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- Description:
- Implement a vector (mutable array with automatic resizing):
- Practice coding using arrays and pointers, and pointer math to jump to an index instead of using indexing.
- new raw data array with allocated memory
- can allocate int array under the hood, just not use its features
- start with 16, or if starting number is greater, use power of 2 - 16, 32, 64, 128
- size() - number of items
- capacity() - number of items it can hold
- is_empty()
- at(index) - returns item at given index, blows up if index out of bounds
- push(item)
- insert(index, item) - inserts item at index, shifts that index's value and trailing elements to the right
- prepend(item) - can use insert above at index 0
- pop() - remove from end, return value
- delete(index) - delete item at index, shifting all trailing elements left
- remove(item) - looks for value and removes index holding it (even if in multiple places)
- find(item) - looks for value and returns first index with that value, -1 if not found
- resize(new_capacity) // private function
- when you reach capacity, resize to double the size
- when popping an item, if size is 1/4 of capacity, resize to half
- Time
- O(1) to add/remove at end (amortized for allocations for more space), index, or update
- O(n) to insert/remove elsewhere
- Space
- contiguous in memory, so proximity helps performance
- space needed = (array capacity, which is >= n) * size of item, but even if 2n, still O(n)
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- Description:
- C Code (video) - not the whole video, just portions about Node struct and memory allocation.
- Linked List vs Arrays:
- why you should avoid linked lists (video)
- Gotcha: you need pointer to pointer knowledge: (for when you pass a pointer to a function that may change the address where that pointer points) This page is just to get a grasp on ptr to ptr. I don't recommend this list traversal style. Readability and maintainability suffer due to cleverness.
- implement (I did with tail pointer & without):
- size() - returns number of data elements in list
- empty() - bool returns true if empty
- value_at(index) - returns the value of the nth item (starting at 0 for first)
- push_front(value) - adds an item to the front of the list
- pop_front() - remove front item and return its value
- push_back(value) - adds an item at the end
- pop_back() - removes end item and returns its value
- front() - get value of front item
- back() - get value of end item
- insert(index, value) - insert value at index, so current item at that index is pointed to by new item at index
- erase(index) - removes node at given index
- value_n_from_end(n) - returns the value of the node at nth position from the end of the list
- reverse() - reverses the list
- remove_value(value) - removes the first item in the list with this value
- Doubly-linked List
- Description (video)
- No need to implement
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- Stacks (video)
- Using Stacks Last-In First-Out (video)
- Will not implement. Implementing with array is trivial.
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- Using Queues First-In First-Out(video)
- Queue (video)
- Circular buffer/FIFO
- Priority Queues (video)
- Implement using linked-list, with tail pointer:
- enqueue(value) - adds value at position at tail
- dequeue() - returns value and removes least recently added element (front)
- empty()
- Implement using fixed-sized array:
- enqueue(value) - adds item at end of available storage
- dequeue() - returns value and removes least recently added element
- empty()
- full()
- Cost:
- a bad implementation using linked list where you enqueue at head and dequeue at tail would be O(n) because you'd need the next to last element, causing a full traversal each dequeue
- enqueue: O(1) (amortized, linked list and array [probing])
- dequeue: O(1) (linked list and array)
- empty: O(1) (linked list and array)
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Videos:
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Online Courses:
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implement with array using linear probing
- hash(k, m) - m is size of hash table
- add(key, value) - if key already exists, update value
- exists(key)
- get(key)
- remove(key)
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- Binary Search (video)
- Binary Search (video)
- detail
- Implement:
- binary search (on sorted array of integers)
- binary search using recursion
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- Bits cheat sheet - you should know many of the powers of 2 from (2^1 to 2^16 and 2^32)
- Get a really good understanding of manipulating bits with: &, |, ^, ~, >>, <<
- 2s and 1s complement
- count set bits
- swap values:
- absolute value:
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- Series: Core Trees (video)
