0x1D. C - Binary trees

Requirements

General

• Allowed editors: vi, vim, emacs
• All your files will be compiled on Ubuntu 20.04 LTS using gcc, using the options -Wall -Werror -Wextra -pedantic -std=gnu89
• All your files should end with a new line
• A README.md file, at the root of the folder of the project, is mandatory
• Your code should use the Betty style. It will be checked using betty-style.pl and betty-doc.pl
• You are not allowed to use global variables
• No more than 5 functions per file
• You are allowed to use the standard library
• In the following examples, the main.c files are shown as examples. You can use them to test your functions, but you don’t have to push them to your repo (if you do we won’t take them into account). We will use our own main.c files at compilation. Our main.c files might be different from the one shown in the examples
• The prototypes of all your functions should be included in your header file called binary_trees.h
• Don’t forget to push your header file
• All your header files should be include guarded

More Info

Data Structures

Please use the following data structures and types for binary trees. Don’t forget to include them in your header file.

Basic Binary Tree

/**
 * struct binary_tree_s - Binary tree node
 *
 * @n: Integer stored in the node
 * @parent: Pointer to the parent node
 * @left: Pointer to the left child node
 * @right: Pointer to the right child node
 */
struct binary_tree_s
{
    int n;
    struct binary_tree_s *parent;
    struct binary_tree_s *left;
    struct binary_tree_s *right;
};

typedef struct binary_tree_s binary_tree_t;

Binary Search Tree

typedef struct binary_tree_s bst_t;

AVL Tree

typedef struct binary_tree_s avl_t;

Max Binary Heap

typedef struct binary_tree_s heap_t;

Note: For tasks 0 to 23 (included), you have to deal with simple binary trees. They are not BSTs, thus they don’t follow any kind of rule.

Print function

To match the examples in the tasks, you are given this function

This function is used only for visualization purposes. You don’t have to push it to your repo. It may not be used during the correction

Tasks

0. New node

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

alex@/tmp/binary_trees$ cat 0-main.c 
#include <stdlib.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);

    root->left = binary_tree_node(root, 12);
    root->left->left = binary_tree_node(root->left, 6);
    root->left->right = binary_tree_node(root->left, 16);

    root->right = binary_tree_node(root, 402);
    root->right->left = binary_tree_node(root->right, 256);
    root->right->right = binary_tree_node(root->right, 512);

    binary_tree_print(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 0-main.c 0-binary_tree_node.c -o 0-node
alex@/tmp/binary_trees$ ./0-node
       .-------(098)-------.
  .--(012)--.         .--(402)--.
(006)     (016)     (256)     (512)
alex@/tmp/binary_trees$

1. Insert left

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 or if parent is NULL
• 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.

alex@/tmp/binary_trees$ cat 1-main.c 
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_print(root);
    printf("\n");
    binary_tree_insert_left(root->right, 128);
    binary_tree_insert_left(root, 54);
    binary_tree_print(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 1-main.c 1-binary_tree_insert_left.c 0-binary_tree_node.c -o 1-left
alex@/tmp/binary_trees$ ./1-left
  .--(098)--.
(012)     (402)

       .--(098)-------.
  .--(054)       .--(402)
(012)          (128)                                            
alex@/tmp/binary_trees$

2. Insert right

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 or if parent is NULL
• 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.

alex@/tmp/binary_trees$ cat 2-main.c 
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_print(root);
    printf("\n");
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 2-main.c 2-binary_tree_insert_right.c 0-binary_tree_node.c -o 2-right
alex@/tmp/binary_trees$ ./2-right 
  .--(098)--.
(012)     (402)

  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
alex@/tmp/binary_trees$

3. Delete

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
• If tree is NULL, do nothing

alex@/tmp/binary_trees$ cat 3-main.c 
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);
    binary_tree_delete(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 3-main.c 3-binary_tree_delete.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 3-del
alex@/tmp/binary_trees$ valgrind ./3-del
==13264== Memcheck, a memory error detector
==13264== Copyright (C) 2002-2013, and GNU GPL'd, by Julian Seward et al.
==13264== Using Valgrind-3.10.1 and LibVEX; rerun with -h for copyright info
==13264== Command: ./3-del
==13264== 
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
==13264== 
==13264== HEAP SUMMARY:
==13264==     in use at exit: 0 bytes in 0 blocks
==13264==   total heap usage: 9 allocs, 9 frees, 949 bytes allocated
==13264== 
==13264== All heap blocks were freed -- no leaks are possible
==13264== 
==13264== For counts of detected and suppressed errors, rerun with: -v
==13264== ERROR SUMMARY: 0 errors from 0 contexts (suppressed: 0 from 0)
alex@/tmp/binary_trees$

