My technical interview cheat sheet, modified from this reference: https://gist.github.com/TSiege/cbb0507082bb18ff7e4b

Studying for a Tech Interview Sucks, so here’s a Cheat Sheet to Help

This list is meant to be a both a quick guide and reference for further research into these topics. It’s basically a summary of that comp sci course you never took or forgot about, so there’s no way it can cover everything in depth.

Data Structure Basics

Note: The following data structures are called “Dynamic Sets” which basically means that you can change the value of a member.

Array

Definition:

  • Stores data elements based on an sequential, most commonly 0 based, index.
  • Based on tuples from set theory.

What you need to know:

  • Optimal for indexing; bad at searching, inserting, and deleting (except at the end).
  • Linear arrays, or one dimensional arrays, are the most basic.
    • Are static in size, meaning that they are declared with a fixed size.
  • Dynamic arrays are like one dimensional arrays, but have reserved space for additional elements.
    • If a dynamic array is full, it copies it’s contents to a larger array.
  • Two dimensional arrays have x and y indices like a grid or nested arrays.

Big O efficiency:

  • Indexing: Linear array: O(1), Dynamic array: O(1)
  • Search:
    • If unsorted: Linear array: O(n), Dynamic array: O(n)
    • If sorted: Linear array: O(log n), Dynamic array: O(log n)
  • Optimized Search: Linear array: O(log n), Dynamic array: O(log n)
  • Insertion: Linear array: n/a Dynamic array: O(n)
  • Set, Check element at a particular index: O(1)
  • Deletion: Not available. One can symbolically delete an element by setting it to a value like -1 or None.

Linked List

Definition:

  • Stores data with nodes that point to other nodes.
    • Nodes, at its most basic it has one datum and one reference (another node).
    • A linked list chains nodes together by pointing one node’s reference towards another node.

What you need to know:

  • Designed to optimize insertion and deletion, slow at indexing and searching.
  • Doubly linked list has nodes that reference the previous node.
  • Circularly linked list is simple linked list whose tail, the last node, references the head, the first node.
  • Stack, commonly implemented with linked lists but can be made from arrays too.
    • Stacks are last in, first out (LIFO) data structures.
    • Made with a linked list by having the head be the only place for insertion and removal.
  • Queues, too can be implemented with a linked list or an array.
    • Queues are a first in, first out (FIFO) data structure.
    • Made with a doubly linked list that only removes from head and adds to tail.

Big O efficiency:

  • Unordered Singly-Linked List:
    • Insert: O(1)
    • Delete: O(1)
    • Search: O(n)
    • Successor: O(n)
    • Predecessor: O(n)
    • Min: O(n)
    • Max: O(n)
  • Ordered Singly-Linked List:
    • Insert: O(n)
    • Delete: O(1)
    • Search: O(n)
    • Successor: O(1)
    • Predecessor: O(n)
    • Min: O(1)
    • Max: O(1) if tail is available, O(n) otherwise
  • Unordered Doubly-Linked List:
    • Insert: O(1)
    • Delete: O(1)
    • Search: O(n)
    • Successor: O(n)
    • Predecessor: O(n)
    • Min: O(n)
    • Max: O(n)
  • Ordered Doubly-Linked List:
    • Insert: O(n)
    • Delete: O(1)
    • Search: O(n)
    • Successor: O(1)
    • Predecessor: O(1)
    • Min: O(1)
    • Max: O(1) if tail is available, O(n) otherwise
  • ArrayList (Java has the data structure ArrayList which refers to array with dynamic size)
    • Add: Amortized O(1)
    • Remove: O(n)
    • Contains: O(n)
    • Size: O(1)
  • Stack:
    • Push: O(1)
    • Pop: O(1)
    • Top: O(1)
    • Search: O(n)
  • Queue/Deque/Circular Queue:
    • Enqueue: O(1)
    • Dequeue: O(1)
    • Search: O(n)

Hash Table or Hash Map or Hash Set

Definition:

  • Stores data with key value pairs.
  • Hash functions accept a key and return an output unique only to that specific key.
    • This is known as hashing, which is the concept that an input and an output have a one-to-one correspondence to map information.
    • Hash functions return a unique address in memory for that data.

