[LeetCode] 460. LFU Cache 最近最不常用页面置换缓存器

Posted 2021-01-02 轻风舞动

Design and implement a data structure for Least Frequently Used (LFU) 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 reaches its capacity, it should invalidate the least frequently used item before inserting a new item. For the purpose of this problem, when there is a tie (i.e., two or more keys that have the same frequency), the least recently used key would be evicted.

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

Example:

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

 

双向链表（Doubly Linked List） + 哈希表（Hash Table）

 Java:

public class LFUCache {
    Node head = null;
    final int capacity;
    Map<Integer, Integer> valueMap;
    Map<Integer, Node> nodeMap;

    public LFUCache (int capacity) {
        this.capacity = capacity;
        valueMap = new HashMap<>(this.capacity, 1f);
        nodeMap = new HashMap<>(this.capacity, 1f);
    }

    public int get(int key) {
        if (valueMap.containsKey(key)) increase(key, valueMap.get(key));
        return valueMap.getOrDefault(key, -1);
    }

    private void increase(int key, int value) {
        Node node = nodeMap.get(key);
        node.keys.remove(key);
        if (Objects.isNull(node.next)) node.next = new Node(node, null, 1 + node.count, key);
        else if (node.next.count == node.count + 1) node.next.keys.add(key);
        else node.next = node.next.prev = new Node(node, node.next, node.count + 1, key);
        nodeMap.put(key, node.next);
        valueMap.put(key, value);
        if (node.keys.isEmpty()) remove(node);
    }

    private void remove(Node node) {
        if (head == node) head = node.next;
        else node.prev.next = node.next;
        if (Objects.nonNull(node.next)) node.next.prev = node.prev;
    }

    public void set(int key, int value) {
        if (0 == this.capacity) return;
        if (valueMap.containsKey(key)) {
            increase(key, value);
        } else {
            if (valueMap.size() == this.capacity) remove();
            valueMap.put(key, value);
            add(key);
        }
    }

    private void add(int key) {
        if (Objects.isNull(head)) head = new Node(null, null, 1, key);
        else if (head.count == 1) head.keys.add(key);
        else head = head.prev = new Node(null, head, 1, key);
        nodeMap.put(key, head);
    }

    private void remove() {
        if (Objects.isNull(head)) return;
        int oldest = head.keys.iterator().next();
        head.keys.remove(oldest);
        if (head.keys.isEmpty()) remove(head);
        nodeMap.remove(oldest);
        valueMap.remove(oldest);
    }

    class Node {
        public Node prev, next;
        public final int count;
        public LinkedHashSet<Integer> keys = new LinkedHashSet<>();

        public Node(Node prev, Node next, int count, int key) {
            this.prev = prev;
            this.next = next;
            this.count = count;
            keys.add(key);
        }
    }
}　

Python:

class KeyNode(object):
    def __init__(self, key, value, freq = 1):
        self.key = key
        self.value = value
        self.freq = freq
        self.prev = self.next = None

class FreqNode(object):
    def __init__(self, freq, prev, next):
        self.freq = freq
        self.prev = prev
        self.next = next
        self.first = self.last = None

class LFUCache(object):

    def __init__(self, capacity):
        """
        
        :type capacity: int
        """
        self.capacity = capacity
        self.keyDict = dict()
        self.freqDict = dict()
        self.head = None

    def get(self, key):
        """
        :type key: int
        :rtype: int
        """
        if key in self.keyDict:
            keyNode = self.keyDict[key]
            value = keyNode.value
            self.increase(key, value)
            return value
        return -1

    def set(self, key, value):
        """
        :type key: int
        :type value: int
        :rtype: void
        """
        if self.capacity == 0:
            return
        if key in self.keyDict:
            self.increase(key, value)
            return
        if len(self.keyDict) == self.capacity:
            self.removeKeyNode(self.head.last)
        self.insertKeyNode(key, value)

    def increase(self, key, value):
        """
        Increments the freq of an existing KeyNode<key, value> by 1.
        :type key: str
        :rtype: void
        """
        keyNode = self.keyDict[key]
        keyNode.value = value
        freqNode = self.freqDict[keyNode.freq]
        nextFreqNode = freqNode.next
        keyNode.freq += 1
        if nextFreqNode is None or nextFreqNode.freq > keyNode.freq:
            nextFreqNode = self.insertFreqNodeAfter(keyNode.freq, freqNode)
        self.unlinkKey(keyNode, freqNode)
        self.linkKey(keyNode, nextFreqNode)

