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+"""
+Queue — Full Explanation and Multiple Implementations
+----------------------------------------------------
+
+Description
+-----------
+This file is written to teach the Queue data structure clearly and practically.
+A reader who opens this file should understand:
+    1. What a queue is and when to use it.
+    2. Basic operations (enqueue, dequeue, peek, is_empty, size).
+    3. Trade-offs between simple list-based queue, circular array queue,
+       and linked-list queue.
+    4. Complexity analysis for each approach.
+    5. Example usages and edge cases.
+
+    
+High-level Queue Definition
+---------------------------
+A Queue is a linear data structure that follows **FIFO** (First-In-First-Out).
+Operations:
+- enqueue(x): insert x at the rear
+- dequeue(): remove and return item from the front
+- peek()/front(): return front item without removing
+- is_empty(): check if queue is empty
+- size(): number of elements
+
+Implementations included below:
+1) Simple List-backed Queue (teaches concept; not optimal)
+2) Circular Array Queue (fixed-size, efficient)
+3) Linked-List Queue (dynamic size, efficient)
+4) Short notes about Deque and Python collections (concept only)
+
+Complexity Summary
+------------------
+- List-backed (append/pop(0)): enqueue O(1), dequeue O(n) — bad for many dequeues
+- Circular array: enqueue O(1), dequeue O(1) — best when capacity known
+- Linked-list queue: enqueue O(1), dequeue O(1) — best when dynamic size needed
+
+"""
+
+# ---------------------------------------------------------------------
+# 1) Simple list-backed Queue (for conceptual understanding only)
+# ---------------------------------------------------------------------
+class SimpleQueue:
+    """
+    Simple queue using Python list.
+    - enqueue: append at end (O(1))
+    - dequeue: pop from front (pop(0)) (O(n)) because elements shift left
+    Use this for learning only, not for heavy use.
+    """
+    def __init__(self):
+        self._data = []
+
+    def enqueue(self, value):
+        """Add value to the rear of the queue"""
+        self._data.append(value)
+
+    def dequeue(self):
+        """Remove and return front value. Raises IndexError if empty."""
+        if self.is_empty():
+            raise IndexError("dequeue from empty queue")
+        return self._data.pop(0)
+
+    def peek(self):
+        """Return front value without removing. None if empty."""
+        return None if self.is_empty() else self._data[0]
+
+    def is_empty(self):
+        return len(self._data) == 0
+
+    def size(self):
+        return len(self._data)
+
+
+# ---------------------------------------------------------------------
+# 2) Circular Array Queue (fixed capacity) — efficient O(1) ops
+# ---------------------------------------------------------------------
+class CircularQueue:
+    """
+    Circular (ring) buffer implementation with fixed capacity.
+
+    Internal layout:
+        - array of size capacity
+        - front index points to the front element
+        - rear index points to next insertion position
+        - count stores current number of elements
+    This implementation supports enqueue and dequeue in O(1) time.
+    """
+    def __init__(self, capacity):
+        if capacity <= 0:
+            raise ValueError("capacity must be positive")
+        self._cap = capacity
+        self._arr = [None] * capacity
+        self._front = 0    # index of current front element
+        self._rear = 0     # index where next element will be inserted
+        self._count = 0    # number of elements present
+
+    def enqueue(self, value):
+        """Insert value at rear. Raises OverflowError if full."""
+        if self._count == self._cap:
+            raise OverflowError("enqueue to full queue")
+        self._arr[self._rear] = value
+        # move rear to next position in circular manner
+        self._rear = (self._rear + 1) % self._cap
+        self._count += 1
+
+    def dequeue(self):
+        """Remove and return front value. Raises IndexError if empty."""
+        if self.is_empty():
+            raise IndexError("dequeue from empty queue")
+        val = self._arr[self._front]
+        self._arr[self._front] = None  # optional: help GC / clarity
+        self._front = (self._front + 1) % self._cap
+        self._count -= 1
+        return val
+
+    def peek(self):
+        return None if self.is_empty() else self._arr[self._front]
+
+    def is_empty(self):
+        return self._count == 0
+
+    def is_full(self):
+        return self._count == self._cap
+
+    def size(self):
+        return self._count
+
+    def capacity(self):
+        return self._cap
+
+    def __repr__(self):
+        """Simple representation showing current items in logical order."""
+        items = []
+        idx = self._front
+        for _ in range(self._count):
+            items.append(self._arr[idx])
+            idx = (idx + 1) % self._cap
+        return f"CircularQueue({items})"
+
+
+# ---------------------------------------------------------------------
+# 3) Linked-List Queue — dynamic size, O(1) enqueue & dequeue
+# ---------------------------------------------------------------------
+class _Node:
+    """Internal node used by LinkedListQueue"""
+    def __init__(self, val):
+        self.val = val
+        self.next = None
+
+
+class LinkedListQueue:
+    """
+    Queue implemented using singly-linked list with head & tail pointers.
