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: 6
((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 <bits/stdc++.h>using namespace std;// Function to return the number of ways// to insert the bracket pairsint cntWays(string str, int n){ int x = n + 1; int ways = x * x * (x * x - 1) / 12; return ways;}// Driver codeint main(){ string str = "ab"; int n = str.length(); cout << cntWays(str, n); return 0;} |
Java
// Java implementation of the approachimport java.util.*;class GFG{// Function to return the number of ways// to insert the bracket pairsstatic int cntWays(String str, int n){ int x = n + 1; int ways = x * x * (x * x - 1) / 12; return ways;}// Driver codepublic 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 approachusing System; class GFG{// Function to return the number of ways// to insert the bracket pairsstatic int cntWays(String str, int n){ int x = n + 1; int ways = x * x * (x * x - 1) / 12; return ways;}// Driver codepublic 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
<script>// Javascript implementation of the approach// Function to return the number of ways// to insert the bracket pairsfunction cntWays(str, n){ var x = n + 1; var ways = x * x * (x * x - 1) / 12; return ways;}// Driver codevar str = "ab";var n = str.length;document.write(cntWays(str, n));// This code is contributed by rutvik_56.</script> |
Output:
6
Time Complexity: O(1)
Auxiliary Space: O(1)
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