Lecture 153:- Minimum Bracket Reversal

The problem of finding the minimum number of bracket reversals required to balance a given string of brackets (containing only '{' and '}') can be solved using a stack. Each opening bracket '{' can be paired with a closing bracket '}', and vice versa.

Here's a C++ implementation to find the minimum number of bracket reversals required:

cppCopy code

#include <iostream> #include <stack> int minBracketReversals(const std::string& expression) { int n = expression.length(); // If the length of the expression is odd, it can never be balanced if (n % 2 != 0) { return -1; } std::stack<char> charStack; for (char ch : expression) { if (ch == '{') { charStack.push(ch); } else if (!charStack.empty() && charStack.top() == '{') { charStack.pop(); } else { charStack.push(ch); } } int unbalancedOpenBrackets = 0; int unbalancedClosingBrackets = 0; while (!charStack.empty()) { if (charStack.top() == '{') { unbalancedOpenBrackets++; } else { unbalancedClosingBrackets++; } charStack.pop(); } int totalUnbalanced = unbalancedOpenBrackets + unbalancedClosingBrackets; // The minimum number of reversals required is half of the unbalanced brackets // For example, "{{}{{}}" needs 2 reversals return totalUnbalanced / 2; } int main() { std::string expression = "{{}{{}}}"; int minReversals = minBracketReversals(expression); if (minReversals == -1) { std::cout << "Cannot balance the expression." << std::endl; } else { std::cout << "Minimum bracket reversals required: " << minReversals << std::endl; } return 0; }

In this example, the minBracketReversals function calculates the minimum number of bracket reversals required to balance the given expression. If the length of the expression is odd, it can never be balanced, so the function returns -1 in that case.

For the input "{{}{{}}", the output will be 2, as two reversals are required to balance the expression.

The time complexity of this solution is O(n), where n is the length of the expression, and the space complexity is O(n) due to the stack used for storage.