DSA: Introduction to Data Structures and Algorithms
Understand what DSA is, why it matters, and the foundational concepts every programmer needs.
What are Data Structures and Algorithms?
A data structure is a way of organizing and storing data so it can be accessed and modified efficiently. An algorithm is a step-by-step procedure for solving a problem or performing a computation. Together they form the core of computer science.
Data Structures and Algorithms
Every program you write uses both: data structures to hold information, and algorithms to process it.
- Data Structure: how data is organized in memory (array, list, tree, graph)
- Algorithm: the logic used to process or transform that data
- Choosing the right data structure often determines how efficient your algorithm can be
- DSA knowledge is essential for writing fast, scalable software
Data Structure + Algorithm
C++An array stores the data; the loop is the algorithm that finds the maximum.
Why DSA Matters
DSA is not just academic theory. It directly affects how fast your programs run, how much memory they use, and how well they scale from 10 users to 10 million.
Why You Need DSA
Understanding DSA helps you write code that is not just correct, but efficient and maintainable.
- Efficiency: the right algorithm can reduce runtime from hours to milliseconds
- Problem solving: DSA gives you a toolkit of reusable patterns for complex problems
- Interviews: top tech companies test DSA knowledge directly in hiring assessments
- Scalability: poorly chosen structures break under large data loads
Linear vs Binary Search
C++Binary search is dramatically faster on sorted data. Both find index 7.
Types of Data Structures
Data structures are classified along two axes: their shape (linear vs non-linear) and their memory behavior (static vs dynamic).
Classification of Data Structures
Understanding the category of a data structure tells you what operations it supports and at what cost.
- Linear: elements arranged in a sequence (Array, Linked List, Stack, Queue)
- Non-linear: elements with hierarchical or networked relationships (Tree, Graph)
- Static: fixed size allocated at compile time (plain arrays in C++)
- Dynamic: size grows or shrinks at runtime (vector, linked list)
| Category | Examples | Key Trait |
|---|---|---|
| Linear | Array, Stack, Queue, Linked List | Elements in a sequence |
| Non-linear | Tree, Graph, Heap | Hierarchical or networked |
| Static | Fixed-size array (int arr[10]) | Size defined at compile time |
| Dynamic | vector, linked list | Size changes at runtime |
Abstract Data Types vs Data Structures
An Abstract Data Type (ADT) defines what operations a type supports, without specifying how they are implemented. A data structure is the concrete implementation of an ADT.
ADT vs Data Structure
Think of an ADT as a contract and the data structure as the code that fulfills it.
- ADT Stack: defines push, pop, peek operations
- Implementation: can be built with an array or a linked list
- The same ADT (e.g. Queue) can have many different implementations
- ADTs let you reason about behavior without worrying about memory layout
Stack ADT in C++
C++std::stack is the ADT interface; the underlying container is the concrete data structure.
Algorithm Characteristics
A valid algorithm must satisfy five key properties. A procedure that violates any one of them is not a true algorithm.
Five Properties of an Algorithm
These properties ensure an algorithm is well-defined, predictable, and executable.
- Input: zero or more well-defined inputs
- Output: at least one output produced from the inputs
- Definiteness: every step is clear and unambiguous
- Finiteness: it terminates after a finite number of steps
- Effectiveness: every step is basic enough to be carried out in principle
Algorithm with All Five Properties
C++Each comment maps to one of the five algorithm characteristics.
Algorithm Design Approaches
Different problem types suit different design strategies. Knowing which approach to reach for first saves significant development time.
Common Design Approaches
Each approach trades off simplicity, optimality, and implementation complexity differently.
- Brute Force: try all possibilities, guaranteed correct but often slow
- Divide and Conquer: split problem in half recursively (Merge Sort, Binary Search)
- Dynamic Programming: cache subproblem results to avoid recomputation
- Greedy: always pick the locally optimal choice
- Backtracking: explore options and undo choices that lead to dead ends
Three Ways to Sum an Array
C++Same result, different design strategies. Each has different readability and overhead tradeoffs.
Problem-Solving Strategies
Before writing a single line of code, strong engineers follow a structured approach to understand and decompose a problem.
Steps for Solving Any Problem
A repeatable process prevents wasted effort and leads to cleaner solutions.
- Understand: read the problem carefully, identify inputs, outputs, and constraints
- Examples: trace through sample inputs by hand to build intuition
- Plan: write pseudocode or a flowchart before coding
- Implement: translate the plan to code, starting with a working solution
- Optimize: analyze time and space complexity, then improve if needed
- Test: verify with edge cases (empty input, single element, large input)
Pseudocode and Flowcharts
Pseudocode and flowcharts let you design algorithm logic at a high level, free from language syntax, before committing to an implementation.
Pseudocode
Pseudocode is structured English that reads like code but has no strict syntax rules.
- Use indentation to show structure (loops, conditionals)
- Use plain verbs: SET, IF, WHILE, RETURN, PRINT
- Focus on logic, not language-specific syntax
- Pseudocode is language-agnostic and easy to convert to any language
Pseudocode to C++ Code
C++The comments show the pseudocode; the function below is the direct C++ translation.
Knowledge Check
1. What is an Abstract Data Type (ADT)?
2. Which of the following is a non-linear data structure?
3. What does "finiteness" mean as an algorithm characteristic?
4. What is the time complexity of binary search on a sorted array?
5. Which algorithm design approach breaks a problem into smaller subproblems and solves each only once?
6. Which of the following is a static data structure?
7. What is pseudocode used for?
8. Which problem-solving strategy tries all possible solutions to find the best one?