4. Is leaf

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, otherwise 0
• If node is NULL, return 0

alex@/tmp/binary_trees$ cat 4-main.c 
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    int ret;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);

    ret = binary_tree_is_leaf(root);
    printf("Is %d a leaf: %d\n", root->n, ret);
    ret = binary_tree_is_leaf(root->right);
    printf("Is %d a leaf: %d\n", root->right->n, ret);
    ret = binary_tree_is_leaf(root->right->right);
    printf("Is %d a leaf: %d\n", root->right->right->n, ret);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 4-binary_tree_is_leaf.c 4-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 4-leaf
alex@/tmp/binary_trees$ ./4-leaf 
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
Is 98 a leaf: 0
Is 128 a leaf: 0
Is 402 a leaf: 1
alex@/tmp/binary_trees$

5. Is root

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, otherwise 0
• If node is NULL, return 0

alex@/tmp/binary_trees$ cat 5-main.c 
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    int ret;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);

    ret = binary_tree_is_root(root);
    printf("Is %d a root: %d\n", root->n, ret);
    ret = binary_tree_is_root(root->right);
    printf("Is %d a root: %d\n", root->right->n, ret);
    ret = binary_tree_is_root(root->right->right);
    printf("Is %d a root: %d\n", root->right->right->n, ret);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 5-binary_tree_is_root.c 5-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 5-root
alex@/tmp/binary_trees$ ./5-root 
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
Is 98 a root: 1
Is 128 a root: 0
Is 402 a root: 0
alex@/tmp/binary_trees$

6. Pre-order traversal

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.
• If tree or func is NULL, do nothing

alex@/tmp/binary_trees$ cat 6-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * print_num - Prints a number
 *
 * @n: Number to be printed
 */
void print_num(int n)
{
    printf("%d\n", n);
}

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    root->left->left = binary_tree_node(root->left, 6);
    root->left->right = binary_tree_node(root->left, 56);
    root->right->left = binary_tree_node(root->right, 256);
    root->right->right = binary_tree_node(root->right, 512);

    binary_tree_print(root);
    binary_tree_preorder(root, &print_num);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 6-main.c 6-binary_tree_preorder.c 0-binary_tree_node.c -o 6-pre
alex@/tmp/binary_trees$ ./6-pre
       .-------(098)-------.
  .--(012)--.         .--(402)--.
(006)     (056)     (256)     (512)
98
12
6
56
402
256
512
alex@/tmp/binary_trees$

7. In-order traversal

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.
• If tree or func is NULL, do nothing

alex@/tmp/binary_trees$ cat 7-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * print_num - Prints a number
 *
 * @n: Number to be printed
 */
void print_num(int n)
{
    printf("%d\n", n);
}

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    root->left->left = binary_tree_node(root->left, 6);
    root->left->right = binary_tree_node(root->left, 56);
    root->right->left = binary_tree_node(root->right, 256);
    root->right->right = binary_tree_node(root->right, 512);

    binary_tree_print(root);
    binary_tree_inorder(root, &print_num);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 7-main.c 7-binary_tree_inorder.c 0-binary_tree_node.c -o 7-in
alex@/tmp/binary_trees$ ./7-in
       .-------(098)-------.
  .--(012)--.         .--(402)--.
(006)     (056)     (256)     (512)
6
12
56
98
256
402
512
alex@/tmp/binary_trees$

8. Post-order traversal

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.
• If tree or func is NULL, do nothing

alex@/tmp/binary_trees$ cat 8-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * print_num - Prints a number
 *
 * @n: Number to be printed
 */
void print_num(int n)
{
    printf("%d\n", n);
}

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    root->left->left = binary_tree_node(root->left, 6);
    root->left->right = binary_tree_node(root->left, 56);
    root->right->left = binary_tree_node(root->right, 256);
    root->right->right = binary_tree_node(root->right, 512);

    binary_tree_print(root);
    binary_tree_postorder(root, &print_num);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 8-main.c 8-binary_tree_postorder.c 0-binary_tree_node.c -o 8-post
alex@/tmp/binary_trees$ ./8-post
       .-------(098)-------.
  .--(012)--.         .--(402)--.
(006)     (056)     (256)     (512)
6
56
12
256
512
402
98
alex@/tmp/binary_trees$

