from typing import Callable, Optional


class DoubleLinkedListNode:
    """
    Double Linked List Node built specifically for LFU Cache
    """

    def __init__(self, key: int, val: int):
        self.key = key
        self.val = val
        self.freq = 0
        self.next = None
        self.prev = None


class DoubleLinkedList:
    """
    Double Linked List built specifically for LFU Cache
    """

    def __init__(self):
        self.head = DoubleLinkedListNode(None, None)
        self.rear = DoubleLinkedListNode(None, None)
        self.head.next, self.rear.prev = self.rear, self.head

    def add(self, node: DoubleLinkedListNode) -> None:
        """
        Adds the given node at the head of the list and shifting it to proper position
        """

        temp = self.rear.prev

        self.rear.prev, node.next = node, self.rear
        temp.next, node.prev = node, temp
        node.freq += 1
        self._position_node(node)

    def _position_node(self, node: DoubleLinkedListNode) -> None:
        while node.prev.key and node.prev.freq > node.freq:
            node1, node2 = node, node.prev
            node1.prev, node2.next = node2.prev, node1.prev
            node1.next, node2.prev = node2, node1

    def remove(self, node: DoubleLinkedListNode) -> DoubleLinkedListNode:
        """
        Removes and returns the given node from the list
        """

        temp_last, temp_next = node.prev, node.next
        node.prev, node.next = None, None
        temp_last.next, temp_next.prev = temp_next, temp_last
        return node


class LFUCache:
    """
    LFU Cache to store a given capacity of data. Can be used as a stand-alone object
    or as a function decorator.

    >>> cache = LFUCache(2)
    >>> cache.set(1, 1)
    >>> cache.set(2, 2)
    >>> cache.get(1)
    1
    >>> cache.set(3, 3)
    >>> cache.get(2)  # None is returned
    >>> cache.set(4, 4)
    >>> cache.get(1)  # None is returned
    >>> cache.get(3)
    3
    >>> cache.get(4)
    4
    >>> cache
    CacheInfo(hits=3, misses=2, capacity=2, current_size=2)
    >>> @LFUCache.decorator(100)
    ... def fib(num):
    ...     if num in (1, 2):
    ...         return 1
    ...     return fib(num - 1) + fib(num - 2)

    >>> for i in range(1, 101):
    ...     res = fib(i)

    >>> fib.cache_info()
    CacheInfo(hits=196, misses=100, capacity=100, current_size=100)
    """

    # class variable to map the decorator functions to their respective instance
    decorator_function_to_instance_map = {}

    def __init__(self, capacity: int):
        self.list = DoubleLinkedList()
        self.capacity = capacity
        self.num_keys = 0
        self.hits = 0
        self.miss = 0
        self.cache = {}

    def __repr__(self) -> str:
        """
        Return the details for the cache instance
        [hits, misses, capacity, current_size]
        """

        return (
            f"CacheInfo(hits={self.hits}, misses={self.miss}, "
            f"capacity={self.capacity}, current_size={self.num_keys})"
        )

    def __contains__(self, key: int) -> bool:
        """
        >>> cache = LFUCache(1)
        >>> 1 in cache
        False
        >>> cache.set(1, 1)
        >>> 1 in cache
        True
        """
        return key in self.cache

    def get(self, key: int) -> Optional[int]:
        """
        Returns the value for the input key and updates the Double Linked List. Returns
        None if key is not present in cache
        """

        if key in self.cache:
            self.hits += 1
            self.list.add(self.list.remove(self.cache[key]))
            return self.cache[key].val
        self.miss += 1
        return None

    def set(self, key: int, value: int) -> None:
        """
        Sets the value for the input key and updates the Double Linked List
        """

        if key not in self.cache:
            if self.num_keys >= self.capacity:
                key_to_delete = self.list.head.next.key
                self.list.remove(self.cache[key_to_delete])
                del self.cache[key_to_delete]
                self.num_keys -= 1
            self.cache[key] = DoubleLinkedListNode(key, value)
            self.list.add(self.cache[key])
            self.num_keys += 1

        else:
            node = self.list.remove(self.cache[key])
            node.val = value
            self.list.add(node)

    @staticmethod
    def decorator(size: int = 128):
        """
        Decorator version of LFU Cache
        """

        def cache_decorator_inner(func: Callable):
            def cache_decorator_wrapper(*args, **kwargs):
                if func not in LFUCache.decorator_function_to_instance_map:
                    LFUCache.decorator_function_to_instance_map[func] = LFUCache(size)

                result = LFUCache.decorator_function_to_instance_map[func].get(args[0])
                if result is None:
                    result = func(*args, **kwargs)
                    LFUCache.decorator_function_to_instance_map[func].set(
                        args[0], result
                    )
                return result

            def cache_info():
                return LFUCache.decorator_function_to_instance_map[func]

            cache_decorator_wrapper.cache_info = cache_info

            return cache_decorator_wrapper

        return cache_decorator_inner


if __name__ == "__main__":
    import doctest

    doctest.testmod()