1670. Design Front Middle Back Queue

Description

Design a queue that supports push and pop operations in the front, middle, and back.

Implement the FrontMiddleBack class:

• FrontMiddleBack() Initializes the queue.
• void pushFront(int val) Adds val to the front of the queue.
• void pushMiddle(int val) Adds val to the middle of the queue.
• void pushBack(int val) Adds val to the back of the queue.
• int popFront() Removes the front element of the queue and returns it. If the queue is empty, return -1.
• int popMiddle() Removes the middle element of the queue and returns it. If the queue is empty, return -1.
• int popBack() Removes the back element of the queue and returns it. If the queue is empty, return -1.

Notice that when there are two middle position choices, the operation is performed on the frontmost middle position choice. For example:

• Pushing 6 into the middle of [1, 2, 3, 4, 5] results in [1, 2, 6, 3, 4, 5].
• Popping the middle from [1, 2, 3, 4, 5, 6] returns 3 and results in [1, 2, 4, 5, 6].

 

Example 1:

Input:
["FrontMiddleBackQueue", "pushFront", "pushBack", "pushMiddle", "pushMiddle", "popFront", "popMiddle", "popMiddle", "popBack", "popFront"]
[[], [1], [2], [3], [4], [], [], [], [], []]
Output:
[null, null, null, null, null, 1, 3, 4, 2, -1]

Explanation:
FrontMiddleBackQueue q = new FrontMiddleBackQueue();
q.pushFront(1);   // [1]
q.pushBack(2);    // [1, 2]
q.pushMiddle(3);  // [1, 3, 2]
q.pushMiddle(4);  // [1, 4, 3, 2]
q.popFront();     // return 1 -> [4, 3, 2]
q.popMiddle();    // return 3 -> [4, 2]
q.popMiddle();    // return 4 -> [2]
q.popBack();      // return 2 -> []
q.popFront();     // return -1 -> [] (The queue is empty)

 

Constraints:

• 1 <= val <= 109
• At most 1000 calls will be made to pushFront, pushMiddle, pushBack, popFront, popMiddle, and popBack.

Solutions

Solution 1: Two Deques

We use two deques, where $q_1$ stores the first half, and $q_2$ stores the second half. The rebalance function is used to maintain the balance between the two queues, i.e., keeping the length of $q_2$ greater than or equal to the length of $q_1$, and the difference in length does not exceed $1$.

In the pushFront, pushMiddle, and pushBack functions, we only need to add elements to $q_1$ or $q_2$, and call the rebalance function.

For the popFront function, we need to check whether $q_1$ and $q_2$ are empty. If both are empty, return $-1$. Otherwise, we need to check whether $q_1$ is empty. If not, pop the front element of $q_1$, otherwise pop the front element of $q_2$, and call the rebalance function.

For the popMiddle function, we need to check whether $q_1$ and $q_2$ are empty. If both are empty, return $-1$. Otherwise, we need to check whether the lengths of $q_1$ and $q_2$ are equal. If they are equal, pop the last element of $q_1$, otherwise pop the front element of $q_2$, and call the rebalance function.

For the popBack function, we only need to check whether $q_2$ is empty. If it is empty, return $-1$. Otherwise, pop the last element of $q_2$, and call the rebalance function.

The time complexity of the above operations is $O(1)$, and the space complexity is $O(n)$, where $n$ is the number of elements in the queue.

Python3JavaC++GoTypeScriptJavaScript

class FrontMiddleBackQueue:
    def __init__(self):
        self.q1 = deque()
        self.q2 = deque()

    def pushFront(self, val: int) -> None:
        self.q1.appendleft(val)
        self.rebalance()

    def pushMiddle(self, val: int) -> None:
        self.q1.append(val)
        self.rebalance()

    def pushBack(self, val: int) -> None:
        self.q2.append(val)
        self.rebalance()

    def popFront(self) -> int:
        if not self.q1 and not self.q2:
            return -1
        if self.q1:
            val = self.q1.popleft()
        else:
            val = self.q2.popleft()
        self.rebalance()
        return val

    def popMiddle(self) -> int:
        if not self.q1 and not self.q2:
            return -1
        if len(self.q1) == len(self.q2):
            val = self.q1.pop()
        else:
            val = self.q2.popleft()
        self.rebalance()
        return val

    def popBack(self) -> int:
        if not self.q2:
            return -1
        val = self.q2.pop()
        self.rebalance()
        return val

    def rebalance(self):
        if len(self.q1) > len(self.q2):
            self.q2.appendleft(self.q1.pop())
        if len(self.q2) > len(self.q1) + 1:
            self.q1.append(self.q2.popleft())


# Your FrontMiddleBackQueue object will be instantiated and called as such:
# obj = FrontMiddleBackQueue()
# obj.pushFront(val)
# obj.pushMiddle(val)
# obj.pushBack(val)
# param_4 = obj.popFront()
# param_5 = obj.popMiddle()
# param_6 = obj.popBack()

class FrontMiddleBackQueue {
    private Deque<Integer> q1 = new ArrayDeque<>();
    private Deque<Integer> q2 = new ArrayDeque<>();

    public FrontMiddleBackQueue() {
    }

    public void pushFront(int val) {
        q1.offerFirst(val);
        rebalance();
    }

    public void pushMiddle(int val) {
        q1.offerLast(val);
        rebalance();
    }

    public void pushBack(int val) {
        q2.offerLast(val);
        rebalance();
    }

    public int popFront() {
        if (q1.isEmpty() && q2.isEmpty()) {
            return -1;
        }
        int val = q1.isEmpty() ? q2.pollFirst() : q1.pollFirst();
        rebalance();
        return val;
    }

    public int popMiddle() {
        if (q1.isEmpty() && q2.isEmpty()) {
            return -1;
        }
        int val = q1.size() == q2.size() ? q1.pollLast() : q2.pollFirst();
        rebalance();
        return val;
    }

    public int popBack() {
        if