diff --git a/queues/README.md b/queues/README.md
index 141955e..18b7fd6 100644
--- a/queues/README.md
+++ b/queues/README.md
@@ -3,7 +3,13 @@
* queues are **first in, first out structures (FIFO)** (i.e., items are removed at the same order they are added) that can be implemented with two arrays or a dynamic array (linked list), as long as items are added and removed from opposite sides.
-* if implemented with a dynamic array, a more efficient solution is to use a circular queue (ring buffer), i.e. a fixed-size array and two pointers to indicate the starting and ending positions. an advantage of circular queues is that we can use the spaces in front of the queue. in a normal queue, once the queue becomes full, we cannot insert the next element even if there is a space in front of the queue. but using the circular queue, we can use the space to store new values.
+
+
+* if implemented with a dynamic array, a more efficient solution is to use a circular queue (ring buffer), i.e. a fixed-size array and two pointers to indicate the starting and ending positions.
+ * an advantage of circular queues is that we can use the spaces in front of the queue.
+ * in a normal queue, once the queue becomes full, we cannot insert the next element even if there is a space in front of the queue. but using the circular queue, we can use the space to store new values.
+
+
* queues are often used in breath-first search (where you store a list of nodes to be processed) or when implementing a cache.
@@ -24,7 +30,7 @@ tail_index = (head_index + queue_length - 1) % queue_capacity
-* here is an example of an implementation using a "fixed-sized" array (sort of):
+* here is an example of an implementation using a "fixed-sized" array (sort of) using arrays:
@@ -84,6 +90,80 @@ class CircularQueue:
return self._get_next_position(self.tail) == self.head
```
+
+
+* and here is a much clear example using a linked list:
+
+
+
+```python
+class Node:
+
+ def __init__(self, value, next=None):
+ self.value = value
+ self.next = next
+
+
+class CircularQueue:
+
+ def __init__(self, k: int):
+
+ self.capacity = k
+ self.count = 0
+ self.head = None
+ self.tail = None
+
+ def enqueue(self, value: int) -> bool:
+
+ if self.count == self.capacity:
+ return False
+
+ if self.count == 0:
+ self.head = Node(value)
+ self.tail = self.head
+ else:
+ new_node = Node(value)
+ self.tail.next = new_node
+ self.tail = new_node
+
+ self.count += 1
+
+ return True
+
+ def dequeue(self) -> bool:
+
+ if self.count == 0:
+ return False
+
+ self.head = self.head.next
+ self.count -= 1
+
+ return True
+
+ def front(self) -> int:
+
+ if self.count == 0:
+ return -1
+
+ return self.head.value
+
+ def rear(self) -> int:
+
+ if self.count == 0:
+ return -1
+
+ return self.tail.value
+
+ def is_empty(self) -> bool:
+
+ return self.count == 0
+
+ def is_full(self) -> bool:
+
+ return self.count == self.capacity
+```
+
+
* note that this queue is not thread-safe: the data structure could be corrupted in a multi-threaded environment (as race-condition could occur). to mitigate this problem, one could add the protection of a lock.