diff --git a/cycle2.py b/cycle2.py
new file mode 100644
index 00000000..944f4a9e
--- /dev/null
+++ b/cycle2.py
@@ -0,0 +1,32 @@
+"""
+time = o(n)
+space = o(1)
+we maintain slow and fast pointers and find if there is a cycle in the linked list, if there is a cycle slow and fast meet at a node.
+we then start from head with a new pointer and then move slow and new pointer one node at a time, till they meet and they will meet at the start of the cycle
+the algorithm behind this is floyd's tortoise algorithm
+"""
+from typing import Optional
+# Definition for singly-linked list.
+class ListNode:
+    def __init__(self, x):
+        self.val = x
+        self.next = None
+
+class Solution:
+    def detectCycle(self, head: Optional[ListNode]) -> Optional[ListNode]:
+        fast = slow = head
+        while fast and fast.next:
+            slow = slow.next
+            fast = fast.next.next
+            if slow==fast:
+                break
+        if not fast or not fast.next:
+            return None
+        p1 = head
+        while p1!=slow:
+            p1=p1.next
+            slow = slow.next
+        return slow
+
+
+        
\ No newline at end of file
diff --git a/remove_nth_from_end.py b/remove_nth_from_end.py
new file mode 100644
index 00000000..49329024
--- /dev/null
+++ b/remove_nth_from_end.py
@@ -0,0 +1,27 @@
+"""
+space - o(1)
+time - o(n)
+we keep a dummy node and use two pointers, move one pointer to nth position from head (with head as 1) and once this happens, we move both pointers one node
+at a time till second pointer reaches the last node, at this point we remove the node next to the first pointer.
+"""
+from typing import Optional
+# Definition for singly-linked list.
+class ListNode:
+    def __init__(self, val=0, next=None):
+        self.val = val
+        self.next = next
+class Solution:
+    def removeNthFromEnd(self, head: Optional[ListNode], n: int) -> Optional[ListNode]:
+        dummy = ListNode(0)
+        dummy.next = head
+        p1 = head
+        p2 = dummy
+        for _ in range(1,n):
+            p1 = p1.next
+        while p1 and p1.next:
+            p1 = p1.next
+            p2 = p2.next
+        if p2.next:
+            p2.next = p2.next.next
+        return dummy.next
+        
\ No newline at end of file
diff --git a/reverse_ll.py b/reverse_ll.py
new file mode 100644
index 00000000..00baee05
--- /dev/null
+++ b/reverse_ll.py
@@ -0,0 +1,32 @@
+"""
+time - o(n)
+space - o(1)
+we take three variables, current, previous and next, we basically make the current node's next as previous and for the next iteration make next as current and current as previous
+we maintain a dummy node at the start to return the result
+"""
+from typing import Optional
+# Definition for singly-linked list.
+class ListNode:
+    def __init__(self, val=0, next=None):
+        self.val = val
+        self.next = next
+class Solution:
+    def __init__(self):
+        self.new_head = None
+    def reverseList(self, head: Optional[ListNode]) -> Optional[ListNode]:
+        if not head:
+            return head
+        self.helper(head)
+        return self.new_head
+    
+    def helper(self, head):
+        if not head.next:
+            self.new_head = head
+            return head
+        
+        node = self.helper(head.next)
+        node.next = head
+        head.next = None
+        return head
+
+        
\ No newline at end of file