Below is a comprehensive study guide for stack-based problems. This guide is divided into two main sections:
Each section includes examples and references to the specific problems and solution outlines in this collection (e.g., Valid Parentheses, Basic Calculator, Evaluate Reverse Polish Notation, Min Stack, and Simplify Path).
Stack problems typically share common characteristics that make a stack the natural data structure to use. Here are key identifiers:
Nested or Hierarchical Structures:
Many problems involve nested or hierarchically organized data. For example, checking balanced brackets in Valid Parentheses or interpreting nested arithmetic expressions in Basic Calculator both require you to “remember” the context (or state) as you dive into inner levels. The Last-In-First-Out (LIFO) property of stacks suits these patterns perfectly.
Backtracking and Reversal:
Stacks naturally support scenarios where you need to “backtrack” from a current state. For instance, Simplify Path splits a Unix-style path into components and uses a stack to simulate moving “up” a directory when encountering a parent-directory indicator (..).
Maintaining Dynamic State Information:
Some problems require not only basic push/pop operations but also tracking additional state. For example, the Min Stack problem demands that you return the minimum element in the stack at any time. Here, an auxiliary stack is maintained to keep track of the current minimum as elements are pushed or popped.
"()[]{}" in Valid Parentheses)"1+(4+5+2)-3" in Basic Calculator or tokens like ["2", "1", "+", "3", "*"] in Evaluate Reverse Polish Notation). or .. (as seen in Simplify Path).By examining the problem statement for these clues—nested structures, explicit mention of parentheses or operators, or requirements like “in-place” operations—the use of a stack often becomes clear.
Below is an ordered list of strategies, from the most widely applied techniques to some that are more specialized, along with examples from this collection.
Description:
Using a stack is the most straightforward technique for problems that involve matching pairs, validating order, or reversals. The stack is used to store intermediate or pending elements so that when a closing element is encountered, you can pop from the stack to check for a valid pairing.
Common Examples:
Valid Parentheses:
The solution (see stack/valid-parentheses/solution.md) iterates through a string of brackets; when it sees an opening bracket it pushes it onto the stack, and when it encounters a closing bracket it pops the top of the stack to verify a match.
Simplify Path:
In stack/simplify-path/solution.md, the input path is split by '/', and a stack is used to accumulate directory names. When encountering “..”, the top directory is popped to simulate moving up a level.
Key Idea:
Maintain a stack to handle the LIFO order so that nested or sequential operations occur in reverse order of arrival.
Description:
Many stack problems require evaluating expressions—either in infix or postfix notation—by processing tokens and applying operators at the correct time.
Common Examples:
Basic Calculator:
The solution (stack/basic-calculator/solution.md) uses a stack to store intermediate results and the current sign when an open parenthesis is encountered. This preserves the state as the expression is nested and then recombines the sub-expression result when a closing parenthesis is processed.
Evaluate Reverse Polish Notation:
As seen in stack/evaluate-reverse-polish-notation/solution.md, a stack is used to push operands, and upon encountering an operator, it pops the necessary number of operands, computes the operation, and pushes the result back.
Key Idea:
Process the expression in one pass by pushing numbers onto a stack and using operators to combine the numbers, ensuring the correct order of operations without using recursion.
Description:
Sometimes, a single stack isn’t enough because you need to track extra information. An auxiliary stack can maintain secondary data (e.g., current minima or maxima).
Common Examples:
Key Idea:
Keep an extra stack to store metadata (like the minimum value so far) so that operations such as getMin() run in O(1) time.
Description:
Some problems require simulating a process (such as navigating a file system) and naturally map to stack operations.
Common Examples:
..”).Key Idea:
Simulate real-world operations (such as directory navigation) by treating each component as an instruction to either enter (push) or exit (pop) a level.
Description:
Effective use of stacks often includes careful handling of boundary conditions—such as empty inputs or the absence of expected elements—and maintaining dynamic state during traversal.
Common Examples:
Valid Parentheses:
When popping from an empty stack, a dummy value (like '#') is used to simplify the logic and avoid errors. This is reflected in the solution (stack/valid-parentheses/solution.md).
Basic Calculator:
The solution carefully resets counters (like the current number and sign) when shifting contexts (entering and exiting parentheses) to maintain the correct overall result.
Key Idea:
Plan for scenarios where the stack might be empty or additional state must be preserved (e.g., the running total or current sign), and design your stack operations to accommodate these cases safely.
Stack problems are prevalent because many real-world and algorithmic challenges naturally follow a last-in, first-out processing order. By identifying key patterns—such as nested structures, balanced matching, and sequence reversals—you can immediately decide that a stack is an appropriate choice. Then, by selecting the right technique (whether it is a single stack for matching, dual stacks for auxiliary data, or simulation of hierarchical processes), you can craft efficient, clear solutions.
Remember these references:
By mapping problem requirements to these techniques, you will become more adept at recognizing when and how to apply stack-based solutions. Happy coding!