Mastering Bracket Problems for Competitive Programming Last Updated : 07 Nov, 2023 Comments Improve Suggest changes Like Article Like Report Bracket problems in programming typically refer to problems that involve working with parentheses, and/or braces in expressions or sequences. It typically refers to problems related to the correct and balanced usage of parentheses, and braces in expressions or code. These problems often involve checking if a given sequence of these symbols is well-formed, meaning that each opening symbol has a corresponding closing symbol in the correct order, and there are no unmatched or incorrectly nested symbols. Why stack is used to solve most of the bracket problems?Stacks are used in most bracket(parenthesis) problems because they provide an elegant and efficient way to handle the balancing and nesting of parentheses. Here are some reasons why stacks are commonly used in these problems: Stacks follow the LIFO principle, meaning that the last element added to the stack is the first one to be removed. This property aligns well with the way parentheses work in expressions. When you encounter a closing parenthesis, you want to match it with the most recently opened parenthesis. Stacks allow you to maintain this order efficiently.A stack is a useful data structure for keeping track of the opening parentheses encountered so far. When a closing parenthesis is encountered, you can efficiently verify if it corresponds to the most recent opening parenthesis on the stack. If they match, you can remove (pop) the opening parenthesis from the stack, indicating that it has been properly closed. This process ensures that the parentheses are balanced and nested correctly in the expression.Balanced Parenthesis ProblemThe most basic problem that falls under this category is balanced parenthesis, which state that Given a string containing various types of parentheses, such as '(', ')', '{', '}', '[', ']', you need to determine if the parentheses are balanced. This problem is solved using a stack data structure. A stack can help you keep track of the opening parentheses you've seen so far. When you encounter a closing parenthesis, you can easily check if the top element of the stack matches it. If it does, you pop the opening parenthesis from the stack, indicating that it has been properly closed. Tip: Most of the bracket problems involves balancing of brackets. Here is the collection of the Top Bracket Problems for practice:Easy:Problems Check if given Parentheses expression is balanced or not Check for Balanc ed Brackets in an expression (well-formedness) Modify a numeric string to a balanced parentheses by replacements Check if the bracket sequence can be balanced with at most one change in the position of a bracket Length of longest balanced parentheses prefix Medium:Problems Number of closing brackets needed to complete a regular bracket sequence Minimum number of Parentheses to be added to make it valid Minimum number of bracket reversals needed to make an expression balanced Find the number of valid parentheses expressions of given length Construct Binary Tree from String with bracket representation Construct a Binary Tree from String with bracket representation | Set 2 Binary tree to string with brackets Print the string obtained after removal of outermost parentheses Hard:Problems Print all combinations of balanced parentheses Length of the longest valid substring Calculate score of parentheses from a given string Count pairs of parentheses sequences such that parentheses are balanced Remove Invalid Parentheses Count removal of pairs required to be empty all Balanced Parenthesis subsequences Minimum sum possible of any bracket sequence of length N Count all indices of cyclic regular parenthesis Check if it is possible to obtain a Balanced Parenthesis by shifting brackets to either end at most K times Pairs involved in Balanced Parentheses Number of ways to partition a string into two balanced subsequences Comment More infoAdvertise with us Next Article Check for balanced with only one type of brackets M mridul_gfg Follow Improve Article Tags : Stack DSA Practice Tags : Stack Similar Reads Mastering Bracket Problems for Competitive Programming Bracket problems in programming typically refer to problems that involve working with parentheses, and/or braces in expressions or sequences. It typically refers to problems related to the correct and balanced usage of parentheses, and braces in expressions or code. These problems often involve chec 4 min read Check for balanced with only one type of brackets Given a string str of length N, consisting of '(' and ')' only, the task is to check whether it is balanced or not.Examples:Input: str = "((()))()()" Output: BalancedInput: str = "())((())" Output: Not Balanced Approach 1: Declare a Flag variable which denotes expression is balanced or not.Initialis 9 min read Valid Parentheses in an Expression Given a string s representing an expression containing various types of brackets: {}, (), and [], the task is to determine whether the brackets in the expression are balanced or not. A balanced expression is one where every opening bracket has a corresponding closing bracket in the correct order.Exa 8 min read Length of longest balanced parentheses prefix Given a string of open bracket '(' and closed bracket ')'. The task is to find the length of longest balanced prefix. Examples: Input : S = "((()())())((" Output : 10From index 0 to index 9, they are forming a balanced parentheses prefix.Input : S = "()(())((()"Output : 6The idea is take value of op 9 min read Modify a numeric string to a balanced parentheses by replacements Given a numeric string S made up of characters '1', '2' and '3' only, the task is to replace characters with either an open bracket ( '(' ) or a closed bracket ( ')' ) such that the newly formed string becomes a balanced bracket sequence. Note: All occurrences of a character must be replaced by the 10 min read Check if the bracket sequence can be balanced with at most one change in the position of a bracket Given an unbalanced bracket sequence as a string str, the task is to find whether the given string can be balanced by moving at most one bracket from its original place in the sequence to any other position.Examples: Input: str = ")(()" Output: Yes As by moving s[0] to the end will make it valid. "( 6 min read Number of closing brackets needed to complete a regular bracket sequence Given an incomplete bracket sequence S. The task is to find the number of closing brackets ')' needed to make it a regular bracket sequence and print the complete bracket sequence. You are allowed to add the brackets only at the end of the given bracket sequence. If it is not possible to complete th 7 min read Minimum number of Parentheses to be added to make it valid Given a string S of parentheses '(' or ')' where, 0\leq len(S)\leq 1000 . The task is to find a minimum number of parentheses '(' or ')' (at any positions) we must add to make the resulting parentheses string is valid. Examples: Input: str = "())" Output: 1 One '(' is required at beginning. Input: s 9 min read Minimum bracket reversals to make an expression balanced 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: s = "}{{}}{{{"Output: 3Explanation: We need to reverse minimum 3 brackets to make "{{{}}{}}". Input: s = "{{"Output: 1Explanation: 15+ min read Find the number of valid parentheses expressions of given length Given a number n, the task is to find the number of valid parentheses expressions of that length. Examples : Input: 2Output: 1 Explanation: There is only possible valid expression of length 2, "()"Input: 4Output: 2 Explanation: Possible valid expression of length 4 are "(())" and "()()" Input: 6Outp 11 min read Like