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Java Data Structures Cheat Sheet by


- Stores data elements based on an sequen­tial, most commonly 0 based, index. - Based on [tuple­s](­htt­p:/­/en.wi­kip­edi­a.o­rg/­wik­i/T­uple) from set theory. - They are one of the oldest, most commonly used data struct­ures.
- 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: Linear array: O(n), Dynamic array: O(n) - Optimized Search: Linear array: O(log n), Dynamic array: O(log n) - Insertion: Linear array: n/a Dynamic array: O(n)

Linked List

- 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.
- 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
- Indexing: Linked Lists: O(n) - Search: Linked Lists: O(n) - Optimized Search: Linked Lists: O(n) - Insertion: Linked Lists: O(1)

Hash Map

- 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.
- Designed to optimize searching, insertion, and deletion. - Hash collis­ions are when a hash function returns the same output for two distinct inputs. - 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: Hash Tables: O(1) - Search: Hash Tables: O(1) - Insertion: Hash Tables: O(1)

Binary Tree

- Is a tree like data structure where every node has at most two children. - There is one left and right child node.
- 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. An AVL Tree is a balanced binary search tree. -The process for inserting or deleting is the same as in a regula­r(u­nba­lanced) BST, except you have to rebalance after each operation. A node in an AVL tree is balanced if its balance factor is either -1,0, or 1
Big-O effici­ency
- Indexing: Binary Search Tree: O(log n) - Search: Binary Search Tree: O(log n) - Insertion: Binary Search Tree: O(log n)
The balance factor of a node is the height of its right subtree minus the height of its left subtree

Search Basics


Breadth First Search

- 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).
- 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

Depth First Search

- 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).
- 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

Breadth First Search Vs. Depth First Search

- 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


- 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]­(ht­tp:­//x­­m/761/) for more inform­ation.
- Breadth First Search tends to be a looping algorithm.
- Depth First Search tends to be a recursive algorithm.

Efficient Sorting Basics


Merge Sort

- 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.
- 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)


- 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.
- 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

- 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.
- 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(n2) - Worst Case Sort: Merge Sort: O(n2)

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.

Heap Sort

Sorts using a complete binary Tree.
Arra­yList can be used to store a Heap
For a node of i:
-Left child: 2i+1
-Right child: 2i+2
-Parent: (i - 1)/2

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