9. Height

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.
• If tree is NULL, your function must return 0

alex@/tmp/binary_trees$ cat 9-main.c 
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    size_t height;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);

    height = binary_tree_height(root);
    printf("Height from %d: %lu\n", root->n, height);
    height = binary_tree_height(root->right);
    printf("Height from %d: %lu\n", root->right->n, height);
    height = binary_tree_height(root->left->right);
    printf("Height from %d: %lu\n", root->left->right->n, height);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 9-binary_tree_height.c 9-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 9-height
alex@/tmp/binary_trees$ ./9-height 
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
Height from 98: 2
Height from 128: 1
Height from 54: 0
alex@/tmp/binary_trees$

10. Depth

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

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

alex@/tmp/binary_trees$ cat 10-main.c 
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    size_t depth;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);

    depth = binary_tree_depth(root);
    printf("Depth of %d: %lu\n", root->n, depth);
    depth = binary_tree_depth(root->right);
    printf("Depth of %d: %lu\n", root->right->n, depth);
    depth = binary_tree_depth(root->left->right);
    printf("Depth of %d: %lu\n", root->left->right->n, depth);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 10-binary_tree_depth.c 10-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 10-depth
alex@/tmp/binary_trees$ ./10-depth 
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
Depth of 98: 0
Depth of 128: 1
Depth of 54: 2
alex@/tmp/binary_trees$

11. Size

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
• If tree is NULL, the function must return 0

alex@/tmp/binary_trees$ cat 11-main.c 
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    size_t size;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);

    size = binary_tree_size(root);
    printf("Size of %d: %lu\n", root->n, size);
    size = binary_tree_size(root->right);
    printf("Size of %d: %lu\n", root->right->n, size);
    size = binary_tree_size(root->left->right);
    printf("Size of %d: %lu\n", root->left->right->n, size);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 11-binary_tree_size.c 11-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 11-size
alex@/tmp/binary_trees$ ./11-size 
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
Size of 98: 5
Size of 128: 2
Size of 54: 1
alex@/tmp/binary_trees$

12. Leaves

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 number of leaves
• If tree is NULL, the function must return 0
• A NULL pointer is not a leaf

alex@/tmp/binary_trees$ cat 12-main.c 
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    size_t leaves;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);

    leaves = binary_tree_leaves(root);
    printf("Leaves in %d: %lu\n", root->n, leaves);
    leaves = binary_tree_leaves(root->right);
    printf("Leaves in %d: %lu\n", root->right->n, leaves);
    leaves = binary_tree_leaves(root->left->right);
    printf("Leaves in %d: %lu\n", root->left->right->n, leaves);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 12-binary_tree_leaves.c 12-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 12-leaves
alex@/tmp/binary_trees$ ./12-leaves 
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
Leaves in 98: 2
Leaves in 128: 1
Leaves in 54: 1
alex@/tmp/binary_trees$

13. Nodes

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 number of nodes
• If tree is NULL, the function must return 0
• A NULL pointer is not a node

alex@/tmp/binary_trees$ cat 13-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    size_t nodes;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_print(root);

    nodes = binary_tree_nodes(root);
    printf("Nodes in %d: %lu\n", root->n, nodes);
    nodes = binary_tree_nodes(root->right);
    printf("Nodes in %d: %lu\n", root->right->n, nodes);
    nodes = binary_tree_nodes(root->left->right);
    printf("Nodes in %d: %lu\n", root->left->right->n, nodes);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 13-binary_tree_nodes.c 13-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 13-nodes
alex@/tmp/binary_trees$ ./13-nodes
  .-------(098)--.
(012)--.       (128)--.
     (054)          (402)
Nodes in 98: 3
Nodes in 128: 1
Nodes in 54: 0
alex@/tmp/binary_trees$

14. Balance factor

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
• If tree is NULL, return 0

alex@/tmp/binary_trees$ cat 14-main.c 
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    int balance;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    binary_tree_insert_left(root, 45);
    binary_tree_insert_right(root->left, 50);
    binary_tree_insert_left(root->left->left, 10);
    binary_tree_insert_left(root->left->left->left, 8);
    binary_tree_print(root);

    balance = binary_tree_balance(root);
    printf("Balance of %d: %+d\n", root->n, balance);
    balance = binary_tree_balance(root->right);
    printf("Balance of %d: %+d\n", root->right->n, balance);
    balance = binary_tree_balance(root->left->left->right);
    printf("Balance of %d: %+d\n", root->left->left->right->n, balance);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 14-binary_tree_balance.c 14-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c 1-binary_tree_insert_left.c -o 14-balance
alex@/tmp/binary_trees$ ./14-balance
                      .-------(098)--.
            .-------(045)--.       (128)--.
       .--(012)--.       (050)          (402)
  .--(010)     (054)
(008)
Balance of 98: +2
Balance of 128: -1
Balance of 54: +0
alex@/tmp/binary_trees$