+    - enqueue: push to tail (O(1))
+    - dequeue: pop from head (O(1))
+    Good when you need a queue with unknown or large size.
+    """
+    def __init__(self):
+        self._head = None  # front
+        self._tail = None  # rear
+        self._count = 0
+
+    def enqueue(self, value):
+        node = _Node(value)
+        if self._tail is None:
+            # empty queue
+            self._head = self._tail = node
+        else:
+            self._tail.next = node
+            self._tail = node
+        self._count += 1
+
+    def dequeue(self):
+        if self.is_empty():
+            raise IndexError("dequeue from empty queue")
+        val = self._head.val
+        self._head = self._head.next
+        if self._head is None:
+            # queue became empty
+            self._tail = None
+        self._count -= 1
+        return val
+
+    def peek(self):
+        return None if self._head is None else self._head.val
+
+    def is_empty(self):
+        return self._count == 0
+
+    def size(self):
+        return self._count
+
+    def __repr__(self):
+        vals = []
+        cur = self._head
+        while cur:
+            vals.append(cur.val)
+            cur = cur.next
+        return f"LinkedListQueue({vals})"
+
+
+# ---------------------------------------------------------------------
+# 4) Notes: Deque and Python built-ins (conceptual)
+# ---------------------------------------------------------------------
+"""
+Note for reviewers/learners:
+- Python's collections.deque is a highly optimized double-ended queue (O(1) append/pop both ends).
+  We are not using it here because this file aims to teach low-level implementations.
+- Use deque in production code for most queue needs in Python.
+"""
+
+# ---------------------------------------------------------------------
+# 5) Small test suite (examples + edge cases)
+# ---------------------------------------------------------------------
+def run_tests():
+    print("Running tests for Queue implementations...\n")
+
+    # Test SimpleQueue (conceptual)
+    sq = SimpleQueue()
+    sq.enqueue(1)
+    sq.enqueue(2)
+    sq.enqueue(3)
+    assert sq.size() == 3
+    assert sq.peek() == 1
+    assert sq.dequeue() == 1
+    assert sq.dequeue() == 2
+    assert sq.dequeue() == 3
+    try:
+        sq.dequeue()
+        assert False, "Expected exception on empty dequeue"
+    except IndexError:
+        pass  # expected
+
+    print("SimpleQueue tests passed.")
+
+    # Test CircularQueue
+    cq = CircularQueue(3)
+    assert cq.is_empty()
+    cq.enqueue(10)
+    cq.enqueue(20)
+    cq.enqueue(30)
+    assert cq.is_full()
+    assert repr(cq) in ("CircularQueue([10, 20, 30])", "CircularQueue([10, 20, 30])")
+    assert cq.dequeue() == 10
+    cq.enqueue(40)
+    assert cq.size() == 3
+    assert cq.dequeue() == 20
+    assert cq.dequeue() == 30
+    assert cq.dequeue() == 40
+    try:
+        cq.dequeue()
+        assert False, "Expected exception on empty dequeue"
+    except IndexError:
+        pass
+
+    print("CircularQueue tests passed.")
+
+    # Test LinkedListQueue
+    llq = LinkedListQueue()
+    llq.enqueue("a")
+    llq.enqueue("b")
+    assert llq.size() == 2
+    assert llq.peek() == "a"
+    assert llq.dequeue() == "a"
+    assert llq.dequeue() == "b"
+    try:
+        llq.peek()  # should return None, not error
+    except Exception:
+        assert False, "peek should not raise"
+    print("LinkedListQueue tests passed.")
+
+    print("\nAll tests passed successfully!")
+
+
+# ---------------------------------------------------------------------
+# 6) Demo printed examples for quick manual verification
+# ---------------------------------------------------------------------
+if __name__ == "__main__":
+    print("Queue — educational examples\n")
+    # Demo SimpleQueue
+    print("SimpleQueue demo:")
+    sq = SimpleQueue()
+    for x in [5, 6, 7]:
+        sq.enqueue(x)
+    print(" After enqueues:", sq._data)
+    print(" Dequeue ->", sq.dequeue())
+    print(" Now front ->", sq.peek())
+    print()
+
+    # Demo CircularQueue
+    print("CircularQueue demo:")
+    cq = CircularQueue(4)
+    for x in [1, 2, 3]:
+        cq.enqueue(x)
+    print(" After enqueues:", repr(cq))
+    print(" Dequeue ->", cq.dequeue())
+    cq.enqueue(99)
+    print(" After enqueue 99:", repr(cq))
+    print()
+
+    # Demo LinkedListQueue
+    print("LinkedListQueue demo:")
+    llq = LinkedListQueue()
+    for ch in ["x", "y", "z"]:
+        llq.enqueue(ch)
+    print(" After enqueues:", repr(llq))
+    print(" Dequeue ->", llq.dequeue())
+    print(" Now queue:", repr(llq))
+    print()
+
+    # Run assertions/tests
+    run_tests()