    def insertKeyNode(self, key, value):
        """
        Inserts a new KeyNode<key, value> with freq 1.
        :type key: str
        :rtype: void
        """
        keyNode = self.keyDict[key] = KeyNode(key, value)
        freqNode = self.freqDict.get(1)
        if freqNode is None:
            freqNode = self.freqDict[1] = FreqNode(1, None, self.head)
            if self.head:
                self.head.prev = freqNode
            self.head = freqNode
        self.linkKey(keyNode, freqNode)

    def delFreqNode(self, freqNode):
        """
        Delete freqNode.
        :rtype: void
        """
        prev, next = freqNode.prev, freqNode.next
        if prev: prev.next = next
        if next: next.prev = prev
        if self.head == freqNode: self.head = next
        del self.freqDict[freqNode.freq]

    def insertFreqNodeAfter(self, freq, node):
        """
        Insert a new FreqNode(freq) after node.
        :rtype: FreqNode
        """
        newNode = FreqNode(freq, node, node.next)
        self.freqDict[freq] = newNode
        if node.next: node.next.prev = newNode
        node.next = newNode
        return newNode

    def removeKeyNode(self, keyNode):
        """
        Remove keyNode
        :rtype: void
        """
        self.unlinkKey(keyNode, self.freqDict[keyNode.freq])
        del self.keyDict[keyNode.key]

    def unlinkKey(self, keyNode, freqNode):
        """
        Unlink keyNode from freqNode
        :rtype: void
        """
        next, prev = keyNode.next, keyNode.prev
        if prev: prev.next = next
        if next: next.prev = prev
        if freqNode.first == keyNode: freqNode.first = next
        if freqNode.last == keyNode: freqNode.last = prev
        if freqNode.first is None: self.delFreqNode(freqNode)

    def linkKey(self, keyNode, freqNode):
        """
        Link keyNode to freqNode
        :rtype: void
        """
        firstKeyNode = freqNode.first
        keyNode.prev = None
        keyNode.next = firstKeyNode
        if firstKeyNode: firstKeyNode.prev = keyNode
        freqNode.first = keyNode
        if freqNode.last is None: freqNode.last = keyNode

# Your LFUCache object will be instantiated and called as such:
# obj = LFUCache(capacity)
# param_1 = obj.get(key)
# obj.set(key,value)　　

Python:

class CacheNode(object):
    def __init__(self, key, value, freq_node, pre, nxt):
        self.key = key
        self.value = value
        self.freq_node = freq_node
        self.pre = pre # previous CacheNode
        self.nxt = nxt # next CacheNode

    def free_myself(self):
        if self.freq_node.cache_head == self.freq_node.cache_tail:
            self.freq_node.cache_head = self.freq_node.cache_tail = None
        elif self.freq_node.cache_head == self:
            self.nxt.pre = None
            self.freq_node.cache_head = self.nxt
        elif self.freq_node.cache_tail == self:
            self.pre.nxt = None
            self.freq_node.cache_tail = self.pre
        else:
            self.pre.nxt = self.nxt
            self.nxt.pre = self.pre

        self.pre = None
        self.nxt = None
        self.freq_node = None

class FreqNode(object):
    def __init__(self, freq, pre, nxt):
        self.freq = freq
        self.pre = pre # previous FreqNode
        self.nxt = nxt # next FreqNode
        self.cache_head = None # CacheNode head under this FreqNode
        self.cache_tail = None # CacheNode tail under this FreqNode

    def count_caches(self):
        if self.cache_head is None and self.cache_tail is None:
            return 0
        elif self.cache_head == self.cache_tail:
            return 1
        else:
            return \'2+\'

    def remove(self):
        if self.pre is not None:
            self.pre.nxt = self.nxt
        if self.nxt is not None:
            self.nxt.pre = self.pre

        pre = self.pre
        nxt = self.nxt
        self.pre = self.nxt = self.cache_head = self.cache_tail = None

        return (pre, nxt)

    def pop_head_cache(self):
        if self.cache_head is None and self.cache_tail is None:
            return None
        elif self.cache_head == self.cache_tail:
            cache_head = self.cache_head
            self.cache_head = self.cache_tail = None
            return cache_head
        else:
            cache_head = self.cache_head
            self.cache_head.nxt.pre = None
            self.cache_head = self.cache_head.nxt
            return cache_head

