value of string pre as the string ans.
• After completing the above steps, print the string ans as the resultant string.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to delete pair of adjacent ``// characters which are equal ``string removeAdjacent(string s) ``{ ``    ` `    ``// Base Case ``    ``if` `(s.length() == 1) ``        ``return` `s; ` `    ``// Stores the update string ``    ``string sb = ``""``; ` `    ``// Traverse the string s ``    ``for``(``int` `i = 0; i < s.length() - 1; i++)``    ``{ ``        ``char` `c = s[i];``        ``char` `d = s[i + 1]; ` `        ``// If two unequal pair of ``        ``// adjacent characters are found ``        ``if` `(c != d)``        ``{``            ``sb = sb + c; ` `            ``if` `(i == s.length() - 2)``            ``{ ``                ``sb = sb + d; ``            ``} ``        ``} ` `        ``// If two equal pair of adjacent ``        ``// characters are found ``        ``else``        ``{ ``            ``for``(``int` `j = i + 2; ``                    ``j < s.length(); j++) ` `                ``// Append the remaining string ``                ``// after removing the pair ``                ``sb = sb + s[j]; ` `            ``return` `sb; ``        ``} ``    ``} ` `    ``// Return the final String ``    ``return` `sb; ``} ` `// Function to find the shortest string ``// after repeatedly removing pairs of ``// adjacent characters which are equal ``void` `reduceString(string s) ``{ ``    ` `    ``// Stores the resultant String ``    ``string result = ``""``; ` `    ``// Keeps track of previously ``    ``// iterated string ``    ``string pre = s; ` `    ``while` `(``true``)``    ``{``        ` `        ``// Update the result after ``        ``// deleting adjacent pair of ``        ``// characters which are similar ``        ``result = removeAdjacent(pre); ` `        ``// Termination Conditions ``        ``if` `(result == pre) ``            ``break``; ` `        ``// Update pre variable with ``        ``// the value of result ``        ``pre = result; ``    ``} ` `    ``if` `(result.length() != 0) ``        ``cout << (result) << endl; ` `    ``// Case for "Empty String" ``    ``else``        ``cout << ``"Empty String"` `<< endl; ``} ` `// Driver code    ``int` `main()``{``    ``string S = ``"aaabccddd"``; ``    ` `    ``reduceString(S); ``    ` `    ``return` `0;``}` `// This code is contributed by divyesh072019`

## Java

 `// Java program for the above approach` `import` `java.io.*;``import` `java.lang.*;``import` `java.util.*;` `class` `GFG {` `    ``// Function to delete pair of adjacent``    ``// characters which are equal``    ``static` `String removeAdjacent(String s)``    ``{``        ``// Base Case``        ``if` `(s.length() == ``1``)``            ``return` `s;` `        ``// Stores the update string``        ``StringBuilder sb = ``new` `StringBuilder(``""``);` `        ``// Traverse the string s``        ``for` `(``int` `i = ``0``;``             ``i < s.length() - ``1``; i++) {``            ``char` `c = s.charAt(i);``            ``char` `d = s.charAt(i + ``1``);` `            ``// If two unequal pair of``            ``// adjacent characters are found``            ``if` `(c != d) {``                ``sb.append(c);` `                ``if` `(i == s.length() - ``2``) {``                    ``sb.append(d);``                ``}``            ``}` `            ``// If two equal pair of adjacent``            ``// characters are found``            ``else` `{``                ``for` `(``int` `j = i + ``2``;``                     ``j < s.length(); j++)` `                    ``// Append the remaining string``                    ``// after removing the pair``                    ``sb.append(s.charAt(j));` `                ``return` `sb.toString();``            ``}``        ``}` `        ``// Return the final String``        ``return` `sb.toString();``    ``}` `    ``// Function to find the shortest string``    ``// after repeatedly removing pairs of``    ``// adjacent characters which are equal``    ``public` `static` `void` `reduceString(String s)``    ``{``        ``// Stores the resultant String``        ``String result = ``""``;` `        ``// Keeps track of previously``        ``// iterated string``        ``String pre = s;` `        ``while` `(``true``) {``            ``// Update the result after``            ``// deleting adjacent pair of``            ``// characters which are similar``            ``result = removeAdjacent(pre);` `            ``// Termination Conditions``            ``if` `(result.equals(pre))``                ``break``;` `            ``// Update pre variable with``            ``// the value of result``            ``pre = result;``        ``}` `        ``if` `(result.length() != ``0``)``            ``System.out.println(result);` `        ``// Case for "Empty String"``        ``else``            ``System.out.println(``"Empty String"``);``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``String S = ``"aaabccddd"``;``        ``reduceString(S);``    ``}``}`