What you need to know:

  • Designed to optimize searching, insertion, and deletion.
  • Hash collisions are when a hash function returns the same output for two distinct outputs.
    • All hash functions have this problem.
    • This is often accommodated for by having the hash tables be very large.
  • Hashes are important for associative arrays and database indexing.

Big O efficiency:

  • Indexing: O(1)
  • Search: O(1)
  • Insertion: O(1)
  • Deletion: O(1)
  • Re-size/hash: O(n)
  • Min: O(1)
  • Max: O(1)
  • Successor: O(1)
  • Predecessor: O(n)

Heap/PriorityQueue (min/max)

Big O efficiency:

  • Find Min/Find Max: O(1)
  • Insert: O(log n)
  • Delete: O(log n)
  • Extract Min/Extract Max: O(log n)
  • Search : O(n), look through each node

What you need to know:

How to delete node x from a min-heap:

  1. save the value V in the rightmost node in the bottom level then delete this node.
  2. Put V into the node containing x and then SIFT V UP, if it is smaller than its parent, or SIFT it DOWN if it is larger than either of its children. Summary: delete the last node and move the value to the node to be deleted

Binary Tree

Definition:

  • Is a tree like data structure where every node has at most two children.
    • There is one left and right child node.
  • Each node may have: key, satellite data, left ptr, right ptr, parent ptr

What you need to know:

  • Designed to optimize searching and sorting.
  • A degenerate tree is an unbalanced tree, which if entirely one-sided is a essentially a linked list.
  • They are comparably simple to implement than other data structures.
  • Used to make binary search trees.
    • A binary tree that uses comparable keys to assign which direction a child is.
    • Left child has a key smaller than it’s parent node.
    • Right child has a key greater than it’s parent node.
    • There can be no duplicate node.
    • Because of the above it is more likely to be used as a data structure than a binary tree.
  • Three types of tree walks:
    • Inorder: print out all keys following this order: left subtree, root, right subtree
    • Postorder: roots after left and right subtree
    • Preorder: root before left and right subtree

Big O efficiency:

  • Indexing: Average O(log n), Worst Case: O(n)
  • Search: Average O(log n), Worst Case: O(n)
  • Insertion: Average O(log n), Worst Case: O(n)
  • Deletion: Average O(log n), Worst Case: O(n)
  • Min: Average case: O(log n), Worst Case: O(n)
  • Max: Average case: O(log n), Worst Case: O(n)
  • Successor: Average case: O(log n), Worst Case: O(n)
  • Predecessor: Average case: O(log n), Worst Case: O(n)
  • Inorder-walk: O(n)

How to solve the worst case issue with Binary Tree: Use Balanced Tree

Red-Black Tree( Other examples are splay tree, AVL tree)

What you need to know:

https://www.cs.auckland.ac.nz/software/AlgAnim/red_black.html

Guarantee O(logn) search times - in a dynamic environment. Can be re-balanced in O(logn) time.

Big O efficiency:

Insert, delete and search: Average case: O(log n), Worst Case: O(log n)

Search Basics

Definition:

  • An algorithm that searches a tree (or graph) by searching levels of the tree first, starting at the root.
    • It finds every node on the same level, most often moving left to right.
    • While doing this it tracks the children nodes of the nodes on the current level.
    • When finished examining a level it moves to the left most node on the next level.
    • The bottom-right most node is evaluated last (the node that is deepest and is farthest right of it’s level).

What you need to know:

  • Optimal for searching a tree that is wider than it is deep.
  • Uses a queue to store information about the tree while it traverses a tree.
    • Because it uses a queue it is more memory intensive than depth first search.
    • The queue uses more memory because it needs to stores pointers

Big O efficiency:

  • Search: Breadth First Search: O( E + V )
  • E is number of edges
  • V is number of vertices

Definition:

  • An algorithm that searches a tree (or graph) by searching depth of the tree first, starting at the root.
    • It traverses left down a tree until it cannot go further.
    • Once it reaches the end of a branch it traverses back up trying the right child of nodes on that branch, and if possible left from the right children.
    • When finished examining a branch it moves to the node right of the root then tries to go left on all it’s children until it reaches the bottom.
    • The right most node is evaluated last (the node that is right of all it’s ancestors).

