Insert Delete GetRandom O(1)

Problem

https://leetcode.com/problems/insert-delete-getrandom-o1/

Implement the RandomizedSet class:

RandomizedSet() Initializes the RandomizedSet object.
bool insert(int val) Inserts an item val into the set if not present. Returns true if the item was not present, false otherwise.
bool remove(int val) Removes an item val from the set if present. Returns true if the item was present, false otherwise.
int getRandom() Returns a random element from the current set of elements (it’s guaranteed that at least one element exists when this method is called). Each element must have the same probability of being returned.

You must implement the functions of the class such that each function works in average O(1) time complexity.

Example 1:

Input
["RandomizedSet", "insert", "remove", "insert", "getRandom", "remove", "insert", "getRandom"]
[[], [1], [2], [2], [], [1], [2], []]
Output
[null, true, false, true, 2, true, false, 2]

Explanation
RandomizedSet randomizedSet = new RandomizedSet();
randomizedSet.insert(1); // Inserts 1 to the set. Returns true as 1 was inserted successfully.
randomizedSet.remove(2); // Returns false as 2 does not exist in the set.
randomizedSet.insert(2); // Inserts 2 to the set, returns true. Set now contains [1,2].
randomizedSet.getRandom(); // getRandom() should return either 1 or 2 randomly.
randomizedSet.remove(1); // Removes 1 from the set, returns true. Set now contains [2].
randomizedSet.insert(2); // 2 was already in the set, so return false.
randomizedSet.getRandom(); // Since 2 is the only number in the set, getRandom() will always return 2.

Constraints:

-2:sup:`31`<= val <= 2:sup:`31`- 1
At most 2 * ``\ ``10:sup:`5` calls will be made to insert, remove, and getRandom.
There will be at least one element in the data structure when getRandom is called.

Pattern

Array, Hash Table, Math, Design, Randomized

Solution

By default, we can insert and getRandom elements from an array in \(O(1)\) time. To remove an element from an array in \(O(1)\) time, it needs to be at the end of the array. We can move val to the end. To do this in \(O(1)\) time, we need to find the index of val in the array in \(O(1)\) time. We can use a dictionary to store the indices of each element in the array.

Code

import random


class RandomizedSet:
    """A data structure that supports ``insert``, ``remove``, and ``getRandom``
    in O(1) time.
    """

    def __init__(self):
        self.indices = {}
        self.arr = []

    def insert(self, val: int) -> bool:
        """Inserts ``val`` into the set. Returns ``True`` if ``val`` was not
        present and ``False`` otherwise.
        """
        if val in self.indices:
            return False
        else:
            self.arr.append(val)
            self.indices[val] = len(self.arr) - 1
            return True

    def remove(self, val: int) -> bool:
        """Removes ``val`` from the set. Returns ``True`` if ``val`` was
        present and ``False`` otherwise.
        """
        if val not in self.indices:
            return False
        else:
            i = self.indices[val]
            self.indices[self.arr[-1]] = i

            self.arr[i] = self.arr[-1]

            del self.indices[val]
            self.arr.pop()
            return True

    def getRandom(self) -> int:
        """Returns a random element from the set.
        """
        return random.choice(self.arr)

Test

>>> from insert_delete_getrandom_o1__approach_1 import RandomizedSet
>>> random_set = RandomizedSet()
>>> random_set.insert(1)
True
>>> random_set.remove(2)
False
>>> random_set.getRandom()
1
>>> random_set.insert(2)
True
>>> random_set.remove(1)
True
>>> random_set.insert(2)
False
>>> random_set.getRandom()
2

Complexity

Insert Time: \(O(1)\) — list expansion is amortized
Remove Time: \(O(1)\) — constant time to find index and move element to end
Get Random Time: \(O(1)\) — constant time to choose random element
Auxiliary Space: \(O(n)\) — array and hash map storage

class insert_delete_getrandom_o1__approach_1.RandomizedSet

Bases: object

A data structure that supports insert, remove, and getRandom in O(1) time.

getRandom() → int: Returns a random element from the set.

insert(val: int) → bool: Inserts val into the set. Returns True if val was not present and False otherwise.

remove(val: int) → bool: Removes val from the set. Returns True if val was present and False otherwise.