# Design a data structure that supports insert, delete, search and getRandom in constant time

• Difficulty Level : Medium
• Last Updated : 27 Jun, 2022

Design a data structure that supports the following operations in Θ(1) time.

• insert(x): Inserts an item x to the data structure if not already present.
• remove(x): Removes item x from the data structure if present.
• search(x): Searches an item x in the data structure.
• getRandom(): Returns a random element from current set of elements

We can use hashing to support first 3 operations in Θ(1) time. How to do the 4th operation? The idea is to use a resizable array (ArrayList in Java, vector in C) together with hashing. Resizable arrays support insert in Θ(1) amortized time complexity. To implement getRandom(), we can simply pick a random number from 0 to size-1 (size is the number of current elements) and return the element at that index. The hash map stores array values as keys and array indexes as values.

Following are detailed operations.

• insert(x)
1. Check if x is already present by doing a hash map lookup.
2. If not present, then insert it at the end of the array.
3. Add in the hash table also, x is added as key and last array index as the index.
• remove(x)
1. Check if x is present by doing a hash map lookup.
2. If present, then find its index and remove it from a hash map.
3. Swap the last element with this element in an array and remove the last element.
Swapping is done because the last element can be removed in O(1) time.
4. Update index of the last element in a hash map.
• getRandom()
1. Generate a random number from 0 to last index.
2. Return the array element at the randomly generated index.
• search(x)
• Do a lookup for x in hash map.

Below is the implementation of the data structure.

## C++

 `/* C++ program to design a DS that supports following operations``in Theta(n) time``a) Insert``b) Delete``c) Search``d) getRandom */` `#include``using` `namespace` `std;` `// class to represent the required data structure``class` `myStructure``{``    ``// A resizable array``    ``vector <``int``> arr;``    ` `    ``// A hash where keys are array elements and values are``    ``// indexes in arr[]``    ``map <``int``, ``int``> Map;` `    ``public``:``    ``// A Theta(1) function to add an element to MyDS``    ``// data structure``    ``void` `add(``int` `x)``    ``{``        ``// If element is already present, then nothing to do``        ``if``(Map.find(x) != Map.end())``            ``return``;``            ` `        ``// Else put element at the end of arr[]``        ``int` `index = arr.size();``        ``arr.push_back(x);``            ` `        ``// and hashmap also``        ``Map.insert(std::pair<``int``,``int``>(x, index));``    ``}``        ` `    ``// function to remove a number to DS in O(1)``    ``void` `remove``(``int` `x)``    ``{``        ``// element not found then return``        ``if``(Map.find(x) == Map.end())``            ``return``;``            ` `        ``// remove element from map``        ``int` `index = Map.at(x);``        ``Map.erase(x);``            ` `        ``// swap with last element in arr``        ``// then remove element at back``        ``int` `last = arr.size() - 1;``        ``swap(arr[index], arr[last]);``        ``arr.pop_back();``            ` `        ``// Update hash table for new index of last element``        ``Map.at(arr[index]) = index;``    ``}``        ` `    ``// Returns index of element if element is present, otherwise null``    ``int` `search(``int` `x)``    ``{``        ``if``(Map.find(x) != Map.end())``        ``return` `Map.at(x);``        ``return` `-1;``    ``}``        ` `    ``// Returns a random element from myStructure``    ``int` `getRandom()``    ``{``        ``// Find a random index from 0 to size - 1``        ``srand` `(``time``(NULL));``        ``int` `random_index = ``rand``() % arr.size();``            ` `        ``// Return element at randomly picked index``        ``return` `arr.at(random_index);``    ``}    ``};` `// Driver main``int` `main()``{``    ``myStructure ds;``    ``ds.add(10);``    ``ds.add(20);``    ``ds.add(30);``    ``ds.add(40);``    ``cout << ds.search(30) << endl;``    ``ds.``remove``(20);``    ``ds.add(50);``    ``cout << ds.search(50) << endl;``    ``cout << ds.getRandom() << endl;``}` `// This code is contributed by Aditi Sharma`

