380. Insert Delete GetRandom O(1) (Hard)

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

  1. insert(val): Inserts an item val to the set if not already present.
  2. remove(val): Removes an item val from the set if present.
  3. 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 1 is the only number in the set, getRandom always return 1.
randomSet.getRandom();

Solution:

这道题让我们在常数时间范围内实现插入删除和获得随机数操作,如果这道题没有常数时间的限制,那么将会是一道非常简单的题,我们直接用一个set就可以搞定所有的操作。但是由于时间的限制,我们无法在常数时间内实现获取随机数,所以只能另辟蹊径。此题的正确解法是利用到了一个一维数组和一个哈希表,其中数组用来保存数字,哈希表用来建立每个数字和其在数组中的位置之间的映射,对于插入操作,我们先看这个数字是否已经在哈希表中存在,如果存在的话直接返回false,不存在的话,我们将其插入到数组的末尾,然后建立数字和其位置的映射。删除操作是比较tricky的,我们还是要先判断其是否在哈希表里,如果没有,直接返回false。由于哈希表的删除是常数时间的,而数组并不是,为了使数组删除也能常数级,我们实际上将要删除的数字和数组的最后一个数字调换个位置,然后修改对应的哈希表中的值,这样我们只需要删除数组的最后一个元素即可,保证了常数时间内的删除。而返回随机数对于数组来说就很简单了,我们只要随机生成一个位置,返回该位置上的数字即可,参见代码如下:

Solution:

class RandomizedSet {
public:
    /** 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.count(val)) 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.count(val)) 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() {
        return nums[rand()%nums.size()];
    }
private:
    vector<int> nums;
    unordered_map<int, int> m;
};

/**
 * 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();
 */

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