- Series: Trees (video)
- basic tree construction
- traversal
- manipulation algorithms
- BFS(breadth-first search) and DFS(depth-first search) (video)
- BFS notes:
- level order (BFS, using queue)
- time complexity: O(n)
- space complexity: best: O(1), worst: O(n/2)=O(n)
- DFS notes:
- time complexity: O(n)
- space complexity: best: O(log n) - avg. height of tree worst: O(n)
- inorder (DFS: left, self, right)
- postorder (DFS: left, right, self)
- preorder (DFS: self, left, right)
- BFS notes:
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- Binary Search Tree Review (video)
- Series (video)
- starts with symbol table and goes through BST applications
- Introduction (video)
- MIT (video)
- C/C++:
- Binary search tree - Implementation in C/C++ (video)
- BST implementation - memory allocation in stack and heap (video)
- Find min and max element in a binary search tree (video)
- Find height of a binary tree (video)
- Binary tree traversal - breadth-first and depth-first strategies (video)
- Binary tree: Level Order Traversal (video)
- Binary tree traversal: Preorder, Inorder, Postorder (video)
- Check if a binary tree is binary search tree or not (video)
- Delete a node from Binary Search Tree (video)
- Inorder Successor in a binary search tree (video)
- Implement:
- insert // insert value into tree
- get_node_count // get count of values stored
- print_values // prints the values in the tree, from min to max
- delete_tree
- is_in_tree // returns true if given value exists in the tree
- get_height // returns the height in nodes (single node's height is 1)
- get_min // returns the minimum value stored in the tree
- get_max // returns the maximum value stored in the tree
- is_binary_search_tree
- delete_value
- get_successor // returns next-highest value in tree after given value, -1 if none
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- visualized as a tree, but is usually linear in storage (array, linked list)
- Heap
- Introduction (video)
- Naive Implementations (video)
- Binary Trees (video)
- Tree Height Remark (video)
- Basic Operations (video)
- Complete Binary Trees (video)
- Pseudocode (video)
- Heap Sort - jumps to start (video)
- Heap Sort (video)
- Building a heap (video)
- MIT: Heaps and Heap Sort (video)
- CS 61B Lecture 24: Priority Queues (video)
- Linear Time BuildHeap (max-heap)
- Implement a max-heap:
- insert
- sift_up - needed for insert
- get_max - returns the max item, without removing it
- get_size() - return number of elements stored
- is_empty() - returns true if heap contains no elements
- extract_max - returns the max item, removing it
- sift_down - needed for extract_max
- remove(i) - removes item at index x
- heapify - create a heap from an array of elements, needed for heap_sort
- heap_sort() - take an unsorted array and turn it into a sorted array in-place using a max heap
- note: using a min heap instead would save operations, but double the space needed (cannot do in-place).
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Notes:
- Implement sorts & know best case/worst case, average complexity of each:
- no bubble sort - it's terrible - O(n^2), except when n <= 16
- stability in sorting algorithms ("Is Quicksort stable?")
- Which algorithms can be used on linked lists? Which on arrays? Which on both?
- I wouldn't recommend sorting a linked list, but merge sort is doable.
- Merge Sort For Linked List
- Implement sorts & know best case/worst case, average complexity of each:
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For heapsort, see Heap data structure above. Heap sort is great, but not stable.
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UC Berkeley:
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Merge sort code:
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Quick sort code:
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Implement:
- Mergesort: O(n log n) average and worst case
- Quicksort O(n log n) average case
- Selection sort and insertion sort are both O(n^2) average and worst case
- For heapsort, see Heap data structure above.
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Not required, but I recommended them:
As a summary, here is a visual representation of 15 sorting algorithms. If you need more detail on this subject, see "Sorting" section in Additional Detail on Some Subjects
Graphs can be used to represent many problems in computer science, so this section is long, like trees and sorting were.
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Notes:
- There are 4 basic ways to represent a graph in memory:
- objects and pointers
- adjacency matrix
- adjacency list
- adjacency map
- Familiarize yourself with each representation and its pros & cons
- BFS and DFS - know their computational complexity, their tradeoffs, and how to implement them in real code
- When asked a question, look for a graph-based solution first, then move on if none.
