Add bisect_left and bisect_right (#63)

* Add bisect_left and bisect_right

* Test cases for bisect_left and bisect_right

utilities/python/binary_search.py

@@ -11,6 +11,32 @@ def binary_search(arr, target):
             right = mid - 1
     return -1
 
+def bisect_left(arr, target):
+    """Returns the leftmost position that `target` should
+    go to such that the sequence remains sorted."""
+    left = 0
+    right = len(arr)
+    while left < right:
+        mid = (left + right) // 2
+        if arr[mid] < target:
+            left = mid + 1
+        else:
+            right = mid
+    return left
+
+def bisect_right(arr, target):
+    """Returns the rightmost position that `target` should
+    go to such that the sequence remains sorted."""
+    left = 0
+    right = len(arr)
+    while left < right:
+        mid = (left + right) // 2
+        if arr[mid] > target:
+            right = mid
+        else:
+            left = mid + 1
+    return left
+
 print(binary_search([1, 2, 3, 10], 1) == 0)
 print(binary_search([1, 2, 3, 10], 2) == 1)
 print(binary_search([1, 2, 3, 10], 3) == 2)
@@ -20,3 +46,24 @@ print(binary_search([1, 2, 3, 10], 4) == -1)
 print(binary_search([1, 2, 3, 10], 0) == -1)
 print(binary_search([1, 2, 3, 10], 11) == -1)
 print(binary_search([5, 7, 8, 10], 3) == -1)
+
+print(bisect_left([1, 2, 3, 3, 10], 1) == 0)
+print(bisect_left([1, 2, 3, 3, 10], 2) == 1)
+print(bisect_left([1, 2, 3, 3, 10], 3) == 2) # First "3" is at index 2
+print(bisect_left([1, 2, 3, 3, 10], 10) == 4)
+
+# These return a valid index despite target not being in array.
+print(bisect_left([1, 2, 3, 3, 10], 9) == 4)
+print(bisect_left([1, 2, 3, 3, 10], 0) == 0) # Insert "0" at front
+print(bisect_left([1, 2, 3, 3, 10], 11) == 5) # Insert "5" at back
+
+print(bisect_right([1, 2, 3, 3, 10], 1) == 1)
+print(bisect_right([1, 2, 3, 3, 10], 2) == 2)
+print(bisect_right([1, 2, 3, 3, 10], 3) == 4) # Last "3" is at index 3, so insert new "3" at index 4
+print(bisect_right([1, 2, 3, 3, 10], 10) == 5)
+
+# These return a valid index despite target not being in array.
+print(bisect_right([1, 2, 3, 3, 10], 9) == 4)
+print(bisect_right([1, 2, 3, 3, 10], 0) == 0) # Insert "0" at front
+print(bisect_right([1, 2, 3, 3, 10], 11) == 5) # Insert "5" at back
+