Questions and Answers
What is the primary advantage of using a linked list over an array?
Which data structure follows the First-In-First-Out (FIFO) principle?
What is the purpose of the 'peek' operation in a stack?
Which sorting algorithm has a time complexity of O(n log n) in the best case?
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What is the primary application of Breadth-First Search (BFS) algorithm?
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What is the main idea behind dynamic programming?
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What is the primary advantage of using memoization in dynamic programming?
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Which data structure is commonly used to implement a graph?
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Study Notes
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
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Description
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.