InsertDeleteGetRandomO1

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.

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.

Pattern

Array, Hash Table, Math, Design, Randomized

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 InsertDeleteGetRandomO1 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

class InsertDeleteGetRandomO1.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.