15. Is full

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

alex@/tmp/binary_trees$ cat 15-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    int full;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    root->left->left = binary_tree_node(root->left, 10);
    binary_tree_print(root);

    full = binary_tree_is_full(root);
    printf("Is %d full: %d\n", root->n, full);
    full = binary_tree_is_full(root->left);
    printf("Is %d full: %d\n", root->left->n, full);
    full = binary_tree_is_full(root->right);
    printf("Is %d full: %d\n", root->right->n, full);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 15-binary_tree_is_full.c 15-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 15-full
alex@/tmp/binary_trees$ ./15-full
       .-------(098)--.
  .--(012)--.       (128)--.
(010)     (054)          (402)
Is 98 full: 0
Is 12 full: 1
Is 128 full: 0
alex@/tmp/binary_trees$

16. Is perfect

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

alex@/tmp/binary_trees$ cat 16-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    int perfect;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    binary_tree_insert_right(root->left, 54);
    binary_tree_insert_right(root, 128);
    root->left->left = binary_tree_node(root->left, 10);
    root->right->left = binary_tree_node(root->right, 10);

    binary_tree_print(root);
    perfect = binary_tree_is_perfect(root);
    printf("Perfect: %d\n\n", perfect);

    root->right->right->left = binary_tree_node(root->right->right, 10);
    binary_tree_print(root);
    perfect = binary_tree_is_perfect(root);
    printf("Perfect: %d\n\n", perfect);

    root->right->right->right = binary_tree_node(root->right->right, 10);
    binary_tree_print(root);
    perfect = binary_tree_is_perfect(root);
    printf("Perfect: %d\n", perfect);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 16-binary_tree_is_perfect.c 16-main.c 0-binary_tree_node.c 2-binary_tree_insert_right.c -o 16-perfect
alex@/tmp/binary_trees$ ./16-perfect 
       .-------(098)-------.
  .--(012)--.         .--(128)--.
(010)     (054)     (010)     (402)
Perfect: 1

       .-------(098)-------.
  .--(012)--.         .--(128)-------.
(010)     (054)     (010)       .--(402)
                              (010)
Perfect: 0

       .-------(098)-------.
  .--(012)--.         .--(128)-------.
(010)     (054)     (010)       .--(402)--.
                              (010)     (010)
Perfect: 0
alex@/tmp/binary_trees$

17. Sibling

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
• Your function must return a pointer to the sibling node
• If node is NULL or the parent is NULL, return NULL
• If node has no sibling, return NULL

alex@/tmp/binary_trees$ cat 17-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    binary_tree_t *sibling;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 128);
    root->left->right = binary_tree_node(root->left, 54);
    root->right->right = binary_tree_node(root->right, 402);
    root->left->left = binary_tree_node(root->left, 10);
    root->right->left = binary_tree_node(root->right, 110);
    root->right->right->left = binary_tree_node(root->right->right, 200);
    root->right->right->right = binary_tree_node(root->right->right, 512);

    binary_tree_print(root);
    sibling = binary_tree_sibling(root->left);
    printf("Sibling of %d: %d\n", root->left->n, sibling->n);
    sibling = binary_tree_sibling(root->right->left);
    printf("Sibling of %d: %d\n", root->right->left->n, sibling->n);
    sibling = binary_tree_sibling(root->left->right);
    printf("Sibling of %d: %d\n", root->left->right->n, sibling->n);
    sibling = binary_tree_sibling(root);
    printf("Sibling of %d: %p\n", root->n, (void *)sibling);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 17-main.c 17-binary_tree_sibling.c 0-binary_tree_node.c -o 17-sibling
alex@/tmp/binary_trees$ ./17-sibling
       .-------(098)-------.
  .--(012)--.         .--(128)-------.
(010)     (054)     (110)       .--(402)--.
                              (200)     (512)
Sibling of 12: 128
Sibling of 110: 402
Sibling of 54: 10
Sibling of 98: (nil)
alex@/tmp/binary_trees$

