feat(circular-linked-list): josephus circle

algorithms/josephus_circle/README.md

@@ -0,0 +1,19 @@
+# Josephus Circle
+
+Children often play a counting-out game to randomly select one person from the group by singing a rhyme. The purpose is
+to select one person, either as a straightforward winner, or as someone who is eliminated.
+
+Josephus problem is related to this concept. In this problem, people are standing in one circle waiting to be executed.
+Following points list the specifications of Josephus problem:
+
+The counting out begins at a specified point in a circle and continues around the circle in a fixed direction.
+
+In each step, a certain number of people are skipped and the next person is executed.
+
+For example, if we have 𝑛 people, and 𝑘-1 people are skipped every time, it means that the
+𝑘th person is executed. Here, 𝑘 is the step-size.
+
+## Reference
+
+- https://en.wikipedia.org/wiki/Josephus_problem
+- 

algorithms/josephus_circle/__init__.py

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+from datastructures.linked_lists.circular import CircularLinkedList
+from datastructures.linked_lists.circular.node import CircularNode
+
+
+def josephus_circle(circular_list: CircularLinkedList, step: int) -> CircularNode:
+    current = circular_list.head
+
+    length = len(circular_list)
+    while length > 1:
+        count = 1
+        while count != step:
+            current = current.next
+            count += 1
+        circular_list.delete_node(current)
+        current = current.next
+        length -= 1
+
+    return current

algorithms/josephus_circle/test_josephus_circle.py

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+import unittest
+from datastructures.linked_lists.circular import CircularLinkedList
+from datastructures.linked_lists.circular.node import CircularNode
+from . import josephus_circle
+
+
+class JosephusCircularTestCase(unittest.TestCase):
+    def test_1(self):
+        """should run through the circle of 1-2-3-4 with a step of 2 remaining with 1"""
+        data = [1, 2, 3, 4]
+        circular_linked_list = CircularLinkedList()
+        for d in data:
+            circular_linked_list.append(d)
+
+        step = 2
+        expected = CircularNode(1)
+        actual = josephus_circle(circular_linked_list, step)
+        self.assertEqual(expected, actual)
+
+
+if __name__ == '__main__':
+    unittest.main()

datastructures/linked_lists/circular/__init__.py

@@ -86,8 +86,49 @@ def shift(self):
     def pop(self) -> Optional[Node]:
         pass
 
-    def delete_node(self, n: Node):
-        pass
+    def delete_node(self, node_: CircularNode):
+        if self.head:
+            # if the head node matches the node we are looking for
+            if self.head == node_:
+                # set the current pointer to the head node. This will be used to track the last node as the pointer
+                # moves through the list
+                current = self.head
+                # move through the list until we reach the pointer that points batck to the head node.
+                while current.next != self.head:
+                    current = current.next
+
+                # if the head node equals the next node, that means that this linked list has a length of 1, i.e. just 1
+                # node. The head node can be set to None
+                if self.head == self.head.next:
+                    self.head = None
+                else:
+                    # set the current pointer to point to the current head's next
+                    current.next = self.head.next
+                    # set the head to now become the next node
+                    self.head = self.head.next
+            else:
+                # we have a situation where the head node's key is not equal to the head node, therefore, we need to
+                # traverse the list to find the first node whose key matches the given key. Setting current to the head
+                # node acts as the pointer that we keep track of
+                current = self.head
+                # previous pointer helps to keep track of the previous node as we traverse, it is initially set to None
+                previous: Optional[CircularNode] = None
+
+                # we iterate through the linked list as long as the next pointer of the current head is not equal to
+                # the head node. This is to avoid an infinite loop as this is a circular linked list.
+                while current.next != self.head:
+                    # we set the previous pointer to the current node to keep track of the node before we reset the
+                    # current pointer to the next node
+                    previous = current
+                    # move the current pointer to the next node
+                    current = current.next
+                    # if the current node's key is equal to the key we are searching for
+                    if current == node_:
+                        # we set the previous node's next pointer to point to the current node's next pointer.
+                        # Essentially removing the current node from the list
+                        previous.next = current.next
+                        # set the current node to the current's next node
+                        current = current.next
 
     def delete_node_at_position(self, position: int):
         pass