## Java

 `/* Java program to design a data structure that support following operations``   ``in Theta(n) time``   ``a) Insert``   ``b) Delete``   ``c) Search``   ``d) getRandom */``import` `java.util.*;` `// class to represent the required data structure``class` `MyDS``{``   ``ArrayList arr;   ``// A resizable array` `   ``// A hash where keys are array elements and values are``   ``// indexes in arr[]``   ``HashMap  hash;` `   ``// Constructor (creates arr[] and hash)``   ``public` `MyDS()``   ``{``       ``arr = ``new` `ArrayList();``       ``hash = ``new` `HashMap();``   ``}` `   ``// A Theta(1) function to add an element to MyDS``   ``// data structure``   ``void` `add(``int` `x)``   ``{``      ``// If element is already present, then nothing to do``      ``if` `(hash.get(x) != ``null``)``          ``return``;` `      ``// Else put element at the end of arr[]``      ``int` `s = arr.size();``      ``arr.add(x);` `      ``// And put in hash also``      ``hash.put(x, s);``   ``}` `   ``// A Theta(1) function to remove an element from MyDS``   ``// data structure``   ``void` `remove(``int` `x)``   ``{``       ``// Check if element is present``       ``Integer index = hash.get(x);``       ``if` `(index == ``null``)``          ``return``;` `       ``// If present, then remove element from hash``       ``hash.remove(x);` `       ``// Swap element with last element so that remove from``       ``// arr[] can be done in O(1) time``       ``int` `size = arr.size();``       ``Integer last = arr.get(size-``1``);``       ``Collections.swap(arr, index,  size-``1``);` `       ``// Remove last element (This is O(1))``       ``arr.remove(size-``1``);` `       ``// Update hash table for new index of last element``       ``hash.put(last, index);``    ``}` `    ``// Returns a random element from MyDS``    ``int` `getRandom()``    ``{``       ``// Find a random index from 0 to size - 1``       ``Random rand = ``new` `Random();  ``// Choose a different seed``       ``int` `index = rand.nextInt(arr.size());` `       ``// Return element at randomly picked index``       ``return` `arr.get(index);``    ``}` `    ``// Returns index of element if element is present, otherwise null``    ``Integer search(``int` `x)``    ``{``       ``return` `hash.get(x);``    ``}``}` `// Driver class``class` `Main``{``    ``public` `static` `void` `main (String[] args)``    ``{``        ``MyDS ds = ``new` `MyDS();``        ``ds.add(``10``);``        ``ds.add(``20``);``        ``ds.add(``30``);``        ``ds.add(``40``);``        ``System.out.println(ds.search(``30``));``        ``ds.remove(``20``);``        ``ds.add(``50``);``        ``System.out.println(ds.search(``50``));``        ``System.out.println(ds.getRandom());``    ``}``}`

## Python3

 `'''``Python program to design a DS that``supports following operations``in Theta(n) time:``a) Insert``b) Delete``c) Search``d) getRandom``'''``import` `random` `# Class to represent the required``# data structure``class` `MyDS:` `    ``# Constructor (creates a list and a hash)``    ``def` `__init__(``self``):``        ` `        ``# A resizable array``        ``self``.arr ``=` `[]` `        ``# A hash where keys are lists elements``        ``# and values are indexes of the list``        ``self``.hashd ``=` `{}` `    ``# A Theta(1) function to add an element``    ``# to MyDS data structure``    ``def` `add(``self``, x):``        ` `        ``# If element is already present,``        ``# then nothing has to be done``        ``if` `x ``in` `self``.hashd:``            ``return` `        ``# Else put element at``        ``# the end of the list``        ``s ``=` `len``(``self``.arr)``        ``self``.arr.append(x)` `        ``# Also put it into hash``        ``self``.hashd[x] ``=` `s` `    ``# A Theta(1) function to remove an element``    ``# from MyDS data structure``    ``def` `remove(``self``, x):``        ` `        ``# Check if element is present``        ``index ``=` `self``.hashd.get(x, ``None``)``        ``if` `index ``=``=` `None``:``            ``return` `        ``# If present, then remove``        ``# element from hash``        ``del` `self``.hashd[x]` `        ``# Swap element with last element``        ``# so that removal from the list``        ``# can be done in O(1) time``        ``size ``=` `len``(``self``.arr)``        ``last ``=` `self``.arr[size ``-` `1``]``        ``self``.arr[index], \``        ``self``.arr[size ``-` `1``] ``=` `self``.arr[size ``-` `1``], \``                             ``self``.arr[index]` `        ``# Remove last element (This is O(1))``        ``del` `self``.arr[``-``1``]` `        ``# Update hash table for``        ``# new index of last element``        ``self``.hashd[last] ``=` `index` `    ``# Returns a random element from MyDS``    ``def` `getRandom(``self``):``        ` `        ` `        ``# Find a random index from 0 to size - 1``        ``index ``=` `random.randrange(``0``, ``len``(``self``.arr))` `        ``# Return element at randomly picked index``        ``return` `self``.arr[index]` `    ``# Returns index of element``    ``# if element is present,``    ``# otherwise none``    ``def` `search(``self``, x):``        ``return` `self``.hashd.get(x, ``None``)` `# Driver Code``if` `__name__``=``=``"__main__"``:``    ``ds ``=` `MyDS()``    ``ds.add(``10``)``    ``ds.add(``20``)``    ``ds.add(``30``)``    ``ds.add(``40``)``    ``print``(ds.search(``30``))``    ``ds.remove(``20``)``    ``ds.add(``50``)``    ``print``(ds.search(``50``))``    ``print``(ds.getRandom())` `# This code is contributed``# by Saurabh Singh`

Output

```2
3
30
```