What you need to know:

  • Optimal for searching a tree that is deeper than it is wide.
  • Uses a stack to push nodes onto.
    • Because a stack is LIFO it does not need to keep track of the nodes pointers and is therefore less memory intensive than breadth first search.
    • Once it cannot go further left it begins evaluating the stack.

Big O efficiency:

  • Search: Depth First Search: O( E + V )
  • E is number of edges
  • V is number of vertices
  • The simple answer to this question is that it depends on the size and shape of the tree.
    • For wide, shallow trees use Breadth First Search
    • For deep, narrow trees use Depth First Search

Nuances:

  • Because BFS uses queues to store information about the nodes and its children, it could use more memory than is available on your computer. (But you probably won’t have to worry about this.)
  • If using a DFS on a tree that is very deep you might go unnecessarily deep in the search. See xkcd for more information.
  • Breadth First Search tends to be a looping algorithm.
  • Depth First Search tends to be a recursive algorithm.

Efficient Sorting Basics

When to choose what sorting algorithm

Reference: http://web.mit.edu/1.124/LectureNotes/sorting.html

  • Merge Sort is usually preferred for sorting linked list
  • Quick Sort is O(n^2) in already sorted list

Merge Sort

Definition:

  • A comparison based sorting algorithm
    • Divides entire dataset into groups of at most two.
    • Compares each number one at a time, moving the smallest number to left of the pair.
    • Once all pairs sorted it then compares left most elements of the two leftmost pairs creating a sorted group of four with the smallest numbers on the left and the largest ones on the right.
    • This process is repeated until there is only one set.

What you need to know:

  • This is one of the most basic sorting algorithms.
  • Know that it divides all the data into as small possible sets then compares them.

Big O efficiency:

  • Best Case Sort: Merge Sort: O(n)
  • Average Case Sort: Merge Sort: O(n log n)
  • Worst Case Sort: Merge Sort: O(n log n)

Quicksort

Definition:

  • A comparison based sorting algorithm
    • Divides entire dataset in half by selecting the average element and putting all smaller elements to the left of the average.
    • It repeats this process on the left side until it is comparing only two elements at which point the left side is sorted.
    • When the left side is finished sorting it performs the same operation on the right side.
  • Computer architecture favors the quicksort process.

What you need to know:

  • While it has the same Big O as (or worse in some cases) many other sorting algorithms it is often faster in practice than many other sorting algorithms, such as merge sort.
  • Know that it halves the data set by the average continuously until all the information is sorted.

Big O efficiency:

  • Best Case Sort: Merge Sort: O(n)
  • Average Case Sort: Merge Sort: O(n log n)
  • Worst Case Sort: Merge Sort: O(n^2)

Bubble Sort

Definition:

  • A comparison based sorting algorithm
    • It iterates left to right comparing every couplet, moving the smaller element to the left.
    • It repeats this process until it no longer moves and element to the left.

What you need to know:

  • While it is very simple to implement, it is the least efficient of these three sorting methods.
  • Know that it moves one space to the right comparing two elements at a time and moving the smaller on to left.

Big O efficiency:

  • Best Case Sort: Merge Sort: O(n)
  • Average Case Sort: Merge Sort: O(n^2)
  • Worst Case Sort: Merge Sort: O(n^2)

Merge Sort Vs. Quicksort

  • Quicksort is likely faster in practice.
  • Merge Sort divides the set into the smallest possible groups immediately then reconstructs the incrementally as it sorts the groupings.
  • Quicksort continually divides the set by the average, until the set is recursively sorted.