## Python3

 `# Python program for the above approach` `# Function to delete pair of adjacent``# characters which are equal``def` `removeAdjacent(s):``    ` `    ``# Base Case``    ``if` `(``len``(s) ``=``=` `1``):``        ``return` `s` `    ``# Stores the update string``    ``sb ``=` `""` `    ``# Traverse the string s``    ``for` `i ``in` `range``(``len``(s)``-``1``):``        ``c ``=` `s[i]``        ``d ``=` `s[i ``+` `1``]` `        ``# If two unequal pair of``        ``# adjacent characters are found``        ``if` `(c !``=` `d):``            ``sb ``=` `sb ``+` `c` `            ``if` `(i ``=``=` `len``(s) ``-` `2``):``                ``sb ``=` `sb ``+` `d` `        ``# If two equal pair of adjacent``        ``# characters are found``        ``else``:``            ``for` `j ``in` `range``(i ``+` `2``,``len``(s)):` `                ``# Append the remaining string``                ``# after removing the pair``                ``sb ``=` `sb ``+` `s[j]` `            ``return` `sb` `    ``# Return the final String``    ``return` `sb` `# Function to find the shortest string``# after repeatedly removing pairs of``# adjacent characters which are equal``def` `reduceString(s):``    ` `    ``# Stores the resultant String``    ``result ``=` `""` `    ``# Keeps track of previously``    ``# iterated string``    ``pre ``=` `s` `    ``while` `True``:``        ` `        ``# Update the result after``        ``# deleting adjacent pair of``        ``# characters which are similar``        ``result ``=` `removeAdjacent(pre)` `        ``# Termination Conditions``        ``if` `(result ``=``=` `pre):``            ``break` `        ``# Update pre variable with``        ``# the value of result``        ``pre ``=` `result` `    ``if` `(``len``(result)!``=` `0``):``        ``print``(result)` `    ``# Case for "Empty String"``    ``else``:``        ``print``(``"Empty String"``)` `# Driver code``S ``=` `"aaabccddd"``reduceString(S)``    ` `# This code is contributed by shinjanpatra`

## C#

 `// C# program for the above approach``using` `System;``class` `GFG {``    ` `    ``// Function to delete pair of adjacent ``    ``// characters which are equal ``    ``static` `string` `removeAdjacent(``string` `s) ``    ``{ ``         ` `        ``// Base Case ``        ``if` `(s.Length == 1) ``            ``return` `s; ``     ` `        ``// Stores the update string ``        ``string` `sb = ``""``; ``     ` `        ``// Traverse the string s ``        ``for``(``int` `i = 0; i < s.Length - 1; i++)``        ``{ ``            ``char` `c = s[i];``            ``char` `d = s[i + 1]; ``     ` `            ``// If two unequal pair of ``            ``// adjacent characters are found ``            ``if` `(c != d)``            ``{``                ``sb = sb + c; ``     ` `                ``if` `(i == s.Length - 2)``                ``{ ``                    ``sb = sb + d; ``                ``} ``            ``} ``     ` `            ``// If two equal pair of adjacent ``            ``// characters are found ``            ``else``            ``{ ``                ``for``(``int` `j = i + 2; ``                        ``j < s.Length; j++) ``     ` `                    ``// Append the remaining string ``                    ``// after removing the pair ``                    ``sb = sb + s[j]; ``     ` `                ``return` `sb; ``            ``} ``        ``} ``     ` `        ``// Return the final String ``        ``return` `sb; ``    ``} ``     ` `    ``// Function to find the shortest string ``    ``// after repeatedly removing pairs of ``    ``// adjacent characters which are equal ``    ``static` `void` `reduceString(``string` `s) ``    ``{ ``         ` `        ``// Stores the resultant String ``        ``string` `result = ``""``; ``     ` `        ``// Keeps track of previously ``        ``// iterated string ``        ``string` `pre = s; ``     ` `        ``while` `(``true``)``        ``{``             ` `            ``// Update the result after ``            ``// deleting adjacent pair of ``            ``// characters which are similar ``            ``result = removeAdjacent(pre); ``     ` `            ``// Termination Conditions ``            ``if` `(result == pre) ``                ``break``; ``     ` `            ``// Update pre variable with ``            ``// the value of result ``            ``pre = result; ``        ``} ``     ` `        ``if` `(result.Length != 0) ``            ``Console.WriteLine(result); ``     ` `        ``// Case for "Empty String" ``        ``else``            ``Console.WriteLine(``"Empty String"``); ``    ``} ` `  ``static` `void` `Main() {``    ``string` `S = ``"aaabccddd"``; ``     ` `    ``reduceString(S); ``  ``}``}`

## Javascript

 ``

Output:
`abd`

Time Complexity: O(N2)
Auxiliary Space: O(N)

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