Given a string str which contains pairs of balanced parentheses, the task is to calculate the score of the given string based on the given rules:
- “()” has a score of 1.
- “x y” has a score of x + y where x and y are individual pairs of balanced parentheses.
- “(x)” has a score twice of x (i.e), the score is 2 * score of x.
Examples:
Input: str = “()()”
Output: 2
Explanation:
Here input is of the form “xy” which makes the total score = score of x + score of y
and hence, score = 1 + 1 = 2Input: str = “(())”
Output: 2
Explanation:
Here input is of the form “(x)” which makes the total score = 2 * score of x
and hence, score = 2 * 1 = 2Input: str = “(()()())”
Output: 6
Explanation:
Here input is of the form “(xyz)” which makes the total score = 2 * (score of x +
score of y + score of z) and hence 2*(1 + 1 + 1) = 6
Approach: The idea is to use a tree data structure to solve this problem along with Recursion.
- The root node of our tree structure will represent the outermost pair of our input parentheses.
- For every pair of balanced parentheses included inside the outermost parentheses, we will add a child to our root node.
- This process of declaring a child to a root node will be recursive and hence it will create a node in our tree structure for every pair of balanced parentheses in a hierarchy.
- Every balanced pair of parentheses will be considered as outermost (recursively) and generate a node and hence will allow us to calculate the score.
- When computing score, each leaf node of our tree will be considered with a score of 1 and to get the score of its respective root node we need to add the scores of each child node and double that aggregate.
- The diagram below shows the recursive structure of the tree generated and we start from the bottom to calculate the scores at each level until we reach the outermost ending parentheses.
Below is the implementation of the above approach:
C++
// C++ program to find the score of// parentheses using Tree#include <iostream>#include <vector>using namespace std;// Customized tree class or struct,// contains all required methods.class TreeNode { TreeNode* parent = NULL; vector<TreeNode*> children;public: // Function to add a child into // the list of children void addChild(TreeNode* node) { children.push_back(node); } // Function to change the parent // pointer to the node passed void setParent(TreeNode* node) { parent = node; } // Function to return the parent // of the current node TreeNode* getParent() { return parent; } // Function to compute the score recursively. int computeScore() { // Base case if (children.size() == 0) return 1; int res = 0; // Adds scores of all children for (TreeNode* curr : children) res += curr->computeScore(); if (parent == NULL) return res; else return 2 * res; }};// Function to create the tree structureTreeNode* computeTree(string s){ TreeNode* current = new TreeNode(); TreeNode* root = current; // Creating a node for every "()" for (int i = 0; i < s.size(); i++) { // If we find "(" we add a node as // a child if (s[i] == '(') { TreeNode* child = new TreeNode(); child->setParent(current); current->addChild(child); current = child; } // On finding ")" which confirms that // a pair is closed, we go back // to the parent else { current = current->getParent(); } } return root;}// Driver codeint main(){ string s = "(()(()))"; // Generating the tree TreeNode* root = computeTree(s); // Computing the score cout << root->computeScore(); return 0;} |
Java
// Java program to find the score of// parentheses using Treeimport java.util.*;public class Main{ // Customized tree class or struct, // contains all required methods. static class TreeNode { public TreeNode parent = null; public Vector<TreeNode> children = new Vector<TreeNode>(); // Function to add a child into // the list of children public void addChild(TreeNode node) { children.add(node); } // Function to change the parent // pointer to the node passed public void setParent(TreeNode node) { parent = node; } // Function to return the parent // of the current node public TreeNode getParent() { return parent; } // Function to compute the score // recursively. public int computeScore() { // Base case if (children.size() == 0) return 1; int res = 0; // Adds scores of all children for(TreeNode curr : children) res += curr.computeScore(); if (parent == null) return res; else return 2 * res; } } // Function to create the tree structure static TreeNode computeTree(String s) { TreeNode current = new TreeNode(); TreeNode root = current; // Creating a node for every "()" for(int i = 0; i < s.length(); i++) { // If we find "(" we add a node as // a child if (s.charAt(i) == '(') { TreeNode child = new TreeNode(); child.setParent(current); current.addChild(child); current = child; } // On finding ")" which confirms that // a pair is closed, we go back // to the parent else { current = current.getParent(); } } return root; } public static void main(String[] args) { String s = "(()(()))"; // Generating the tree TreeNode root = computeTree(s); // Computing the score System.out.print(root.computeScore()); }}// This code is contributed by suresh07. |
