Data Structures Fundamentals

Data Structures

Arrays

• A collection of elements of the same data type stored in contiguous memory locations
• Each element is identified by an index or key
• Operations: traversal, insertion, deletion, searching

Linked Lists

• A dynamic collection of elements, each pointing to the next node
• Each node contains a value and a reference to the next node
• Operations: traversal, insertion, deletion, searching
• Advantages: efficient insertion and deletion, flexible size

Stacks

• A Last-In-First-Out (LIFO) data structure
• Elements are added and removed from the top
• Operations: push, pop, peek
• Applications: parsing, evaluating postfix expressions

Queues

• A First-In-First-Out (FIFO) data structure
• Elements are added to the end and removed from the front
• Operations: enqueue, dequeue, peek
• Applications: job scheduling, print queues

Trees

• A hierarchical data structure with nodes and edges
• Each node has a value and zero or more child nodes
• Operations: traversal, insertion, deletion, searching
• Types: binary trees, AVL trees, BSTs

Graphs

• A non-linear data structure with nodes and edges
• Nodes are connected by edges, which may be weighted or directed
• Operations: traversal, searching, shortest path
• Types: undirected graphs, directed graphs, weighted graphs

Algorithms

Sorting Algorithms

• Bubble Sort: iteratively compare adjacent elements and swap if necessary
• Selection Sort: select the smallest element and swap with the first element
• Insertion Sort: insert each element into its proper position
• Merge Sort: divide and conquer, merge sorted subarrays
• Quick Sort: divide and conquer, pivot element, recursive sorting

Searching Algorithms

• Linear Search: iterate through the array and compare each element
• Binary Search: divide and conquer, search for an element in a sorted array

Graph Algorithms

• Breadth-First Search (BFS): traverse the graph level by level
• Depth-First Search (DFS): traverse the graph by exploring as far as possible along each branch
• Dijkstra's Algorithm: find the shortest path in a weighted graph
• Topological Sort: order the nodes in a directed acyclic graph (DAG)

Dynamic Programming

• Memoization: store solutions to subproblems to avoid redundant computation
• Tabulation: store solutions to subproblems in a table for later use
• Applications: Fibonacci sequence, longest common subsequence, knapsack problem

Data Structures

Arrays

• A collection of elements of the same data type stored in contiguous memory locations, allowing for efficient access and modification
• Each element is identified by an index or key, enabling quick lookup and manipulation
• Supports operations such as traversal, insertion, deletion, and searching, making it a versatile data structure

Linked Lists

• A dynamic collection of elements, each pointing to the next node, allowing for efficient insertion and deletion
• Each node contains a value and a reference to the next node, enabling flexible and efficient data management
• Supports operations such as traversal, insertion, deletion, and searching, with advantages including efficient insertion and deletion, and flexible size

Stacks

• A Last-In-First-Out (LIFO) data structure, where elements are added and removed from the top
• Supports operations such as push, pop, and peek, making it ideal for applications requiring sequential processing
• Applications include parsing, evaluating postfix expressions, and implementing recursive algorithms

Queues

• A First-In-First-Out (FIFO) data structure, where elements are added to the end and removed from the front
• Supports operations such as enqueue, dequeue, and peek, making it suitable for job scheduling, print queues, and other queue-based systems

Trees

• A hierarchical data structure with nodes and edges, allowing for efficient data representation and manipulation
• Each node has a value and zero or more child nodes, enabling flexible data organization and traversal
• Supports operations such as traversal, insertion, deletion, and searching, with types including binary trees, AVL trees, and BSTs

Graphs

• A non-linear data structure with nodes and edges, allowing for complex relationships between data elements
• Nodes are connected by edges, which may be weighted or directed, enabling representation of diverse relationships
• Supports operations such as traversal, searching, and shortest path, with types including undirected graphs, directed graphs, and weighted graphs

Algorithms

Sorting Algorithms

• Bubble Sort: iteratively compares adjacent elements and swaps if necessary, until no more swaps are needed
• Selection Sort: selects the smallest element and swaps it with the first element, repeating until the array is sorted
• Insertion Sort: inserts each element into its proper position, building a sorted array incrementally
• Merge Sort: divides the array into smaller subarrays, sorts each subarray, and merges them to produce a sorted array
• Quick Sort: selects a pivot element, partitions the array around it, and recursively sorts the subarrays

Searching Algorithms

• Linear Search: iterates through the array, comparing each element to the target value, until the target is found or the end is reached
• Binary Search: divides the sorted array into halves, searching for the target value in the appropriate half, until the target is found or the subarray is empty

Graph Algorithms

• Breadth-First Search (BFS): traverses the graph level by level, exploring all nodes at a given depth before moving to the next level
• Depth-First Search (DFS): traverses the graph by exploring as far as possible along each branch, before backtracking to explore other branches
• Dijkstra's Algorithm: finds the shortest path in a weighted graph, by iteratively relaxing the distance estimates and selecting the minimum-distance node
• Topological Sort: orders the nodes in a directed acyclic graph (DAG), such that for every edge (u, v), node u comes before node v in the ordering

Dynamic Programming

• Memoization: stores solutions to subproblems in memory, to avoid redundant computation and improve performance
• Tabulation: stores solutions to subproblems in a table, for later use and efficient computation
• Applications include the Fibonacci sequence, longest common subsequence, and knapsack problem

Test your understanding of basic data structures, including arrays and linked lists, and their operations. Learn about the advantages and characteristics of each data structure.