Parentheses are said to be balanced when every opening brace has a closing brace like “()()” or “(())” or “(()())” etc. Incorrect balancing includes “)(” or “))((” etc. The task here is to correct the sequence of parentheses in such a way that it is done in minimum cost. And shifting of parentheses by over one parentheses costs 1. If the parentheses can’t be balanced then print -1.
Examples :
Input : ()
Output : 0
Explanation : Already balancedInput : ))((
Output : 4
Explanation : Firstly, ) at position 1st goes to the last position, costing 3, so we get )((). Then, ) at position 1st goes to the 2nd position costing 1. So, finally we get ()(). Therefore, the total cost is 4.
Algorithm :
- Store the braces in string.
- Run a loop to string size to store the count of opening and closing braces.
- Check if number of opening brace is equal to number of closing brace or not.
- If the braces are not equal then print -1 depicting that the string cant be balanced. Else proceed further.
- Initially, Check at 0th index that whether the string contains opening brace or closing brace. If we get an opening brace then store +1 in the array at index 0, else if closing brace is present then place -1 at 0th index.
- Now run a loop from 1st index to array length.
- If opening brace is present at index i then add +1 to value at previous index i.e. i-1 and store sum at index i.
- If closing brace is present at index i then add -1 to value at previous index i.e. i-1 and store sum at index i.
- If value at index i is negative i.e less than 0, then add the absolute value of array[i] into a variable(ans in below program).
- Finally we get the minimum cost in variable ans.
Below is the implementation of above approach :
C++
// CPP code to calculate the minimum cost// to make the given parentheses balanced#include <bits/stdc++.h>using namespace std;int costToBalance(string s){ if (s.length() == 0) cout << 0 << endl; // To store absolute count of // balanced and unbalanced parentheses int ans = 0; // o(open bracket) stores count of '(' and // c(close bracket) stores count of ')' int o = 0, c = 0; for (int i = 0; i < s.length(); i++) { if (s[i] == '(') o++; if (s[i] == ')') c++; } if (o != c) return -1; int a[s.size()]; if (s[0] == '(') a[0] = 1; else a[0] = -1; if (a[0] < 0) ans += abs(a[0]); for (int i = 1; i < s.length(); i++) { if (s[i] == '(') a[i] = a[i - 1] + 1; else a[i] = a[i - 1] - 1; if (a[i] < 0) ans += abs(a[i]); } return ans;}// Driver codeint main(){ string s; s = ")))((("; cout << costToBalance(s) << endl; s = "))(("; cout << costToBalance(s) << endl; return 0;} |
Java
// Java code to calculate the // minimum cost to make the // given parentheses balancedimport java.io.*;class GFG{ static int costToBalance(String s) { if (s.length() == 0) System.out.println(0); // To store absolute count // of balanced and unbalanced // parentheses int ans = 0; // o(open bracket) stores count // of '(' and c(close bracket) // stores count of ')' int o = 0, c = 0; for (int i = 0; i < s.length(); i++) { if (s.charAt(i) == '(') o++; if (s.charAt(i) == ')') c++; } if (o != c) return -1; int []a = new int[s.length()]; if (s.charAt(0) == '(') a[0] = 1; else a[0] = -1; if (a[0] < 0) ans += Math.abs(a[0]); for (int i = 1; i < s.length(); i++) { if (s.charAt(i) == '(') a[i] = a[i - 1] + 1; else a[i] = a[i - 1] - 1; if (a[i] < 0) ans += Math.abs(a[i]); } return ans; } // Driver code public static void main(String args[]) { String s; s = ")))((("; System.out.println(costToBalance(s)); s = "))(("; System.out.println(costToBalance(s)); }}// This code is contributed by// Manish Shaw(manishshaw1) |
Python3
# Python 3 code to calculate the minimum cost# to make the given parentheses balanceddef costToBalance(s): if (len(s) == 0): print(0) # To store absolute count of # balanced and unbalanced parenthesis ans = 0 # o(open bracket) stores count of '(' and # c(close bracket) stores count of ')' o = 0 c = 0 for i in range(len(s)): if (s[i] == '('): o += 1 if (s[i] == ')'): c += 1 if (o != c): return -1 a = [0 for i in range(len(s))] if (s[0] == '('): a[0] = 1 else: a[0] = -1 if (a[0] < 0): ans += abs(a[0]) for i in range(1, len(s)): if (s[i] == '('): a[i] = a[i - 1] + 1 else: a[i] = a[i - 1] - 1 if (a[i] < 0): ans += abs(a[i]) return ans# Driver codeif __name__ == '__main__': s = ")))(((" print(costToBalance(s)) s = "))((" print(costToBalance(s)) # This code is contributed by# Surendra_Gangwar |
C#
// C# code to calculate the // minimum cost to make the // given parentheses balancedusing System;class GFG{ static int costToBalance(string s) { if (s.Length == 0) Console.WriteLine(0); // To store absolute count // of balanced and unbalanced // parentheses int ans = 0; // o(open bracket) stores count // of '(' and c(close bracket) // stores count of ')' int o = 0, c = 0; for (int i = 0; i < s.Length; i++) { if (s[i] == '(') o++; if (s[i] == ')') c++; } if (o != c) return -1; int []a = new int[s.Length]; if (s[0] == '(') a[0] = 1; else a[0] = -1; if (a[0] < 0) ans += Math.Abs(a[0]); for (int i = 1; i < s.Length; i++) { if (s[i] == '(') a[i] = a[i - 1] + 1; else a[i] = a[i - 1] - 1; if (a[i] < 0) ans += Math.Abs(a[i]); } return ans; } // Driver code static void Main() { string s; s = ")))((("; Console.WriteLine (costToBalance(s)); s = "))(("; Console.WriteLine (costToBalance(s)); }}// This code is contributed by// Manish Shaw(manishshaw1) |
Javascript
<script>// javascript code to calculate the// minimum cost to make the// given parentheses balanced function costToBalance( s) { if (s.length == 0) document.write(0); // To store absolute count // of balanced and unbalanced // parentheses var ans = 0; // o(open bracket) stores count // of '(' and c(close bracket) // stores count of ')' var o = 0, c = 0; for (var i = 0; i < s.length; i++) { if (s[i] == '(') o++; if (s[i] == ')') c++; } if (o != c) return -1; var a = new Array(s.Length); if (s[0] == '(') a[0] = 1; else a[0] = -1; if (a[0] < 0) ans += Math.abs(a[0]); for (var i = 1; i < s.length; i++) { if (s[i] == '(') a[i] = a[i - 1] + 1; else a[i] = a[i - 1] - 1; if (a[i] < 0) ans += Math.abs(a[i]); } return ans; } // Driver code var s; s = ")))((("; document.write(costToBalance(s) + "<br>"); s = "))(("; document.write(costToBalance(s) + "<br>" );// This code is contributed by bunnyram19.</script> |
Output
9 4
Complexity Analysis:
- Time Complexity: O(N),N=String Length
- Auxiliary Space: O(N)
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