Data Structures/Tradeoffs

It is important to fully understand the problem you need to solve before choosing a data structure because each structure is optimized for a particular job. Hash tables, for example, favor fast lookup times over memory usage while arrays are compact and inflexible. Other structures, such as stacks, are optimized to enforce rigid rules on how data is added, removed and accessed throughout the program execution. A good understanding of data structures is fundamental because it gives us the tools for thinking about a program's behavior in a structured way. [TODO:] Use asymptotic behaviour to decide, most importantly seeing how the structure will be used: an infrequent operation does not need to be fast if it means everything else will be much faster [TODO:] Can use a table like this one to compare the asymptotic behaviour of every structure for every operation on it. + Sequences (aka lists): Array Dynamic Array Array Deque Singly Linked List Double Linked List Push (Front) - O(n) O(1) O(1) O(1) Pop (Front) - O(n) O(1) O(1) O(1) Push (Back) - O(1) O(1) O(n), maybe O(1)* O(1) Pop (Back) - O(1) O(1) O(n) O(1) Insert before (given iterator) - O(n) O(n) O(n) O(1) Delete (given iterator) O(n) O(n) O(n) O(1) Insert after (given iterator) O(n) O(n) O(1) O(1) Delete after (given iterator) - O(n) O(n) O(1) O(1) Get nth element (random access) O(1) O(1) O(1) O(n) O(n) Good for implementing stacks no yes (back is top) yes yes (front is top) yes Good for implementing queues no no yes maybe* yes C++ STL std::array std::vector std::deque std::forward_list std::list Java Collections java.util.Array java.util.ArrayList java.util.ArrayDeque - java.util.LinkedList * singly-linked lists can push to the back in O(1) with the modification that you keep a pointer to the last node + Associative containers (sets, associative arrays) Sorted Array Sorted Linked List Self-balancing Binary Search Tree Hash Table Find key O(log n) O(n) O(log n) O(1) average O(n) worst Insert element O(n) O(n) O(log n) O(1) average O(n) worst Erase key O(n) O(n) O(log n) O(1) average O(n) worst Erase element (given iterator) O(n) O(1) O(1) O(1) Can traverse in sorted order? yes yes yes no Needs comparison function comparison function comparison function hash function C++ STL - - std::set std::map std::multiset std::multimap std::unordered_set std::unordered_map std::unordered_multiset std::unordered_multimap Java Collections - - java.util.TreeSet java.util.TreeMap java.util.HashSet java.util.HashMap Please correct any errors +Various Types of Trees Binary Search AVL Tree Binary Heap (min) Binomial Queue (min) Insert element O(log n) O(log n) O(log n) O(1) (on average) Erase element O(log n) O(log n) unavailable unavailable Delete min element O(log n) O(log n) O(log n) O(log n) Find min element O(log n) O(log n) O(1) O(log n) (can be O(1) if ptr to smallest) Increase key unavailable unavailable O(log n) O(log n) Decrease key unavailable unavailable O(log n) O(log n) Find O(log n) O(log n) unavailable unavailable Delete element O(log n) O(log n) unavailable unavailable Create O(1) O(1) O(1) O(1) find kth smallest O(log n) O(log n) O((k-1)*log n) O(k*log n) + Hash table Hash table (hash map) Set Value Ω(1), O(n) Get Value Ω(1), O(n) Remove Ω(1), O(n) [TODO:] Can also add a table that specifies the best structure for some specific need e.g. For queues, double linked. For stacks, single linked. For sets, hash tables. etc... [TODO:] Could also contain table with space complexity information (there is a significative cost in using hashtables or lists implemented via arrays, for example).