[LeetCode]146. LRU Cache 深入浅出讲解和代码示例

1、汇总概要

以下思路涵盖了哈希与双向链表的结合使用、缓存设计等知识点

2、题目

Design and implement a data structure for Least Recently Used (LRU) cache. It should support the following operations: get and put.

get(key) - Get the value (will always be positive) of the key if the key exists in the cache, otherwise return -1.
put(key, value) - Set or insert the value if the key is not already present. When the cache reached its capacity, it should invalidate the least recently used item before inserting a new item.

Follow up:
Could you do both operations in O(1) time complexity?

Example:

LRUCache cache = new LRUCache( 2 /* capacity */ );

cache.put(1, 1);
cache.put(2, 2);
cache.get(1);       // returns 1
cache.put(3, 3);    // evicts key 2
cache.get(2);       // returns -1 (not found)
cache.put(4, 4);    // evicts key 1
cache.get(1);       // returns -1 (not found)
cache.get(3);       // returns 3
cache.get(4);       // returns 4

3、审题

设计一个简单版的最近使用缓存模型。缓存空间有容量限制，时间复杂度要求是O(1)。

其中“最近使用”是指最近被访问过(被cache.get调用过）。

4、解题思路

以上对cache的操作有：添加(put)、查找(get)、替换(put)，因有容量限制，还需有删除，每次当容量满时，将最久未使用的节点删除。

为快速添加和删除，我们可以用双向链表来设计cache，链表中从头到尾的数据顺序依次是，(最近访问)->...(最旧访问)：

1）添加节点：新节点插入到表头即可，时间复杂度O(1)；

2）查找节点：每次节点被查询到时，将节点移动到链表头部，时间复杂度O(n)

3)  替换节点：查找到后替换(更新节点value)，将节点移动到链表头部；

可见在查找节点时，因对链表需遍历，时间复杂度O(n)，为达到O(1)，可以考虑数据结构中加入哈希(hash)。

=>我们需要用两种数据结构来解题：双向链表、哈希表

示意图如下：

5、代码示例 - Java

import java.util.*;

class Node{
	int key;
	int value;
	Node next;
	Node pre;
	public Node(int key,int value,Node pre, Node next){
		this.key = key;
		this.value = value;
		this.pre = pre;
		this.next = next;
	}
}

public class LRUCache {
	int capacity;
	int count;//cache size
	Node head;
	Node tail;
	HashMaphm;
    public LRUCache(int capacity) { //only initial 2 Node is enough, head/tail
    	this.capacity = capacity;
    	this.count = 2;
    	this.head = new Node(-1,-1,null,null);
    	this.tail = new Node(-2,-2,this.head,null);
    	this.head.next = this.tail;
        hm = new HashMap();
        hm.put(this.head.key, this.head);
        hm.put(this.tail.key, this.tail);
    }
    
    public int get(int key) {
    	int value = -1;
    	if(hm.containsKey(key)){
    		Node nd = hm.get(key);
    		value = nd.value;
    		detachNode(nd); //detach nd from current place
    		insertToHead(nd); //insert nd into head
    	}
		return value;
    }
    
    public void put(int key, int value) {
    	if(hm.containsKey(key)){ //update
    		Node nd = hm.get(key);
    		nd.value = value;
    		//move to head
    		detachNode(nd); //detach nd from current place
    		insertToHead(nd); //insert nd into head
    	}else{ //add
    		Node newNd = new Node(key,value,null,this.head);
    		this.head.pre = newNd; //insert into head
    		this.head = newNd;
    		hm.put(key, newNd); //add into hashMap
    		this.count ++;
    		if(this.count > capacity){ //need delete node
    			removeNode();
    		}
    	}
    }
    //common func
    public void insertToHead(Node nd){
    	this.head.pre = nd;
    	nd.next = this.head;
    	nd.pre = null;
    	this.head = nd;
    }
    public void detachNode(Node nd){
    	nd.pre.next = nd.next;
    	if(nd.next!=null){
    		nd.next.pre = nd.pre;
    	}else{
    		this.tail = nd.pre;
    	}
    }
    public void removeNode(){ //remove from tail
		int tailKey = this.tail.key;
		this.tail = this.tail.pre;
		this.tail.next = null;
		hm.remove(tailKey);
		this.count --;
    }
    public void printCache(){
    	System.out.println("\nPRINT CACHE ------ ");
    	System.out.println("count: "+count);
    	System.out.println("From head:");
    	Node p = this.head;
    	while(p!=null){
    		System.out.println("key: "+p.key+" value: "+p.value);
    		p = p.next;
    	}
    	System.out.println("From tail:");
    	p = this.tail;
    	while(p!=null){
    		System.out.println("key: "+p.key+" value: "+p.value);
    		p = p.pre;
    	}
    	
    }
    
    public static void main(String[] args){
    	LRUCache lc = new LRUCache(3);
    	lc.printCache();
    	
    	lc.put(1, 1);
    	lc.put(2, 2);
    	lc.put(3, 3);
    	lc.printCache();
    	
    	lc.get(2);
    	lc.printCache();
    	
    	lc.put(4, 4);
    	lc.printCache();
    	
    	lc.get(1);
    	lc.printCache();
    	
    	lc.put(3, 33);
    	lc.printCache();	
    }
}

【注：】这里要区分下hashmap和hashtable在java中使用的区别(继承于不同的类、线程安全、扩容等方面)

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