LRU Cache

描述

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

get(key) - Get the value (will always be positive) of the key if the key exists in the cache, otherwise return -1.

set(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.

分析

为了使查找、插入和删除都有较高的性能,这题的关键是要使用一个双向链表和一个HashMap,因为:

  • HashMap保存每个节点的地址,可以基本保证在O(1)时间内查找节点
  • 双向链表能后在O(1)时间内添加和删除节点,单链表则不行

具体实现细节:

  • 越靠近链表头部,表示节点上次访问距离现在时间最短,尾部的节点表示最近访问最少
  • 访问节点时,如果节点存在,把该节点交换到链表头部,同时更新hash表中该节点的地址
  • 插入节点时,如果cache的size达到了上限capacity,则删除尾部节点,同时要在hash表中删除对应的项;新节点插入链表头部
LRU Cche
Figure: LRU Cche

代码

C++的std::list 就是个双向链表,且它有个 splice()方法,O(1)时间,非常好用。

// LRU Cache
// 时间复杂度O(logn),空间复杂度O(n)
class LRUCache{
private:
    struct CacheNode {
        int key;
        int value;
        CacheNode(int k, int v) :key(k), value(v){}
    };
public:
    LRUCache(int capacity) {
        this->capacity = capacity;
    }

    int get(int key) {
        if (cacheMap.find(key) == cacheMap.end()) return -1;

        // 把当前访问的节点移到链表头部,并且更新map中该节点的地址
        cacheList.splice(cacheList.begin(), cacheList, cacheMap[key]); 
        cacheMap[key] = cacheList.begin();
        return cacheMap[key]->value;
    }

    void set(int key, int value) {
        if (cacheMap.find(key) == cacheMap.end()) {
            if (cacheList.size() == capacity) { //删除链表尾部节点(最少访问的节点)
                cacheMap.erase(cacheList.back().key);
                cacheList.pop_back();
            }
            // 插入新节点到链表头部, 并且在map中增加该节点
            cacheList.push_front(CacheNode(key, value));
            cacheMap[key] = cacheList.begin();
        } else {
            //更新节点的值,把当前访问的节点移到链表头部,并且更新map中该节点的地址
            cacheMap[key]->value = value;
            cacheList.splice(cacheList.begin(), cacheList, cacheMap[key]);
            cacheMap[key] = cacheList.begin();
        }
    }
private:
    list<CacheNode> cacheList; // doubly linked list
    unordered_map<int, list<CacheNode>::iterator> cacheMap;
    int capacity;
};

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