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 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 Problem

The 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