380. Insert Delete GetRandom O(1)

Problem description:

Design a data structure that supports all following operations in average O(1) time.

insert(val): Inserts an item val to the set if not already present.
remove(val): Removes an item val from the set if present.
getRandom: Returns a random element from current set of elements. Each element must have the same probability of being returned.
Example:

// Init an empty set.
RandomizedSet randomSet = new RandomizedSet();

// Inserts 1 to the set. Returns true as 1 was inserted successfully.
randomSet.insert(1);

// Returns false as 2 does not exist in the set.
randomSet.remove(2);

// Inserts 2 to the set, returns true. Set now contains [1,2].
randomSet.insert(2);

// getRandom should return either 1 or 2 randomly.
randomSet.getRandom();

// Removes 1 from the set, returns true. Set now contains [2].
randomSet.remove(1);

// 2 was already in the set, so return false.
randomSet.insert(2);

// Since 2 is the only number in the set, getRandom always return 2.
randomSet.getRandom();

Solution:

In this question, we need to randomly pick a element from the inserted numbers. To do so, we need to know two things:

1. The numbers we currently have
2. Where are they(index)

We use a dictionary to store the value-index mapping, an array to store all the numbers.

Also, the question mentioned want to make each operation O(1). We have two choice to delete the element in array:

1. array.remove(val): takes O(n) time
2. move the element to last index then array.pop(): O(1)

class RandomizedSet:

    def __init__(self):
        """
        Initialize your data structure here.
        """
        self.dic, self.nums = {}, []

    def insert(self, val: int) -> bool:
        """
        Inserts a value to the set. Returns true if the set did not already contain the specified element.
        """
        if val in self.dic:
            return False
        else:
            self.nums.append(val)
            self.dic[val] = len(self.nums)-1
            return True
        
    def remove(self, val: int) -> bool:
        """
        Removes a value from the set. Returns true if the set contained the specified element.
        """
        if val in self.dic:
            # move the last index value to where val is
            # then pop the last element in array to achieve O(1) remove 
            idx = self.dic[val]
            last = self.nums[-1]
            last_idx = self.dic[last]
            self.nums[idx] = last
            self.dic[last] = idx
            self.nums.pop()
            del self.dic[val]
            
            return True
        else:
            return False
        

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

class RandomizedSet {
public:
    //store input numbers in vector
    //save index and 
    unordered_map<int, int> m;
    vector<int> nums;
    
    /** Initialize your data structure here. */
    RandomizedSet() {
        
    }
    
    /** Inserts a value to the set. Returns true if the set did not already contain the specified element. */
    bool insert(int val) {
        if (m.find(val) != m.end()) return false;
        nums.push_back(val);
        m[val] = nums.size() - 1;
        return true;
    }
    
    /** Removes a value from the set. Returns true if the set contained the specified element. */
    bool remove(int val) {
        if (m.find(val) == m.end()) return false;
        int last = nums.back();
        m[last] = m[val];
        nums[m[val]] = last;
        nums.pop_back();
        m.erase(val);
        return true;
    }
    
    /** Get a random element from the set. */
    int getRandom() {
        int idx= rand()%nums.size();
        return nums[idx];
    }
};

/**
 * Your RandomizedSet object will be instantiated and called as such:
 * RandomizedSet obj = new RandomizedSet();
 * bool param_1 = obj.insert(val);
 * bool param_2 = obj.remove(val);
 * int param_3 = obj.getRandom();
 */

time complexity: $O(1)$
space complexity: $O(n)$
reference: