Many developers I came across in my career as a software developer are only familiar with the most basic data structures, typically, Array, Map and Linked List. These are fundamental data structures and one could argue that they are generic enough to fit most of the commercial software requirements. But what worries me most is that even seasoned developers are not familiar with the vast repertoire of available data structures and their time complexity. In this post the ADTs (Abstract Data Types) present in the Java Collections (JDK 1.6) are enlisted and the performance of the various data structures, in terms of time, is assessed.

Before we start it is helpful to understand the so-called “Big O” notation. This notation approximately describes how the time to do a given task grows with the size of the input. Roughly speaking, on one end we have

*O(1)*which is “constant time” and on the opposite end we have*O(x*which is “exponential time”. The following chart summarizes the growth in complexity due to growth of input (^{n})*n*). In our data structure walk-through we sometimes use the symbol*h*to signify the Hash Table capacity.**List**

*A list is an ordered collection of elements.*

Add | Remove | Get | Contains | Data Structure | |

ArrayList | O(1) | O(n) | O(1) | O(n) | Array |

LinkedList | O(1) | O(1) | O(n) | O(n) | Linked List |

CopyonWriteArrayList | O(n) | O(n) | O(1) | O(n) | Array |

**Set**

*A collection that contains no duplicate elements.*

Add | Contains | Next | Data Structure | |

HashSet | O(1) | O(1) | O(h/n) | Hash Table |

LinkedHashSet | O(1) | O(1) | O(1) | Hash Table + Linked List |

EnumSet | O(1) | O(1) | O(1) | Bit Vector |

TreeSet | O(log n) | O(log n) | O(log n) | Red-black tree |

CopyonWriteArraySet | O(n) | O(n) | O(1) | Array |

ConcurrentSkipList | O(log n) | O(log n) | O(1) | Skip List |

**Queue**

*A collection designed for holding elements prior to processing.*

Offer | Peak | Poll | Size | Data Structure | |

PriorityQueue | O(log n ) | O(1) | O(log n) | O(1) | Priority Heap |

LinkedList | O(1) | O(1) | O(1) | O(1) | Array |

ArrayDequeue | O(1) | O(1) | O(1) | O(1) | Linked List |

ConcurrentLinkedQueue | O(1) | O(1) | O(1) | O(n) | Linked List |

ArrayBlockingQueue | O(1) | O(1) | O(1) | O(1) | Array |

PriorirityBlockingQueue | O(log n) | O(1) | O(log n) | O(1) | Priority Heap |

SynchronousQueue | O(1) | O(1) | O(1) | O(1) | None! |

DelayQueue | O(log n) | O(1) | O(log n) | O(1) | Priority Heap |

LinkedBlockingQueue | O(1) | O(1) | O(1) | O(1) | Linked List |

**Map**

*An object that maps keys to values. A map cannot duplicate keys; each key can map to at most one value.*

Get | ContainsKey | Next | Data Structure | |

HashMap | O(1) | O(1) | O(h / n) | Hash Table |

LinkedHashMap | O(1) | O(1) | O(1) | Hash Table + Linked List |

IdentityHashMap | O(1) | O(1) | O(h / n) | Array |

WeakHashMap | O(1) | O(1) | O(h / n) | Hash Table |

EnumMap | O(1) | O(1) | O(1) | Array |

TreeMap | O(log n) | O(log n) | O(log n) | Red-black tree |

ConcurrentHashMap | O(1) | O(1) | O(h / n) | Hash Tables |

ConcurrentSkipListMap | O(log n) | O(log n) | O(1) | Skip List |

Please, correct the description for LinkedList remove operation. It is two-step operation and the complexity is O(n), not O(1).

ReplyDeleteI second that. The element should be found in the list before it can be removed by changing the pointers so it is O(n).

DeleteIt is common to just write how long removal itself will take without actual search. You have to take it as: if you have pointer to object o in linked list then removal will take O(1).

DeleteIt is done this way, so you can see difference between different collections:

ArrayList has remove O(n) + search, while LinkedList have O(1)+ search. Removal would have O(n) complexity for both even though LinkedList removal is way faster.

Quote Baryshev

DeleteI agree with Robin but the problem is that it is kind of misleading. If a less "seasoned" programmer sees the chart then he will immediately assume that removing an element in LinkedList will just be O(1). An extra column needs to be put or a simple explanation should be given in the opening paragraphs.

DeleteOtherwise, great post!

every queue implementation has O(N) on contains() method?

ReplyDeleteThis comment has been removed by the author.

DeleteArray and LinkedList has O(n) on contains() method for sure. If element is not in array or list you have to traverse all elements just to be sure. In Priority Heap as name suggest use some kind of heap (couldn't find exactly which, so I will assume it is binary heap), which is data structure similar to binary tree, with special rules. Contains() on binary heap takes O(log n).

DeleteLinked List not use Array Data Structure

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Thank you for nice article but I just want some more explanation because I am prepring this for my interview, like reason for each data structure complexity.good explained for arraylist and linkedlist but I need this type of explanation for each is it possible here??

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Many of this runtimes are not correct. One should distinguish between per-operation, amortized and (stochastic) expected worst-case runtimes. The runtimes here are mixed up and always choose the beset of the three.

ReplyDeleteE.g. ArrayList#add has a worst case complexity of O(n) (array size doubling), but the amortized complexity over a series of operations is in O(1). HashSet#contains has a worst case complexity of O(n) (<= Java 7) and O(log n) otherwise, but the expected complexity is in O(1).

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What does “Next” mean for Set and Map? There is no such operation. If you mean the next() method of their Iterators, then the complexities are dead wrong. Iterators keep a reference to the current node, so it’s always O(1) for the hash maps instead of O(h / n).

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