added `sorted_insert.py`

algorithms/Python/arrays/sorted_insert.py

@@ -0,0 +1,34 @@
+"""
+Algorithm Type : Array Insertion
+Time Complexity : O(log n)
+Space Complexity : O(1)
+"""
+
+import math
+
+def sortedIndex(a: list, item):
+  start = 0
+  end = len(a)
+  depth = math.log(len(a) + 1, 2) # the depth of the binary tree
+  i = 0
+  while i <= math.ceil(depth): # iterative binary search
+    mid = (start + end) // 2
+    if start >= end:
+      break
+    if item == a[mid]:
+      return mid # returns the index of the duplicate element
+    elif item > a[mid]:
+      start = mid + 1
+    else:
+      end = mid
+    i += 1
+  return mid # returns the insertion position for new element
+
+def sortedInsert(a: list, item):
+  a.insert(sortedIndex(a, item), item)
+  return a
+
+if __name__ == "__main__":
+  print(sortedIndex(['a', 'b', 'c', 'd'], 'b')) # 1
+  print(sortedIndex([0, 1, 2, 3], 1.5)) # 2
+  print(sortedInsert([0, 1, 2, 3], 1.5)) # [0, 1, 1.5, 2, 3]