- There are 4 basic ways to represent a graph in memory:
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MIT(videos):
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Skiena Lectures - great intro:
- CSE373 2012 - Lecture 11 - Graph Data Structures (video)
- CSE373 2012 - Lecture 12 - Breadth-First Search (video)
- CSE373 2012 - Lecture 13 - Graph Algorithms (video)
- CSE373 2012 - Lecture 14 - Graph Algorithms (con't) (video)
- CSE373 2012 - Lecture 15 - Graph Algorithms (con't 2) (video)
- CSE373 2012 - Lecture 16 - Graph Algorithms (con't 3) (video)
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Graphs (review and more):
- 6.006 Single-Source Shortest Paths Problem (video)
- 6.006 Dijkstra (video)
- 6.006 Bellman-Ford (video)
- 6.006 Speeding Up Dijkstra (video)
- Aduni: Graph Algorithms I - Topological Sorting, Minimum Spanning Trees, Prim's Algorithm - Lecture 6 (video)
- Aduni: Graph Algorithms II - DFS, BFS, Kruskal's Algorithm, Union Find Data Structure - Lecture 7 (video)
- Aduni: Graph Algorithms III: Shortest Path - Lecture 8 (video)
- Aduni: Graph Alg. IV: Intro to geometric algorithms - Lecture 9 (video)
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CS 61B 2014 (starting at 58:09) (video) - CS 61B 2014: Weighted graphs (video)
- Greedy Algorithms: Minimum Spanning Tree (video)
- Strongly Connected Components Kosaraju's Algorithm Graph Algorithm (video)
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Full Coursera Course:
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I'll implement:
- DFS with adjacency list (recursive)
- DFS with adjacency list (iterative with stack)
- DFS with adjacency matrix (recursive)
- DFS with adjacency matrix (iterative with stack)
- BFS with adjacency list
- BFS with adjacency matrix
- single-source shortest path (Dijkstra)
- minimum spanning tree
- DFS-based algorithms (see Aduni videos above):
- check for cycle (needed for topological sort, since we'll check for cycle before starting)
- topological sort
- count connected components in a graph
- list strongly connected components
- check for bipartite graph
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- Stanford lectures on recursion & backtracking:
- when it is appropriate to use it
- how is tail recursion better than not?
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- You probably won't see any dynamic programming problems in your interview, but it's worth being able to recognize a problem as being a candidate for dynamic programming.
- This subject can be pretty difficult, as each DP soluble problem must be defined as a recursion relation, and coming up with it can be tricky.
- I suggest looking at many examples of DP problems until you have a solid understanding of the pattern involved.
- Videos:
- the Skiena videos can be hard to follow since he sometimes uses the whiteboard, which is too small to see
- Skiena: CSE373 2012 - Lecture 19 - Introduction to Dynamic Programming (video)
- Skiena: CSE373 2012 - Lecture 20 - Edit Distance (video)
- Skiena: CSE373 2012 - Lecture 21 - Dynamic Programming Examples (video)
- Skiena: CSE373 2012 - Lecture 22 - Applications of Dynamic Programming (video)
- Simonson: Dynamic Programming 0 (starts at 59:18) (video)
- Simonson: Dynamic Programming I - Lecture 11 (video)
- Simonson: Dynamic programming II - Lecture 12 (video)
- List of individual DP problems (each is short): Dynamic Programming (video)
- Yale Lecture notes:
- Coursera:
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- Math Skills: How to find Factorial, Permutation and Combination (Choose) (video)
- Make School: Probability (video)
- Make School: More Probability and Markov Chains (video)
- Khan Academy:
- Course layout:
- Just the videos - 41 (each are simple and each are short):
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- Know about the most famous classes of NP-complete problems, such as traveling salesman and the knapsack problem, and be able to recognize them when an interviewer asks you them in disguise.
- Know what NP-complete means.
- Computational Complexity (video)
- Simonson:
- Skiena:
- Complexity: P, NP, NP-completeness, Reductions (video)
- Complexity: Approximation Algorithms (video)
- Complexity: Fixed-Parameter Algorithms (video)
- Peter Norvig discusses near-optimal solutions to traveling salesman problem:
- Pages 1048 - 1140 in CLRS if you have it.
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- Note there are different kinds of tries. Some have prefixes, some don't, and some use string instead of bits to track the path.
- I read through code, but will not implement.
- Sedgewick - Tries (3 videos)
- Notes on Data Structures and Programming Techniques
- Short course videos:
- The Trie: A Neglected Data Structure
- TopCoder - Using Tries
- Stanford Lecture (real world use case) (video)
- MIT, Advanced Data Structures, Strings (can get pretty obscure about halfway through) (video)
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Know at least one type of balanced binary tree (and know how it's implemented):
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"Among balanced search trees, AVL and 2/3 trees are now passé, and red-black trees seem to be more popular. A particularly interesting self-organizing data structure is the splay tree, which uses rotations to move any accessed key to the root." - Skiena
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Of these, I chose to implement a splay tree. From what I've read, you won't implement a balanced search tree in your interview. But I wanted exposure to coding one up and let's face it, splay trees are the bee's knees. I did read a lot of red-black tree code.
