README.md

460. LFU Cache

Design and implement a data structure for a Least Frequently Used (LFU) cache.

Implement the LFUCache class:

• LFUCache(int capacity) Initializes the object with the capacity of the data structure.
• int get(int key) Gets the value of the key if the key exists in the cache. Otherwise, returns -1.
• void put(int key, int value) Update the value of the key if present, or inserts the key if not already present. When the cache reaches its capacity, it should invalidate and remove the least frequently used key before inserting a new item. For this problem, when there is a tie (i.e., two or more keys with the same frequency), the least recently used key would be invalidated.

To determine the least frequently used key, a use counter is maintained for each key in the cache. The key with the smallest use counter is the least frequently used key.

When a key is first inserted into the cache, its use counter is set to 1 (due to the put operation). The use counter for a key in the cache is incremented either a get or put operation is called on it.

The functions get and put must each run in O(1) average time complexity.

Example 1:

Input:
["LFUCache", "put", "put", "get", "put", "get", "get", "put", "get", "get", "get"]
[[2], [1, 1], [2, 2], [1], [3, 3], [2], [3], [4, 4], [1], [3], [4]]
Output:
[null, null, null, 1, null, -1, 3, null, -1, 3, 4]
Explanation:
// cnt(x) = the use counter for key x
// cache=[] will show the last used order for tiebreakers (leftmost element is  most recent)
LFUCache lfu = new LFUCache(2);
lfu.put(1, 1);   // cache=[1,_], cnt(1)=1
lfu.put(2, 2);   // cache=[2,1], cnt(2)=1, cnt(1)=1
lfu.get(1);      // return 1
                 // cache=[1,2], cnt(2)=1, cnt(1)=2
lfu.put(3, 3);   // 2 is the LFU key because cnt(2)=1 is the smallest, invalidate 2.
                 // cache=[3,1], cnt(3)=1, cnt(1)=2
lfu.get(2);      // return -1 (not found)
lfu.get(3);      // return 3
                 // cache=[3,1], cnt(3)=2, cnt(1)=2
lfu.put(4, 4);   // Both 1 and 3 have the same cnt, but 1 is LRU, invalidate 1.
                 // cache=[4,3], cnt(4)=1, cnt(3)=2
lfu.get(1);      // return -1 (not found)
lfu.get(3);      // return 3
                 // cache=[3,4], cnt(4)=1, cnt(3)=3
lfu.get(4);      // return 4
                 // cache=[4,3], cnt(4)=2, cnt(3)=3

Constraints:

• 1 <= capacity <= 104
• 0 <= key <= 105
• 0 <= value <= 109
• At most 2 * 105 calls will be made to get and put.

Solutions (Python)

1. Solution

class ListNode:

    def __init__(self, key=-1, val=0, prev=None, next=None):
        self.key = key
        self.val = val
        self.prev = prev
        self.next = next
        self.count = 0


class LFUCache:

    def __init__(self, capacity: int):
        self.capacity = capacity
        self.cache = {}
        self.headtails = {}
        self.hair = ListNode()

    def get(self, key: int) -> int:
        if key not in self.cache:
            return -1

        node = self.cache[key]
        head, tail = self.headtails[node.count]
        if head.key == node.key and tail.key == node.key:
            self.headtails.pop(node.count)
        elif head.key == node.key:
            self.headtails[node.count][0] = node.next
        elif tail.key == node.key:
            self.headtails[node.count][1] = node.prev
        node.prev.next = node.next
        if node.next is not None:
            node.next.prev = node.prev

        node.count += 1
        if tail.next is None or tail.next.count > node.count:
            if tail.key == node.key:
                tail = node.prev
            self.headtails[node.count] = [node, node]
        else:
            tail = self.headtails[node.count][1]
            self.headtails[node.count][1] = node
        node.prev = tail
        node.next = tail.next
        tail.next = node
        if node.next is not None:
            node.next.prev = node

        return node.val

    def put(self, key: int, value: int) -> None:
        if key not in self.cache:
            if len(self.cache) == self.capacity:
                head, tail = self.headtails[self.hair.next.count]
                self.cache.pop(head.key)
                if head.key == tail.key:
                    self.headtails.pop(head.count)
                else:
                    self.headtails[head.count][0] = head.next
                self.hair.next = head.next
                if head.next is not None:
                    head.next.prev = self.hair

            node = ListNode(key, value, self.hair, self.hair.next)
            self.cache[key] = node
            self.headtails[0] = [node, node]
            self.hair.next = node
            if node.next is not None:
                node.next.prev = node

        self.cache[key].val = value
        self.get(key)


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