LFU Cache
<p>Design and implement a data structure for a <a href="https://en.wikipedia.org/wiki/Least_frequently_used" target="_blank">Least Frequently Used (LFU)</a> cache.</p>

<p>Implement the <code>LFUCache</code> class:</p>

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

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

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

<p>The functions&nbsp;<code data-stringify-type="code">get</code>&nbsp;and&nbsp;<code data-stringify-type="code">put</code>&nbsp;must each run in <code>O(1)</code> average time complexity.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input</strong>
[&quot;LFUCache&quot;, &quot;put&quot;, &quot;put&quot;, &quot;get&quot;, &quot;put&quot;, &quot;get&quot;, &quot;get&quot;, &quot;put&quot;, &quot;get&quot;, &quot;get&quot;, &quot;get&quot;]
[[2], [1, 1], [2, 2], [1], [3, 3], [2], [3], [4, 4], [1], [3], [4]]
<strong>Output</strong>
[null, null, null, 1, null, -1, 3, null, -1, 3, 4]

<strong>Explanation</strong>
// 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.
&nbsp;                // 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
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= capacity&nbsp;&lt;= 10<sup>4</sup></code></li>
	<li><code>0 &lt;= key &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= value &lt;= 10<sup>9</sup></code></li>
	<li>At most <code>2 * 10<sup>5</sup></code>&nbsp;calls will be made to <code>get</code> and <code>put</code>.</li>
</ul>

<p>&nbsp;</p>
<span style="display: none;">&nbsp;</span>
Design; Hash Table; Linked List; Doubly-Linked List
use std::cell::RefCell;
use std::collections::HashMap;
use std::rc::Rc;

struct Node {
    key: i32,
    value: i32,
    freq: i32,
    prev: Option<Rc<RefCell<Node>>>,
    next: Option<Rc<RefCell<Node>>>,
}

impl Node {
    fn new(key: i32, value: i32) -> Self {
        Self {
            key,
            value,
            freq: 1,
            prev: None,
            next: None,
        }
    }
}

struct LinkedList {
    head: Option<Rc<RefCell<Node>>>,
    tail: Option<Rc<RefCell<Node>>>,
}

impl LinkedList {
    fn new() -> Self {
        Self {
            head: None,
            tail: None,
        }
    }

    fn push_front(&mut self, node: &Rc<RefCell<Node>>) {
        match self.head.take() {
            Some(head) => {
                head.borrow_mut().prev = Some(Rc::clone(node));
                node.borrow_mut().prev = None;
                node.borrow_mut().next = Some(head);
                self.head = Some(Rc::clone(node));
            }
            None => {
                node.borrow_mut().prev = None;
                node.borrow_mut().next = None;
                self.head = Some(Rc::clone(node));
                self.tail = Some(Rc::clone(node));
            }
        };
    }

    fn remove(&mut self, node: &Rc<RefCell<Node>>) {
        match (node.borrow().prev.as_ref(), node.borrow().next.as_ref()) {
            (None, None) => {
                self.head = None;
                self.tail = None;
            }
            (None, Some(next)) => {
                self.head = Some(Rc::clone(next));
                next.borrow_mut().prev = None;
            }
            (Some(prev), None) => {
                self.tail = Some(Rc::clone(prev));
                prev.borrow_mut().next = None;
            }
            (Some(prev), Some(next)) => {
                next.borrow_mut().prev = Some(Rc::clone(prev));
                prev.borrow_mut().next = Some(Rc::clone(next));
            }
        };
    }

    fn pop_back(&mut self) -> Option<Rc<RefCell<Node>>> {
        match self.tail.take() {
            Some(tail) => {
                self.remove(&tail);
                Some(tail)
            }
            None => None,
        }
    }

    fn is_empty(&self) -> bool {
        self.head.is_none()
    }
}

struct LFUCache {
    cache: HashMap<i32, Rc<RefCell<Node>>>,
    freq_map: HashMap<i32, LinkedList>,
    min_freq: i32,
    capacity: usize,
}

/**
 * `&self` means the method takes an immutable reference.
 * If you need a mutable reference, change it to `&mut self` instead.
 */
impl LFUCache {
    fn new(capacity: i32) -> Self {
        Self {
            cache: HashMap::new(),
            freq_map: HashMap::new(),
            min_freq: 0,
            capacity: capacity as usize,
        }
    }

    fn get(&mut self, key: i32) -> i32 {
        if self.capacity == 0 {
            return -1;
        }

        match self.cache.get(&key) {
            Some(node) => {
                let node = Rc::clone(node);
                self.incr_freq(&node);
                let value = node.borrow().value;
                value
            }
            None => -1,
        }
    }

    fn put(&mut self, key: i32, value: i32) {
        if self.capacity == 0 {
            return;
        }

        match self.cache.get(&key) {
            Some(node) => {
                let node = Rc::clone(node);
                node.borrow_mut().value = value;
                self.incr_freq(&node);
            }
            None => {
                if self.cache.len() == self.capacity {
                    let list = self.freq_map.get_mut(&self.min_freq).unwrap();
                    self.cache.remove(&list.pop_back().unwrap().borrow().key);
                }
                let node = Rc::new(RefCell::new(Node::new(key, value)));
                self.add_node(&node);
                self.cache.insert(key, node);
                self.min_freq = 1;
            }
        };
    }

    fn incr_freq(&mut self, node: &Rc<RefCell<Node>>) {
        let freq = node.borrow().freq;
        let list = self.freq_map.get_mut(&freq).unwrap();
        list.remove(node);
        if list.is_empty() {
            self.freq_map.remove(&freq);
            if freq == self.min_freq {
                self.min_freq += 1;
            }
        }
        node.borrow_mut().freq += 1;
        self.add_node(node);
    }

    fn add_node(&mut self, node: &Rc<RefCell<Node>>) {
        let freq = node.borrow().freq;
        match self.freq_map.get_mut(&freq) {
            Some(list) => {
                list.push_front(node);
            }
            None => {
                let mut list = LinkedList::new();
                list.push_front(node);
                self.freq_map.insert(node.borrow().freq, list);
            }
        };
    }
}