Others

  • Insertion Sort: traverse the list, put each entry in its position
  • Selection sort: select the smallest entry and swap it to the 1st position, then the 2nd smallest entry into 2nd position.
  • Bucket sort: linear time, assuming input from uniform distribution
  • Radix Sort: linear time, assuming the input are integers
  • Heap sort: O(n) + O(nlogn) = O(nlogn)
    • build a max-heap O(n), from n/2 to 1(all non-leaf nodes), max-heapify each element
    • i= n to 2, swap a[i] with root a[1], s.t. a[i] becomes the largest, remove it from the heap, max-heapify(a, 1). O(n*lgn)
    • Misc: Build a max-heap in linear time (for the first-half/non-leaf nodes, run max_heapify which itself takes O(lgn))

Basic Types of Algorithms

Recursive Algorithms

Definition:

  • An algorithm that calls itself in its definition.
    • Recursive case a conditional statement that is used to trigger the recursion.
    • Base case a conditional statement that is used to break the recursion.

What you need to know:

  • Stack level too deep and stack overflow.
    • If you’ve seen either of these from a recursive algorithm, you messed up.
    • It means that your base case was never triggered because it was faulty or the problem was so massive you ran out of RAM before reaching it.
    • Knowing whether or not you will reach a base case is integral to correctly using recursion.
    • Often used in Depth First Search

Iterative Algorithms

Definition:

  • An algorithm that is called repeatedly but for a finite number of times, each time being a single iteration.
    • Often used to move incrementally through a data set.

What you need to know:

  • Generally you will see iteration as loops, for, while, and until statements.
  • Think of iteration as moving one at a time through a set.
  • Often used to move through an array.

Recursion Vs. Iteration

  • The differences between recursion and iteration can be confusing to distinguish since both can be used to implement the other. But know that,
    • Recursion is, usually, more expressive and easier to implement.
    • Iteration uses less memory.
  • Functional languages tend to use recursion. (i.e. Haskell)
  • Imperative languages tend to use iteration. (i.e. Ruby)
  • Check out this Stack Overflow post for more info.

Pseudo Code of Moving Through an Array (this is why iteration is used for this)

Recursion                         | Iteration
----------------------------------|----------------------------------
recursive method (array, n)       | iterative method (array)
  if array[n] is not nil          |   for n from 0 to size of array
    print array[n]                |     print(array[n])
    recursive method(array, n+1)  |
  else                            |
    exit loop                     |

Greedy Algorithm

Definition:

  • An algorithm that, while executing, selects only the information that meets a certain criteria.
  • The general five components, taken from Wikipedia:
    • A candidate set, from which a solution is created.
    • A selection function, which chooses the best candidate to be added to the solution.
    • A feasibility function, that is used to determine if a candidate can be used to contribute to a solution.
    • An objective function, which assigns a value to a solution, or a partial solution.
    • A solution function, which will indicate when we have discovered a complete solution.

What you need to know:

  • Used to find the optimal solution for a given problem.
  • Generally used on sets of data where only a small proportion of the information evaluated meets the desired result.
  • Often a greedy algorithm can help reduce the Big O of an algorithm.

Pseudo Code of a Greedy Algorithm to Find Largest Difference of any Two Numbers in an Array.

greedy algorithm (array)
  var largest difference = 0
  var new difference = find next difference (array[n], array[n+1])
  largest difference = new difference if new difference is > largest difference
  repeat above two steps until all differences have been found
  return largest difference

This algorithm never needed to compare all the differences to one another, saving it an entire iteration.

Dynamic Programming

Definition:

  • Programming here means planning.
  • This is an algorithm that caches previous results for later use in the case where the subproblems overlap.

What you need to know:

  • Difference with Recursion: In recursion, subproblems do not overlap.
  • Often very efficient at the cost of extra space.

NP-complete problems

Classic examples:

traveling salesman

knapsack problem

Operating System:

Key concepts

  • processes
  • threads
  • concurrency issues
  • locks, mutexes, semaphores, monitors, deadlock, livelock
  • context switching works
  • scheduling ( Problems in this category can be formulated with priority queue )