0x1C. C - Binary trees

0. New node mandatory

Write a function that creates a binary tree node

Prototype: binary_tree_t *binary_tree_node(binary_tree_t *parent, int value);
Where parent is a pointer to the parent node of the node to create
And value is the value to put in the new node
When created, a node does not have any child
Your function must return a pointer to the new node, or NULL on failure

1. Insert left mandatory

Write a function that inserts a node as the left-child of another node

Prototype: binary_tree_t *binary_tree_insert_left(binary_tree_t *parent, int value);
Where parent is a pointer to the node to insert the left-child in
And value is the value to store in the new node
Your function must return a pointer to the created node, or NULL on failure
If parent already has a left-child, the new node must take its place, and the old left-child must be set as the left-child of the new node.

2. Insert right mandatory

Write a function that inserts a node as the right-child of another node

Prototype: binary_tree_t *binary_tree_insert_right(binary_tree_t *parent, int value);
Where parent is a pointer to the node to insert the right-child in
And value is the value to store in the new node
Your function must return a pointer to the created node, or NULL on failure
If parent already has a right-child, the new node must take its place, and the old right-child must be set as the right-child of the new node.

3. Delete mandatory

Write a function that deletes an entire binary tree

Prototype: void binary_tree_delete(binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to delete

4. Is leaf mandatory

Write a function that checks if a node is a leaf

Prototype: int binary_tree_is_leaf(const binary_tree_t *node);
Where node is a pointer to the node to check
Your function must return 1 if node is a leaf, and 0 otherwise
If node is NULL, return 0

5. Is root mandatory

Write a function that checks if a given node is a root

Prototype: int binary_tree_is_root(const binary_tree_t *node);
Where node is a pointer to the node to check
Your function must return 1 if node is a root, and 0 otherwise
If node is NULL, return 0

6. Pre-order traversal mandatory

Write a function that goes through a binary tree using pre-order traversal

Prototype: void binary_tree_preorder(const binary_tree_t *tree, void (*func)(int));
Where tree is a pointer to the root node of the tree to traverse
And func is a pointer to a function to call for each node. The value in the node must be passed as a parameter to this function.

7. In-order traversal mandatory

Write a function that goes through a binary tree using in-order traversal

Prototype: void binary_tree_inorder(const binary_tree_t *tree, void (*func)(int));
Where tree is a pointer to the root node of the tree to traverse
And func is a pointer to a function to call for each node. The value in the node must be passed as a parameter to this function.

8. Post-order traversal mandatory

Write a function that goes through a binary tree using post-order traversal

Prototype: void binary_tree_postorder(const binary_tree_t *tree, void (*func)(int));
Where tree is a pointer to the root node of the tree to traverse
And func is a pointer to a function to call for each node. The value in the node must be passed as a parameter to this function.

9. Height mandatory

Write a function that measures the height of a binary tree

Prototype: size_t binary_tree_height(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to measure the height of
If tree is NULL, your function must return 0

10. Depth mandatory

Write a function that measures the depth of a node in a binary tree

Prototype: size_t binary_tree_depth(const binary_tree_t *node);
Where tree is a pointer to the node to measure the depth of
If node is NULL, your function must return 0

11. Size mandatory

Write a function that measures the size of a binary tree

Prototype: size_t binary_tree_size(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to measure the size of

12. Leaves mandatory

Write a function that counts the leaves in a binary tree

Prototype: size_t binary_tree_leaves(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to count the leaves in
A NULL pointer is not a leaf

13. Nodes mandatory

Write a function that counts the nodes with at least 1 child in a binary tree

Prototype: size_t binary_tree_nodes(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to count the nodes in
A NULL pointer is not a node

14. Balance factor mandatory

Write a function that measures the balance factor of a binary tree

Prototype: int binary_tree_balance(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to measure the balance factor of
If tree is NULL, return 0

15. Is full mandatory

Write a function that checks if a binary tree is full

Prototype: int binary_tree_is_full(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to check
If tree is NULL, your function must return 0

16. Is perfect mandatory

Write a function that checks if a binary tree is perfect

Prototype: int binary_tree_is_perfect(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to check
If tree is NULL, your function must return 0

