Given an expression with only ‘}’ and ‘{‘. The expression may not be balanced. Find minimum number of bracket reversals to make the expression balanced.

Examples:

Input: exp = "}{" Output: 2 We need to change '}' to '{' and '{' to '}' so that the expression becomes balanced, the balanced expression is '{}' Input: exp = "{{{" Output: Can't be made balanced using reversals Input: exp = "{{{{" Output: 2 Input: exp = "{{{{}}" Output: 1 Input: exp = "}{{}}{{{" Output: 3

One simple observation is, the string can be balanced only if total number of brackets is even (there must be equal no of ‘{‘ and ‘}’)

A **Naive Solution** is to consider every bracket and recursively count number of reversals by taking two cases (i) keeping the bracket as it is (ii) reversing the bracket. If we get a balanced expression, we update result if number of steps followed for reaching here is smaller than the minimum so far. Time complexity of this solution is O(2^{n}).

An **Efficient Solution** can solve this problem in O(n) time. The idea is to first remove all balanced part of expression. For example, convert “}**{{}}**{{{” to “}{{{” by removing highlighted part. If we take a closer look, we can notice that, after removing balanced part, we always end up with an expression of the form }}…}{{…{, an expression that contains 0 or more number of closing brackets followed by 0 or more numbers of opening brackets.

How many minimum reversals are required for an expression of the form “}}..}{{..{” ?. Let m be the total number of closing brackets and n be the number of opening brackets. We need ⌈m/2⌉ + ⌈n/2⌉ reversals. For example }}}}{{ requires 2+1 reversals.

Below is implementation of above idea.

## C++

// C++ program to find minimum number of // reversals required to balance an expression #include<bits/stdc++.h> using namespace std; // Returns count of minimum reversals for making // expr balanced. Returns -1 if expr cannot be // balanced. int countMinReversals(string expr) { int len = expr.length(); // length of expression must be even to make // it balanced by using reversals. if (len%2) return -1; // After this loop, stack contains unbalanced // part of expression, i.e., expression of the // form "}}..}{{..{" stack<char> s; for (int i=0; i<len; i++) { if (expr[i]=='}' && !s.empty()) { if (s.top()=='{') s.pop(); else s.push(expr[i]); } else s.push(expr[i]); } // Length of the reduced expression // red_len = (m+n) int red_len = s.size(); // count opening brackets at the end of // stack int n = 0; while (!s.empty() && s.top() == '{') { s.pop(); n++; } // return ceil(m/2) + ceil(n/2) which is // actually equal to (m+n)/2 + n%2 when // m+n is even. return (red_len/2 + n%2); } // Driver program to test above function int main() { string expr = "}}{{"; cout << countMinReversals(expr); return 0; }

## Java

//Java Code to count minimum reversal for //making an expression balanced. import java.util.Stack; public class GFG { // Method count minimum reversal for //making an expression balanced. //Returns -1 if expression cannot be balanced static int countMinReversals(String expr) { int len = expr.length(); // length of expression must be even to make // it balanced by using reversals. if (len%2 != 0) return -1; // After this loop, stack contains unbalanced // part of expression, i.e., expression of the // form "}}..}{{..{" Stack<Character> s=new Stack<>(); for (int i=0; i<len; i++) { char c = expr.charAt(i); if (c =='}' && !s.empty()) { if (s.peek()=='{') s.pop(); else s.push(c); } else s.push(c); } // Length of the reduced expression // red_len = (m+n) int red_len = s.size(); // count opening brackets at the end of // stack int n = 0; while (!s.empty() && s.peek() == '{') { s.pop(); n++; } // return ceil(m/2) + ceil(n/2) which is // actually equal to (m+n)/2 + n%2 when // m+n is even. return (red_len/2 + n%2); } // Driver method public static void main(String[] args) { String expr = "}}{{"; System.out.println(countMinReversals(expr)); } } //This code is contributed by Sumit Ghosh

Output:

2

Time Complexity: O(n)

Auxiliary Space: O(n)

Thanks to Utkarsh Trivedi for suggesting above approach.

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