- splay tree: insert, search, delete functions If you end up implementing red/black tree try just these:
- search and insertion functions, skipping delete
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I want to learn more about B-Tree since it's used so widely with very large data sets.
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AVL trees
- In practice: From what I can tell, these aren't used much in practice, but I could see where they would be: The AVL tree is another structure supporting O(log n) search, insertion, and removal. It is more rigidly balanced than red–black trees, leading to slower insertion and removal but faster retrieval. This makes it attractive for data structures that may be built once and loaded without reconstruction, such as language dictionaries (or program dictionaries, such as the opcodes of an assembler or interpreter).
- MIT AVL Trees / AVL Sort (video)
- AVL Trees (video)
- AVL Tree Implementation (video)
- Split And Merge
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Splay trees
- In practice: Splay trees are typically used in the implementation of caches, memory allocators, routers, garbage collectors, data compression, ropes (replacement of string used for long text strings), in Windows NT (in the virtual memory, networking and file system code) etc.
- CS 61B: Splay Trees (video)
- MIT Lecture: Splay Trees:
- Gets very mathy, but watch the last 10 minutes for sure.
- Video
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Red/black trees
- these are a translation of a 2-3 tree (see below)
- In practice: Red–black trees offer worst-case guarantees for insertion time, deletion time, and search time. Not only does this make them valuable in time-sensitive applications such as real-time applications, but it makes them valuable building blocks in other data structures which provide worst-case guarantees; for example, many data structures used in computational geometry can be based on red–black trees, and the Completely Fair Scheduler used in current Linux kernels uses red–black trees. In the version 8 of Java, the Collection HashMap has been modified such that instead of using a LinkedList to store identical elements with poor hashcodes, a Red-Black tree is used.
- Aduni - Algorithms - Lecture 4 (link jumps to starting point) (video)
- Aduni - Algorithms - Lecture 5 (video)
- Red-Black Tree
- An Introduction To Binary Search And Red Black Tree
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2-3 search trees
- In practice: 2-3 trees have faster inserts at the expense of slower searches (since height is more compared to AVL trees).
- You would use 2-3 tree very rarely because its implementation involves different types of nodes. Instead, people use Red Black trees.
- 23-Tree Intuition and Definition (video)
- Binary View of 23-Tree
- 2-3 Trees (student recitation) (video)
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2-3-4 Trees (aka 2-4 trees)
- In practice: For every 2-4 tree, there are corresponding red–black trees with data elements in the same order. The insertion and deletion operations on 2-4 trees are also equivalent to color-flipping and rotations in red–black trees. This makes 2-4 trees an important tool for understanding the logic behind red–black trees, and this is why many introductory algorithm texts introduce 2-4 trees just before red–black trees, even though 2-4 trees are not often used in practice.
- CS 61B Lecture 26: Balanced Search Trees (video)
- Bottom Up 234-Trees (video)
- Top Down 234-Trees (video)
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N-ary (K-ary, M-ary) trees
- note: the N or K is the branching factor (max branches)
- binary trees are a 2-ary tree, with branching factor = 2
- 2-3 trees are 3-ary
- K-Ary Tree
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B-Trees
- fun fact: it's a mystery, but the B could stand for Boeing, Balanced, or Bayer (co-inventor)
- In Practice: B-Trees are widely used in databases. Most modern filesystems use B-trees (or Variants). In addition to its use in databases, the B-tree is also used in filesystems to allow quick random access to an arbitrary block in a particular file. The basic problem is turning the file block i address into a disk block (or perhaps to a cylinder-head-sector) address.
- B-Tree
- B-Tree Datastructure
- Introduction to B-Trees (video)
- B-Tree Definition and Insertion (video)
- B-Tree Deletion (video)
- MIT 6.851 - Memory Hierarchy Models (video) - covers cache-oblivious B-Trees, very interesting data structures - the first 37 minutes are very technical, may be skipped (B is block size, cache line size)
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XCODE
MacBook Pro (13-inch, 2019, Two Thunderbolt 3 ports)
Processor Name: Quad-Core Intel Core i5
Processor Speed: 1.4 GHz
Memory: 8 GB