17. Sibling mandatory

Write a function that finds the sibling of a node

Prototype: binary_tree_t *binary_tree_sibling(binary_tree_t *node);
Where node is a pointer to the node to find the sibling of
Your function must return a pointer to the sibling node
If node has no sibling, return NULL

18. Uncle mandatory

Write a function that finds the uncle of a node

Prototype: binary_tree_t *binary_tree_uncle(binary_tree_t *node);
Where node is a pointer to the node to find the uncle of
Your function must return a pointer to the uncle node
If node has no uncle, return NULL

19. Lowest common ancestor #advanced

Write a function that finds the lowest common ancestor of two nodes

Prototype: binary_tree_t *binary_trees_ancestor(const binary_tree_t *first, const binary_tree_t *second);
Where first is a pointer to the first node
And second is a pointer to the second node
Your function must return a pointer to the lowest common ancestor node of the two given nodes
If no common ancestor was found, your function must return NULL

20. Level-order traversal #advanced

Write a function that goes through a binary tree using level-order traversal

Prototype: void binary_tree_levelorder(const binary_tree_t *tree, void (*func)(int));
Where tree is a pointer to the root node of the tree to traverse
And func is a pointer to a function to call for each node. The value in the node must be passed as a parameter to this function.

21. Is complete #advanced

Write a function that checks if a binary tree is complete

Prototype: int binary_tree_is_complete(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to check
If tree is NULL, your function must return 0

22. Rotate left #advanced

Write a function that performs a left-rotation on a binary tree

Prototype: binary_tree_t *binary_tree_rotate_left(binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to rotate
Your function must return a pointer to the new root node of the tree once rotated

23. Rotate right #advanced

Write a function that performs a right-rotation on a binary tree

Prototype: binary_tree_t *binary_tree_rotate_right(binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to rotate
Your function must return a pointer to the new root node of the tree once rotated

24. Is BST #advanced

Write a function that checks if a binary tree is a valid Binary Search Tree

Prototype: int binary_tree_is_bst(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to check
Your function must return 1 if tree is a valid BST, and 0 otherwise
If tree is NULL, return 0

Properties of a Binary Search Tree:

The left subtree of a node contains only nodes with values less than the node’s value
The right subtree of a node contains only nodes with values greater than the node’s value
The left and right subtree each must also be a binary search tree
There must be no duplicate values

25. BST - Insert #advanced

Write a function that inserts a value in a Binary Search Tree

Prototype: bst_t *bst_insert(bst_t **tree, int value);
Where tree is a double pointer to the root node of the BST to insert the value in
And value is the value to store in the node to be inserted
Your function must return a pointer to the created node, or NULL on failure
If the address stored in tree is NULL, the created node must become the root node.
If the value is already present in the tree, it must be ignored

Your file 0-binary_tree_node.c will be compile during the correction

26. BST - Array to BST #advanced

Write a function that builds a Binary Search Tree from an array

Prototype: bst_t *array_to_bst(int *array, size_t size);
Where array is a pointer to the first element of the array to be converted
And size is the number of element in the array
Your function must return a pointer to the root node of the created BST, or NULL on failure
If a value of the array is already present in the tree, this value must be ignored

Your files 111-bst_insert.c and 0-binary_tree_node.c will be compiled during the correction

27. BST - Search #advanced

Write a function that searches for a value in a Binary Search Tree

Prototype: bst_t *bst_search(const bst_t *tree, int value);
Where tree is a pointer to the root node of the BST to search
And value is the value to look for
Your function must return a pointer to the node containing a value equals to value
If tree is NULL or if nothing is found, your function must return NULL

28. BST - Remove #advanced

Write a function that removes a node from a Binary Search Tree

Prototype: bst_t *bst_remove(bst_t *root, int value);
Where root is a pointer to the root node of the tree to remove a node of
And value is the value to look for
Once located, the node containing a value equals to value must be removed and freed
If the node to be deleted has two children, it must be replaced with its first in-order successor (not predecessor)
Your function must return a pointer to the new root node of the tree after removing the desired value

