Related Articles

# Number of ways to insert two pairs of parentheses into a string of N characters

• Last Updated : 01 Apr, 2021

Given a string str of length N, the task is to find the number of ways to insert only 2 pairs of parentheses into the given string such that the resultant string is still valid.
Examples:

Input: str = “ab”
Output:
((a))b, ((a)b), ((ab)), (a)(b), (a(b)), a((b))
which are a total of 6 ways.
Input: str = “aab”
Output: 20

Approach: it can be observed that for the lengths of the string 1, 2, 3, …, N a series will be formed as 1, 6, 20, 50, 105, 196, 336, 540, … whose Nth term is (N + 1)2 * ((N + 1)2 – 1) / 12.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to return the number of ways``// to insert the bracket pairs``int` `cntWays(string str, ``int` `n)``{``    ``int` `x = n + 1;``    ``int` `ways = x * x * (x * x - 1) / 12;``    ``return` `ways;``}` `// Driver code``int` `main()``{``    ``string str = ``"ab"``;``    ``int` `n = str.length();` `    ``cout << cntWays(str, n);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``import` `java.util.*;` `class` `GFG``{` `// Function to return the number of ways``// to insert the bracket pairs``static` `int` `cntWays(String str, ``int` `n)``{``    ``int` `x = n + ``1``;``    ``int` `ways = x * x * (x * x - ``1``) / ``12``;``    ``return` `ways;``}` `// Driver code``public` `static` `void` `main(String []args)``{``    ``String str = ``"ab"``;``    ``int` `n = str.length();` `    ``System.out.println(cntWays(str, n));``}``}` `// This code is contributed by Rajput-Ji`

## Python3

 `# Python3 implementation of the approach` `# Function to return the number of ways``# to insert the bracket pairs``def` `cntWays(string, n) :` `    ``x ``=` `n ``+` `1``;``    ``ways ``=` `x ``*` `x ``*` `(x ``*` `x ``-` `1``) ``/``/` `12``;``    ``return` `ways;` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:` `    ``string ``=` `"ab"``;``    ``n ``=` `len``(string);` `    ``print``(cntWays(string, n));` `# This code is contributed by AnkitRai01`

## C#

 `// C# implementation of the approach``using` `System;``    ` `class` `GFG``{` `// Function to return the number of ways``// to insert the bracket pairs``static` `int` `cntWays(String str, ``int` `n)``{``    ``int` `x = n + 1;``    ``int` `ways = x * x * (x * x - 1) / 12;``    ``return` `ways;``}` `// Driver code``public` `static` `void` `Main(String []args)``{``    ``String str = ``"ab"``;``    ``int` `n = str.Length;` `    ``Console.WriteLine(cntWays(str, n));``}``}` `// This code is contributed by Rajput-Ji`

## Javascript

 ``
Output:
`6`

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

My Personal Notes arrow_drop_up