Backbones of Plan

Language Resource

Algorithm Resource

Data Structures and Algorithms in Python Also read java and read same for golang
Introduction to Algorithm
Algorithm Design Manual

Calculate Big O

Harvard CS50 - Asymptotic Notation (video)
Big O Notations (general quick tutorial) (video)
Big O Notation (and Omega and Theta) - best mathematical explanation (video)
Skiena (video)
UC Berkeley Big O (video)
Amortized Analysis (video)
TopCoder (includes recurrence relations and master theorem):
- Computational Complexity: Section 1
- Computational Complexity: Section 2
Cheat sheet
[Review] Big-O notation in 5 minutes (video)

Data Structures

Arrays
- About Arrays:
  - Arrays CS50 Harvard University
  - Arrays (video)
  - UC Berkeley CS61B - Linear and Multi-Dim Arrays (video) (Start watching from 15m 32s)
  - Dynamic Arrays (video)
  - Jagged Arrays (video)
- 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 the 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 the item at a 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 the 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)
Linked Lists
- Description:
  - Linked Lists CS50 Harvard University - this builds the intuition.
  - Singly Linked Lists (video)
  - CS 61B - Linked Lists 1 (video)
  - CS 61B - Linked Lists 2 (video)
  - [Review] Linked lists in 4 minutes (video)
- C Code (video) - not the whole video, just portions about Node struct and memory allocation
- Linked List vs Arrays:
  - Core Linked Lists Vs Arrays (video)
  - In The Real World Linked Lists Vs Arrays (video)
- 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.
  - Pointers to Pointers
- Implement (I did with tail pointer & without):
  - size() - returns the number of data elements in the 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 the 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 the value of the front item
  - back() - get the value of the end item
  - insert(index, value) - insert value at index, so the current item at that index is pointed to by the new item at the index
  - erase(index) - removes node at given index
  - value_n_from_end(n) - returns the value of the node at the 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
Stack
- Stacks (video)
- [Review] Stacks in 3 minutes (video)
- Will not implement. Implementing with the array is trivial
Queue
- Queue (video)
- Circular buffer/FIFO
- [Review] Queues in 3 minutes (video)
- Implement using linked-list, with tail pointer:
  - enqueue(value) - adds value at a position at the tail
  - dequeue() - returns value and removes least recently added element (front)
  - empty()
- Implement using a 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 a linked list where you enqueue at the head and dequeue at the tail would be O(n) because you’d need the next to last element, causing a full traversal of 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)
Hash table
- Videos:
- Online Courses:
  - Core Hash Tables (video)
  - Data Structures (video)
  - Phone Book Problem (video)
  - distributed hash tables:
    - Instant Uploads And Storage Optimization In Dropbox (video)
    - Distributed Hash Tables (video)
- Implement with array using linear probing
  - hash(k, m) - m is the size of the hash table
  - add(key, value) - if the key already exists, update value
  - exists(key)
  - get(key)
  - remove(key)

More Knowledge

Binary search
- Binary Search (video)
- Binary Search (video)
- detail
- blueprint
- [Review] Binary search in 4 minutes (video)
- Implement:
  - binary search (on a sorted array of integers)
  - binary search using recursion
Bitwise operations
- 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:
  - Swap
- Absolute value:
  - Absolute Integer

Trees

Trees - Intro
- Intro to Trees (video)
- Tree Traversal (video)
- 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)
- [Review] Breadth-first search in 4 minutes (video)
- [Review] Depth-first search in 4 minutes (video)
- [Review] Tree Traversal (playlist) in 11 minutes (video)
Binary search trees: BSTs
- Binary Search Tree Review (video)
- Introduction (video)
- MIT (video)
- C/C++:
- 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 a 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 the next-highest value in the tree after given value, -1 if none
Heap / Priority Queue / Binary Heap
- visualized as a tree, but is usually linear in storage (array, linked list)
- Heap
- Introduction (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)
- [Review] Heap (playlist) in 13 minutes (video)
- 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 the heap contains no elements
  - extract_max - returns the max item, removing it
  - sift_down - needed for extract_max
  - remove(x) - 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 or min heap

Sorting

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 of both?
  - I wouldn’t recommend sorting a linked list, but merge sort is doable.
  - Merge Sort For Linked List
For heapsort, see the Heap data structure above. Heap sort is great, but not stable
Sedgewick - Mergesort (5 videos)
Sedgewick - Quicksort (4 videos)
UC Berkeley:
Bubble Sort (video)
Analyzing Bubble Sort (video)
Insertion Sort, Merge Sort (video)
Insertion Sort (video)
Merge Sort (video)
Quicksort (video)
Selection Sort (video)
Merge sort code:
Quick sort code:
[Review] Sorting (playlist) in 18 minutes
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
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 the “Sorting” section in Additional Detail on Some Subjects

Graphs

Graphs can be used to represent many problems in computer science, so this section is long, like trees and sorting.

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 trade-offs, and how to implement them in real code
- When asked a question, look for a graph-based solution first, then move on if none
MIT(videos):
- Breadth-First Search
- Depth-First Search
Skiena Lectures - great intro:
Graphs (review and more):
Full Coursera Course:
- Algorithms on Graphs (video)
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 a cycle (needed for topological sort, since we’ll check for the cycle before starting)
  - topological sort
  - count connected components in a graph
  - list strongly connected components
  - check for bipartite graph

Even More Knowledge

Recursion
- Stanford lectures on recursion & backtracking:
- When it is appropriate to use it?
- How is tail recursion better than not?
  - What Is Tail Recursion Why Is It So Bad?
  - Tail Recursion (video)
- 5 Simple Steps for Solving Any Recursive Problem(video)
Backtracking Blueprint: Java Python
Dynamic Programming
- 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:
- Yale Lecture notes:
  - Dynamic Programming
- Coursera:

Interview Prep Books

You don’t need to buy a bunch of these. Honestly “Cracking the Coding Interview” is probably enough, but I bought more to give myself more practice. But I always do too much.

I bought both of these. They gave me plenty of practice.

Erdem's Second Brain

Explorer

SWE PLAN

Backbones of Plan

Language Resource

Algorithm Resource

Calculate Big O

Data Structures

Arrays

Linked Lists

Stack

Queue

Hash table

More Knowledge

Binary search

Bitwise operations

Trees

Trees - Intro

Binary search trees: BSTs

Heap / Priority Queue / Binary Heap

Sorting

Graphs

Even More Knowledge

Recursion

Dynamic Programming

Interview Prep Books

Graph View

Table of Contents

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