381-增加， 删除， 获取随机数

Description:

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

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Note: Duplicate elements are allowed.

insert(val): Inserts an item val to the collection.remove(val): Removes an item val from the collection if present.getRandom: Returns a random element from current collection of elements. The probability of each element being returned is linearly related to the number of same value the collection contains.

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Example:

// Init an empty collection. RandomizedCollection collection = new RandomizedCollection(); // Inserts 1 to the collection. Returns true as the collection did not contain 1. collection.insert(1); // Inserts another 1 to the collection. Returns false as the collection contained 1. Collection now contains [1,1]. collection.insert(1); // Inserts 2 to the collection, returns true. Collection now contains [1,1,2]. collection.insert(2); // getRandom should return 1 with the probability 2/3, and returns 2 with the probability 1/3. collection.getRandom(); // Removes 1 from the collection, returns true. Collection now contains [1,2]. collection.remove(1); // getRandom should return 1 and 2 both equally likely. collection.getRandom();

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问题描述:

设计一个数据结构，支持以O(1)时间复杂度执行以下操作: 1. insert(val):向集合中插入一个元素。若集合之前无val，返回true，否则返回false。 2. remove(va):如果集合中有val，则删除val。若集合有val，返回true，否则返回false。 3. getRandom():随机返回集合中一个元素，注意返回某元素的概率与该元素在集合中的数目线性相关。

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问题分析:

这题的前置问题是这道题: https://leetcode.com/problems/insert-delete-getrandom-o1/description/ 解法是: https://leetcode.com/problems/insert-delete-getrandom-o1/discuss/85401/Java-solution-using-a-HashMap-and-an-ArrayList-along-with-a-follow-up.-(131-ms)

首先要注意到，操作中并没有获取任一个元素，只是插入，删除还有随机获取元素 需要维护两个结构: 1.nums,存储元素 2.locs,存储元素对应下标

由于插入和随机获取都是O(1),解题的核心是每次删除nums尾部的元素,若被删除元素位于尾部，直接删除list和locs中对应下标，若不是，需要将删除元素与list尾部元素进行替换

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class RandomizedCollection { Map<Integer, Set<Integer>> locs; List<Integer> nums; Random rand; /** Initialize your data structure here. */ public RandomizedCollection() { locs = new HashMap(); nums = new ArrayList(); rand = new Random(); } /** Inserts a value to the collection. Returns true if the collection did not already contain the specified element. */ public boolean insert(int val) { boolean contain = locs.containsKey(val); if(!contain) locs.put(val, new LinkedHashSet()); locs.get(val).add(nums.size()); nums.add(val); return !contain; } /** Removes a value from the collection. Returns true if the collection contained the specified element. */ public boolean remove(int val) { if(!locs.containsKey(val)) return false; int loc = locs.get(val).iterator().next(); locs.get(val).remove(loc); int right = nums.size() - 1; //若不是尾部元素，需要进行替换，替换有两步，一个是元素值的替换，一个是下标的替换 if(loc < right){ int lastOne = nums.get(right); nums.set(loc, lastOne); locs.get(lastOne).remove(right); locs.get(lastOne).add(loc); } nums.remove(right); if(locs.get(val).isEmpty()) locs.remove(val); return true; } /** Get a random element from the collection. */ public int getRandom() { return nums.get(rand.nextInt(nums.size())); } }