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 an 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 folloiwng operationsin Theta(n) timea) Insertb) Deletec) Searchd) getRandom */ #include<bits/stdc++.h>using namespace std; // class to represent the required data structureclass myStructure{ // A resizable array vector <int> arr; // A hash where keys are array elements and vlaues 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 ekement is already present, then noting 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 mainint 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 folloiwng operations in Theta(n) time a) Insert b) Delete c) Search d) getRandom */import java.util.*; // class to represent the required data structureclass MyDS{ ArrayList<Integer> arr; // A resizable array // A hash where keys are array elements and vlaues are // indexes in arr[] HashMap<Integer, Integer> hash; // Constructor (creates arr[] and hash) public MyDS() { arr = new ArrayList<Integer>(); hash = new HashMap<Integer, Integer>(); } // A Theta(1) function to add an element to MyDS // data structure void add(int x) { // If ekement is already present, then noting 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 classclass 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 operationsin Theta(n) time:a) Insertb) Deletec) Searchd) 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 Codeif __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 40
This article is contributed by Manish Gupta. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
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