Python3
# Python3 program to find the score of# parentheses using Tree # Customized tree class or struct,# contains all required methods.class TreeNode: def __init__(self): self.parent = None self.children = [] # Function to add a child into # the list of children def addChild(self, node): self.children.append(node); # Function to change the parent # pointer to the node passed def setParent(self, node): self.parent = node; # Function to return the parent # of the current node def getParent(self): return self.parent; # Function to compute the score recursively. def computeScore(self): # Base case if (len(self.children) == 0): return 1; res = 0; # Adds scores of all children for curr in self.children: res += curr.computeScore(); if (self.parent == None): return res; else: return 2 * res; # Function to create the tree structuredef computeTree(s): current = TreeNode(); root = current; # Creating a node for every "()" for i in range(len(s)): # If we find "(" we add a node as # a child if (s[i] == '('): child = TreeNode(); child.setParent(current); current.addChild(child); current = child; # On finding ")" which confirms that # a pair is closed, we go back # to the parent else: current = current.getParent(); return root;# Driver codeif __name__=='__main__': s = "(()(()))"; # Generating the tree root = computeTree(s); # Computing the score print(root.computeScore()) # This code is contributed by rutvik_56 |
C#
// C# program to find the score of// parentheses using Treeusing System;using System.Collections;class GFG{ // Customized tree class or struct,// contains all required methods.class TreeNode { public TreeNode parent = null; public ArrayList children = new ArrayList(); // Function to add a child into // the list of children public void addChild(TreeNode node) { children.Add(node); } // Function to change the parent // pointer to the node passed public void setParent(TreeNode node) { parent = node; } // Function to return the parent // of the current node public TreeNode getParent() { return parent; } // Function to compute the score // recursively. public int computeScore() { // Base case if (children.Count == 0) return 1; int res = 0; // Adds scores of all children foreach(TreeNode curr in children) res += curr.computeScore(); if (parent == null) return res; else return 2 * res; }}; // Function to create the tree structurestatic TreeNode computeTree(string s){ TreeNode current = new TreeNode(); TreeNode root = current; // Creating a node for every "()" for(int i = 0; i < s.Length; i++) { // If we find "(" we add a node as // a child if (s[i] == '(') { TreeNode child = new TreeNode(); child.setParent(current); current.addChild(child); current = child; } // On finding ")" which confirms that // a pair is closed, we go back // to the parent else { current = current.getParent(); } } return root;} // Driver codepublic static void Main(){ string s = "(()(()))"; // Generating the tree TreeNode root = computeTree(s); // Computing the score Console.Write(root.computeScore());}}// This code is contributed by pratham76 |
Javascript
// JavaScript code for the above approach // Customized tree class or struct, // contains all required methods. class TreeNode { constructor() { this.parent = null; this.children = []; } // Function to add a child into // the list of children addChild(node) { this.children.push(node); } // Function to change the parent // pointer to the node passed setParent(node) { this.parent = node; } // Function to return the parent // of the current node getParent() { return this.parent; } // Function to compute the score recursively. computeScore() { // Base case if (this.children.length === 0) return 1; let res = 0; // Adds scores of all children for (let curr of this.children) res += curr.computeScore(); if (this.parent === null) return res; else return 2 * res; } } // Function to create the tree structure function computeTree(s) { let current = new TreeNode(); let root = current; // Creating a node for every "()" for (let i = 0; i < s.length; i++) { // If we find "(" we add a node as // a child if (s[i] === '(') { let child = new TreeNode(); child.setParent(current); current.addChild(child); current = child; } // On finding ")" which confirms that // a pair is closed, we go back // to the parent else { current = current.getParent(); } } return root; } // Driver code let s = '(()(()))'; // Generating the tree let root = computeTree(s); // Computing the score console.log(root.computeScore());// This code is contributed by Potta Lokesh. |
Output:
6
Time Complexity: O(N), where N is the length of the input string.
Space Complexity: O(N), where N is the length of the input string.
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