diff --git a/python/bisect.py b/python/bisect.py
index a0df9bc7..eee23839 100644
--- a/python/bisect.py
+++ b/python/bisect.py
@@ -1,72 +1,123 @@
-"""Bisection algorithms."""
-
-def insort_right(a, x, lo=0, hi=None):
-    """Insert item x in list a, and keep it sorted assuming a is sorted.
-
-    If x is already in a, insert it to the right of the rightmost x.
-
-    Optional args lo (default 0) and hi (default len(a)) bound the
-    slice of a to be searched.
-    """
-
-    lo = bisect_right(a, x, lo, hi)
-    a.insert(lo, x)
-
+"""
+Optimized bisection algorithms for sorted list insertions.
+These functions provide efficient binary search implementations for finding insertion points
+in sorted sequences and inserting elements while maintaining sorted order.
+"""
 def bisect_right(a, x, lo=0, hi=None):
     """Return the index where to insert item x in list a, assuming a is sorted.
-
+    
     The return value i is such that all e in a[:i] have e <= x, and all e in
-    a[i:] have e > x.  So if x already appears in the list, a.insert(x) will
-    insert just after the rightmost x already there.
-
-    Optional args lo (default 0) and hi (default len(a)) bound the
-    slice of a to be searched.
+    a[i:] have e > x. So if x already appears in the list, the insertion
+    point will be after (to the right of) any existing entries.
+    
+    Args:
+        a: A sorted list-like object supporting comparison and __len__
+        x: The item to be inserted
+        lo: Lower bound of the slice to be searched (inclusive)
+        hi: Upper bound of the slice to be searched (exclusive)
+    
+    Returns:
+        The index where x should be inserted to maintain sorted order
+    
+    Raises:
+        ValueError: If lo is negative
     """
-
     if lo < 0:
         raise ValueError('lo must be non-negative')
+    
     if hi is None:
         hi = len(a)
+    
+    # Fast path for common case: appending to the end
+    if hi > 0 and hi == len(a) and x > a[-1]:
+        return hi
+    
+    # Normal binary search
     while lo < hi:
-        mid = (lo+hi)//2
-        if x < a[mid]: hi = mid
-        else: lo = mid+1
+        mid = (lo + hi) // 2
+        if x < a[mid]:
+            hi = mid
+        else:
+            lo = mid + 1
+    
     return lo
 
-def insort_left(a, x, lo=0, hi=None):
-    """Insert item x in list a, and keep it sorted assuming a is sorted.
-
-    If x is already in a, insert it to the left of the leftmost x.
-
-    Optional args lo (default 0) and hi (default len(a)) bound the
-    slice of a to be searched.
-    """
-
-    lo = bisect_left(a, x, lo, hi)
-    a.insert(lo, x)
-
 
 def bisect_left(a, x, lo=0, hi=None):
     """Return the index where to insert item x in list a, assuming a is sorted.
-
+    
     The return value i is such that all e in a[:i] have e < x, and all e in
-    a[i:] have e >= x.  So if x already appears in the list, a.insert(x) will
-    insert just before the leftmost x already there.
-
-    Optional args lo (default 0) and hi (default len(a)) bound the
-    slice of a to be searched.
+    a[i:] have e >= x. So if x already appears in the list, the insertion
+    point will be before (to the left of) any existing entries.
+    
+    Args:
+        a: A sorted list-like object supporting comparison and __len__
+        x: The item to be inserted
+        lo: Lower bound of the slice to be searched (inclusive)
+        hi: Upper bound of the slice to be searched (exclusive)
+    
+    Returns:
+        The index where x should be inserted to maintain sorted order
+    
+    Raises:
+        ValueError: If lo is negative
     """
-
     if lo < 0:
         raise ValueError('lo must be non-negative')
+    
     if hi is None:
         hi = len(a)
+    
+    # Fast path for common case: appending to the end
+    if hi > 0 and hi == len(a) and x > a[-1]:
+        return hi
+        
+    # Fast path for common case: inserting at the beginning
+    if lo == 0 and hi > 0 and x < a[0]:
+        return 0
+    
+    # Normal binary search
     while lo < hi:
-        mid = (lo+hi)//2
-        if a[mid] < x: lo = mid+1
-        else: hi = mid
+        mid = (lo + hi) // 2
+        if a[mid] < x:
+            lo = mid + 1
+        else:
+            hi = mid
+    
     return lo
 
-# Create aliases
+
+def insort_right(a, x, lo=0, hi=None):
+    """Insert item x in list a, and keep it sorted assuming a is sorted.
+    
+    If x is already in a, insert it to the right of the rightmost x.
+    
+    Args:
+        a: A sorted list-like object supporting comparison, __len__, and insert
+        x: The item to be inserted
+        lo: Lower bound of the slice to be searched (inclusive)
+        hi: Upper bound of the slice to be searched (exclusive)
+    """
+    # Use bisect_right to find the insertion point
+    insertion_point = bisect_right(a, x, lo, hi)
+    a.insert(insertion_point, x)
+
+
+def insort_left(a, x, lo=0, hi=None):
+    """Insert item x in list a, and keep it sorted assuming a is sorted.
+    
+    If x is already in a, insert it to the left of the leftmost x.
+    
+    Args:
+        a: A sorted list-like object supporting comparison, __len__, and insert
+        x: The item to be inserted
+        lo: Lower bound of the slice to be searched (inclusive)
+        hi: Upper bound of the slice to be searched (exclusive)
+    """
+    # Use bisect_left to find the insertion point
+    insertion_point = bisect_left(a, x, lo, hi)
+    a.insert(insertion_point, x)
+
+# Create aliases for backward compatibility
 bisect = bisect_right
 insort = insort_right