    def append_cache_to_tail(self, cache_node):
        cache_node.freq_node = self

        if self.cache_head is None and self.cache_tail is None:
            self.cache_head = self.cache_tail = cache_node
        else:
            cache_node.pre = self.cache_tail
            cache_node.nxt = None
            self.cache_tail.nxt = cache_node
            self.cache_tail = cache_node

    def insert_after_me(self, freq_node):
        freq_node.pre = self
        freq_node.nxt = self.nxt

        if self.nxt is not None:
            self.nxt.pre = freq_node
        
        self.nxt = freq_node

    def insert_before_me(self, freq_node):
        if self.pre is not None:
            self.pre.nxt = freq_node
        
        freq_node.pre = self.pre
        freq_node.nxt = self
        self.pre = freq_node
        
class LFUCache(object):

    def __init__(self, capacity):
        self.cache = {} # {key: cache_node}
        self.capacity = capacity
        self.freq_link_head = None
    
    def get(self, key):
        if key in self.cache:
            cache_node = self.cache[key]
            freq_node = cache_node.freq_node
            value = cache_node.value

            self.move_forward(cache_node, freq_node)

            return value
        else:
            return -1

    def set(self, key, value):
        if self.capacity <= 0:
            return -1
        
        if key not in self.cache:
            if len(self.cache) >= self.capacity:
                self.dump_cache()

            self.create_cache(key, value)
        else:
            cache_node = self.cache[key]
            freq_node = cache_node.freq_node
            cache_node.value = value

            self.move_forward(cache_node, freq_node)

    def move_forward(self, cache_node, freq_node):
        if freq_node.nxt is None or freq_node.nxt.freq != freq_node.freq + 1:
            target_freq_node = FreqNode(freq_node.freq + 1, None, None)
            target_empty = True
        else:
            target_freq_node = freq_node.nxt
            target_empty = False
        
        cache_node.free_myself()
        target_freq_node.append_cache_to_tail(cache_node)

        if target_empty:
            freq_node.insert_after_me(target_freq_node)


        if freq_node.count_caches() == 0:
            if self.freq_link_head == freq_node:
                self.freq_link_head = target_freq_node

            freq_node.remove()

    def dump_cache(self):
        head_freq_node = self.freq_link_head
        self.cache.pop(head_freq_node.cache_head.key)
        head_freq_node.pop_head_cache()

        if head_freq_node.count_caches() == 0:
            self.freq_link_head = head_freq_node.nxt
            head_freq_node.remove()

    def create_cache(self, key, value):
        cache_node = CacheNode(key, value, None, None, None)
        self.cache[key] = cache_node
        
        if self.freq_link_head is None or self.freq_link_head.freq != 0:
            new_freq_node = FreqNode(0, None, None)
            new_freq_node.append_cache_to_tail(cache_node)

            if self.freq_link_head is not None:
                self.freq_link_head.insert_before_me(new_freq_node)
            
            self.freq_link_head = new_freq_node
        else:
            self.freq_link_head.append_cache_to_tail(cache_node)

C++:

class LFUCache {
public:
    LFUCache(int capacity) {
        cap = capacity;
    }
    
    int get(int key) {
        if (m.count(key) == 0) return -1;
        freq[m[key].second].erase(iter[key]);
        ++m[key].second;
        freq[m[key].second].push_back(key);
        iter[key] = --freq[m[key].second].end();
        if (freq[minFreq].size() == 0) ++minFreq;
        return m[key].first;
    }
    
    void put(int key, int value) {
        if (cap <= 0) return;
        if (get(key) != -1) {
            m[key].first = value;
            return;
        }
        if (m.size() >= cap) {
            m.erase(freq[minFreq].front());
            iter.erase(freq[minFreq].front());
            freq[minFreq].pop_front();
        }
        m[key] = {value, 1};
        freq[1].push_back(key);
        iter[key] = --freq[1].end();
        minFreq = 1;
    }

private:
    int cap, minFreq;
    unordered_map<int, pair<int, int>> m;
    unordered_map<int, list<int>> freq;
    unordered_map<int, list<int>::iterator> iter;
};

　　

[LeetCode] 146. LRU Cache 近期最少使用缓存

　　

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