fix: use skip list nodes instead of list.insert for O(log n) insertion

Author: AliQassab

Sprint-2/implement_skip_list/skip_list.py

@@ -1,37 +1,69 @@
+import random
+
+
+class SkipListNode:
+    """Node in a skip list with multiple forward pointers"""
+    def __init__(self, value, levels):
+        self.value = value
+        self.forward = [None] * levels
+
+
 class SkipList:
     def __init__(self):
-        self.data = []
+        self.max_level = 16
+        self.head = SkipListNode(float('-inf'), self.max_level)
+        self.level = 0
+    
+    def _random_level(self):
+        """Generate random level for a new node (coin flip)"""
+        level = 0
+        while random.random() < 0.5 and level < self.max_level - 1:
+            level += 1
+        return level
 
     def insert(self, value):
-        """Insert value in sorted order"""
-        # Find insertion point
-        left, right = 0, len(self.data)
-        while left < right:
-            mid = (left + right) // 2
-            if self.data[mid] < value:
-                left = mid + 1
-            else:
-                right = mid
+        """Insert value in sorted order - O(log n) time complexity"""
+        update = [None] * self.max_level
+        current = self.head
+        
+        for i in range(self.level, -1, -1):
+            while current.forward[i] and current.forward[i].value < value:
+                current = current.forward[i]
+            update[i] = current
+        
+        current = current.forward[0]
+        new_level = self._random_level()
+        
+        if new_level > self.level:
+            for i in range(self.level + 1, new_level + 1):
+                update[i] = self.head
+            self.level = new_level
 
-        # Insert at found position
-        self.data.insert(left, value)
+        new_node = SkipListNode(value, new_level + 1)
+        
+        for i in range(new_level + 1):
+            new_node.forward[i] = update[i].forward[i]
+            update[i].forward[i] = new_node
 
     def contains(self, value) -> bool:
-        """Check if value exists"""
-        left, right = 0, len(self.data)
-        while left < right:
-            mid = (left + right) // 2
-            if self.data[mid] == value:
-                return True
-            elif self.data[mid] < value:
-                left = mid + 1
-            else:
-                right = mid
-        return False
+        """Check if value exists - O(log n) time complexity"""
+        current = self.head
+        
+        for i in range(self.level, -1, -1):
+            while current.forward[i] and current.forward[i].value < value:
+                current = current.forward[i]
+        
+        current = current.forward[0]
+        return current is not None and current.value == value
 
     def to_list(self) -> list:
-        """Convert to sorted list"""
-        return self.data.copy()
+        """Convert to sorted list - O(n) time complexity"""
+        result = []
+        current = self.head.forward[0]
+        while current:
+            result.append(current.value)
+            current = current.forward[0]
+        return result
 
     def __contains__(self, value) -> bool:
         return self.contains(value)