29. Big O #BST #advanced

What are the average time complexities of those operations on a Binary Search Tree (one answer per line):

Inserting the value n
Removing the node with the value n
Searching for a node in a BST of size n

30. Is AVL #advanced

Write a function that checks if a binary tree is a valid AVL Tree

Prototype: int binary_tree_is_avl(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to check
Your function must return 1 if tree is a valid AVL Tree, and 0 otherwise
If tree is NULL, return 0

Properties of an AVL Tree:

An AVL Tree is a BST
The difference between heights of left and right subtrees cannot be more than one
The left and right subtree each must also be a binary search tree

31. AVL - Insert #advanced

Write a function that inserts a value in an AVL Tree

Prototype: avl_t *avl_insert(avl_t **tree, int value);
Where tree is a double pointer to the root node of the AVL tree to insert the value in
And value is the value to store in the node to be inserted
Your function must return a pointer to the created node, or NULL on failure
If the address stored in tree is NULL, the created node must become the root node.
The resulting tree after insertion, must be a balanced AVL Tree

Your files 14-binary_tree_balance.c, 103-binary_tree_rotate_left.c, 104-binary_tree_rotate_right.c and 0-binary_tree_node.c will be compiled during the correction

32. AVL - Array to AVL #advanced

Write a function that builds an AVL tree from an array

Prototype: avl_t *array_to_avl(int *array, size_t size);
Where array is a pointer to the first element of the array to be converted
And size is the number of element in the array
Your function must return a pointer to the root node of the created AVL tree, or NULL on failure
If a value of the array is already present in the tree, this value must be ignored

Your files 121-avl_insert.c, 0-binary_tree_node.c, 14-binary_tree_balance.c, 103-binary_tree_rotate_left.c and 104-binary_tree_rotate_right.c will be compiled during the correction

33. AVL - Remove #advanced

Write a function that removes a node from an AVL tree

Prototype: avl_t *avl_remove(avl_t *root, int value);
Where root is a pointer to the root node of the tree to remove a node of
And value is the value to look for
Once located, the node containing a value equals to value must be removed and freed
If the node to be deleted has two children, it must be replaced with its first in-order successor (not predecessor)
After deletion of the desired node, the tree must be rebalanced if necessary
Your function must return a pointer to the new root node of the tree after removing the desired value, and after rebalancing

Your files 14-binary_tree_balance.c, 103-binary_tree_rotate_left.c and 104-binary_tree_rotate_right.c will be compiled during the correction

34. AVL - From sorted array #advanced

Write a function that builds an AVL tree from an array

Prototype: avl_t *sorted_array_to_avl(int *array, size_t size);
Where array is a pointer to the first element of the array to be converted
And size is the number of element in the array
Your function must return a pointer to the root node of the created AVL tree, or NULL on failure
You can assume there will be no duplicate value in the array
You are not allowed to rotate
You can only have 2 functions in your file

Your file 0-binary_tree_node.c will be compiled during the correction

35. Big O #AVL Tree #advanced

What are the average time complexities of those operations on an AVL Tree (one answer per line):

Inserting the value n
Removing the node with the value n
Searching for a node in an AVL tree of size n

36. Is Binary heap #advanced

Write a function that checks if a binary tree is a valid Max Binary Heap

Prototype: int binary_tree_is_heap(const binary_tree_t *tree);
Where tree is a pointer to the root node of the tree to check
Your function must return 1 if tree is a valid Max Binary Heap, and 0 otherwise
If tree is NULL, return 0

Properties of a Max Binary Heap:

It’s a complete tree
In a Max Binary Heap, the value at root must be maximum among all values present in Binary Heap
The last property must be recursively true for all nodes in Binary Tree

37. Heap - Insert #advanced

Write a function that inserts a value in Max Binary Heap

Prototype: heap_t *heap_insert(heap_t **root, int value)
Where tree is a double pointer to the root node of the Heap to insert the value in
And value is the value to store in the node to be inserted
Your function must return a pointer to the created node, or NULL on failure
If the address stored in tree is NULL, the created node must become the root node.
You have to respect a Max Heap ordering
You are allowed to have up to 6 functions in your file