leetcode-380-Insert-Delete-GetRandom-O(1)

发表于 2014-03-11 |

描述

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();

分析

这道题要求我们实现一个操作数组的 API，比较特别的一点是插入，删除，获取随机数这样的操作的复杂度是 $O(1)$，要解决这个问题，我们需要用到额外的空间复杂度。可以用数组来存储数据，用哈希表来存储数据与索引之间的关系，插入很好解决，直接在数组末尾添加数据，哈希表增加一条数据即可，时间复杂度是常数，对于删除操作，每次删除时，先根据哈希表获得要删除的值在数组中的位置，然后将数组中该位置对应的值与数组末尾的值进行交互，接着删除数组末尾的值，删除哈希表中的数据即可，时间复杂度也是常数，这样就通过空间交换时间的方式的解决了这个问题。

下一题 381. Insert Delete GetRandom O(1) - Duplicates allowed 允许插入重复的值更有意思。

解决方案1(Java)

class RandomizedSet {
    private ArrayList<Integer> nums;
    private HashMap<Integer, Integer> hashIndexMap;
    private java.util.Random rand = new java.util.Random();
    
    /** Initialize your data structure here. */
    public RandomizedSet() {
        this.nums = new ArrayList<Integer>();
        this.hashIndexMap = new HashMap<Integer, Integer>();
    }
    
    /** Inserts a value to the set. Returns true if the set did not already contain the specified element. */
    public boolean insert(int val) {
        boolean hasKey = hashIndexMap.containsKey(val);
        if (hasKey) {
            return false;
        }
        this.hashIndexMap.put(val, nums.size());
        this.nums.add(val);
        return true;
    }
    
    /** Removes a value from the set. Returns true if the set contained the specified element. */
    public boolean remove(int val) {
        boolean hasKey = hashIndexMap.containsKey(val);
        if (!hasKey) {
            return false;
        }
        int index = hashIndexMap.get(val);
        int lastNum = nums.get(nums.size()-1);
        this.nums.set(index, lastNum);
        this.hashIndexMap.put(lastNum, index);
        
        this.hashIndexMap.remove(val);
        this.nums.remove(nums.size()-1);
        return true;
    }
    
    /** Get a random element from the set. */
    public int getRandom() {
        return this.nums.get(rand.nextInt(nums.size()));
    }
}

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

相关问题

(H) Insert Delete GetRandom O(1) - Duplicates allowed

题目来源