new exercises and solutions

Author: essepuntato

exercises/development/advanced/exercise-41.md

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+## Development - Advanced, exercise 41
+
+### Text
+A binary search tree is a binary tree data structure where each node may have at most two children and the value of each node is greater than (or equal to) all the values in the respective node's left subtree and less than (or equal to) the ones in its right subtree. It can be built, recursively following an approach which recalls the binary search strategy, starting from a list of ordered items (e.g. a list of integers), where each item become a node of a tree.
+
+<img src="img/bst.png" alt="Example of a binary search tree" style="max-height:100px;" />
+
+As a reminder, the binary search strategy first checks if the middle item of a list is equal to item to search for and, in case this is not true, it continues to analyse the part of the list that either preceeds or follows the middle item if it is greater than or less than the item to search.
+
+Write a recursive algorithm in Python – `def create_bst(ordered_list, parent)` – which takes in input an ordered list of integers ordered_list and a parent node `parent`, and returns the root node of the binary search tree created from the input list. In the first call, the function is run passing `None` as input of the second parameter `parent`, e.g. 
+
+```
+create_bst([0, 1, 1, 2, 3, 5, 8, 13], None)
+```
+
+and returns the binary search tree (i.e. its root node) shown in the example above.
+
+
+### Solution
+```python
+from anytree import Node, RenderTree
+
+# Test case for the function
+def test_create_bst(ordered_list, parent, expected):
+    result = create_bst(ordered_list, parent)
+    
+    if str(RenderTree(result)) == str(RenderTree(expected)):
+        return True
+    else:
+        return False
+
+
+# Code of the function
+def create_bst(ordered_list, parent):
+    cur_len = len(ordered_list)
+
+    if cur_len == 1:
+        return Node(ordered_list[0], parent)
+    elif cur_len > 1:
+        mid = cur_len // 2
+        
+        r = Node(ordered_list[mid], parent)
+
+        create_bst(ordered_list[:mid], r)
+        create_bst(ordered_list[mid+1:], r)
+        
+        return r
+
+
+# Tests
+print(test_create_bst([9], None, Node(9)))
+
+r1 = Node(5)
+Node(1, r1)
+Node(9, r1)
+print(test_create_bst([1, 5, 9], None, r1))
+
+r2 = Node(5)
+r2_1 = Node(3, r2)
+Node(1, r2_1)
+r2_2 = Node(9, r2)
+Node(7, r2_2)
+print(test_create_bst([1, 3, 5, 7, 9], None, r2))
+
+r3 = Node(3)
+r3_1 = Node(1, r3)
+r3_1_1 = Node(1, r3_1)
+Node(0, r3_1_1)
+Node(2, r3_1)
+r3_2 = Node(8, r3)
+Node(5, r3_2)
+Node(13, r3_2)
+print(test_create_bst([0, 1, 1, 2, 3, 5, 8, 13], None, r3))
+``` 
+
+### Additional material
+The runnable [Python file](exercise_41.py) is available online.

exercises/development/advanced/exercise_41.py

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+# -*- coding: utf-8 -*-
+# Copyright (c) 2022, Silvio Peroni <essepuntato@gmail.com>
+#
+# Permission to use, copy, modify, and/or distribute this software for any purpose
+# with or without fee is hereby granted, provided that the above copyright notice
+# and this permission notice appear in all copies.
+#
+# THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
+# REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
+# FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT,
+# OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE,
+# DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS
+# ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS
+# SOFTWARE.
+
+from anytree import Node, RenderTree
+
+# Test case for the function
+def test_create_bst(ordered_list, parent, expected):
+    result = create_bst(ordered_list, parent)
+    
+    if str(RenderTree(result)) == str(RenderTree(expected)):
+        return True
+    else:
+        return False
+
+
+# Code of the function
+def create_bst(ordered_list, parent):
+    cur_len = len(ordered_list)
+
+    if cur_len == 1:
+        return Node(ordered_list[0], parent)
+    elif cur_len > 1:
+        mid = cur_len // 2
+        
+        r = Node(ordered_list[mid], parent)
+
+        create_bst(ordered_list[:mid], r)
+        create_bst(ordered_list[mid+1:], r)
+        
+        return r
+
+
+# Tests
+print(test_create_bst([9], None, Node(9)))
+
+r1 = Node(5)
+Node(1, r1)
+Node(9, r1)
+print(test_create_bst([1, 5, 9], None, r1))
+
+r2 = Node(5)
+r2_1 = Node(3, r2)
+Node(1, r2_1)
+r2_2 = Node(9, r2)
+Node(7, r2_2)
+print(test_create_bst([1, 3, 5, 7, 9], None, r2))
+
+r3 = Node(3)
+r3_1 = Node(1, r3)
+r3_1_1 = Node(1, r3_1)
+Node(0, r3_1_1)
+Node(2, r3_1)
+r3_2 = Node(8, r3)
+Node(5, r3_2)
+Node(13, r3_2)
+print(test_create_bst([0, 1, 1, 2, 3, 5, 8, 13], None, r3))