From cb2e0ac6e0b39769f714632d7e95df4cbac4c2fb Mon Sep 17 00:00:00 2001
From: Ebrahim Beiaty <ebrahimbeiaty@gmail.com>
Date: Thu, 16 Apr 2026 21:55:39 +0100
Subject: [PATCH] implement_skip_list

---
 Sprint-2/implement_skip_list/skip_list.py | 66 +++++++++++++++++++++++
 1 file changed, 66 insertions(+)
 create mode 100644 Sprint-2/implement_skip_list/skip_list.py

diff --git a/Sprint-2/implement_skip_list/skip_list.py b/Sprint-2/implement_skip_list/skip_list.py
new file mode 100644
index 0000000..7d7c75d
--- /dev/null
+++ b/Sprint-2/implement_skip_list/skip_list.py
@@ -0,0 +1,66 @@
+import math
+
+
+class SkipList:
+    def __init__(self):
+        self.data = []  # sorted list
+        self.skips = []  # list of skip pointers, each is a tuple (index, value)
+
+    def rebuild_skips(self):
+        """Rebuild the skip pointer so we can jump over sqrt(n) elements."""
+        n = len(self.data)
+        if n == 0:
+            self.skips = []
+            return
+
+        step = int(math.sqrt(n)) or 1
+        self.skips = list(range(0, n, step))
+
+    def _find_position(self, value):
+        """Find the position to insert value using skip pointers."""
+        if not self.data:
+            return 0
+
+        # Use skip pointers to find the range where value should be
+        for i in range(len(self.skips) - 1):
+            a = self.skips[i]
+            b = self.skips[i + 1]
+            if self.data[a] <= value < self.data[b]:
+                # linear search between a and b
+                for j in range(a, b):
+                    if self.data[j] >= value:
+                        return j
+                return b
+
+        # Check the last skip pointer
+        start = self.skips[-1]
+        for j in range(start, len(self.data)):
+            if self.data[j] >= value:
+                return j
+        return len(self.data)
+
+    def insert(self, value):
+        """Insert value into the skip list, maintaining sorted order."""
+        pos = self._find_position(value)
+
+        if pos < len(self.data) and self.data[pos] == value:
+            return  # value already exists, do not insert duplicates
+        self.data.insert(pos, value)
+        self.rebuild_skips()
+
+    def __contains__(self, value):
+        if not self.data:
+            return False
+
+        for i in range(len(self.skips) - 1):
+            a = self.skips[i]
+            b = self.skips[i + 1]
+            if self.data[a] <= value < self.data[b]:
+                return value in self.data[a:b]
+
+        start = self.skips[-1]
+        return value in self.data[start::]
+
+    def to_list(self):
+        """Return the skip list as a regular sorted list."""
+        return self.data