18. Uncle

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
• Your function must return a pointer to the uncle node
• If node is NULL, return NULL
• If node has no uncle, return NULL

alex@/tmp/binary_trees$ cat 18-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;
    binary_tree_t *uncle;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 128);
    root->left->right = binary_tree_node(root->left, 54);
    root->right->right = binary_tree_node(root->right, 402);
    root->left->left = binary_tree_node(root->left, 10);
    root->right->left = binary_tree_node(root->right, 110);
    root->right->right->left = binary_tree_node(root->right->right, 200);
    root->right->right->right = binary_tree_node(root->right->right, 512);

    binary_tree_print(root);
    uncle = binary_tree_uncle(root->right->left);
    printf("Uncle of %d: %d\n", root->right->left->n, uncle->n);
    uncle = binary_tree_uncle(root->left->right);
    printf("Uncle of %d: %d\n", root->left->right->n, uncle->n);
    uncle = binary_tree_uncle(root->left);
    printf("Uncle of %d: %p\n", root->left->n, (void *)uncle);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 18-main.c 18-binary_tree_uncle.c 0-binary_tree_node.c -o 18-uncle
alex@/tmp/binary_trees$ ./18-uncle
       .-------(098)-------.
  .--(012)--.         .--(128)-------.
(010)     (054)     (110)       .--(402)--.
                              (200)     (512)
Uncle of 110: 12
Uncle of 54: 128
Uncle of 12: (nil)
alex@/tmp/binary_trees$

19. Lowest common ancestor

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

alex@/tmp/binary_trees$ cat 100-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * launch_test - Test ancestor function and print informations
 *
 * @n1: First node
 * @n2: Second node
 */
void launch_test(binary_tree_t *n1, binary_tree_t *n2)
{
    binary_tree_t *ancestor;

    ancestor = binary_trees_ancestor(n1, n2);
    printf("Ancestor of [%d] & [%d]: ", n1->n, n2->n);
    if (!ancestor)
        printf("(nil)\n");
    else
        printf("%d\n", ancestor->n);
}

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    root->left->right = binary_tree_node(root->left, 54);
    root->right->right = binary_tree_node(root->right, 128);
    root->left->left = binary_tree_node(root->left, 10);
    root->right->left = binary_tree_node(root->right, 45);
    root->right->right->left = binary_tree_node(root->right->right, 92);
    root->right->right->right = binary_tree_node(root->right->right, 65);
    binary_tree_print(root);

    launch_test(root->left, root->right);
    launch_test(root->right->left, root->right->right->right);
    launch_test(root->right->right, root->right->right->right);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 100-main.c 100-binary_trees_ancestor.c 0-binary_tree_node.c -o 100-ancestor
alex@/tmp/binary_trees$ ./100-ancestor
       .-------(098)-------.
  .--(012)--.         .--(402)-------.
(010)     (054)     (045)       .--(128)--.
                              (092)     (065)
Ancestor of [12] & [402]: 98
Ancestor of [45] & [65]: 402
Ancestor of [128] & [65]: 128
alex@/tmp/binary_trees$

20. Level-order traversal

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.
• If tree or func is NULL, do nothing

alex@/tmp/binary_trees$ cat 101-main.c
#include <stdlib.h>
#include <stdio.h>
#include "binary_trees.h"

/**
 * print_num - Prints a number
 *
 * @n: Number to be printed
 */
void print_num(int n)
{
    printf("%d\n", n);
}

/**
 * main - Entry point
 *
 * Return: Always 0 (Success)
 */
int main(void)
{
    binary_tree_t *root;

    root = binary_tree_node(NULL, 98);
    root->left = binary_tree_node(root, 12);
    root->right = binary_tree_node(root, 402);
    root->left->left = binary_tree_node(root->left, 6);
    root->left->right = binary_tree_node(root->left, 56);
    root->right->left = binary_tree_node(root->right, 256);
    root->right->right = binary_tree_node(root->right, 512);

    binary_tree_print(root);
    binary_tree_levelorder(root, &print_num);
    binary_tree_delete(root);
    return (0);
}
alex@/tmp/binary_trees$ gcc -Wall -Wextra -Werror -pedantic binary_tree_print.c 101-main.c 101-binary_tree_levelorder.c 0-binary_tree_node.c 3-binary_tree_delete.c -o 101-lvl
alex@/tmp/binary_trees$ valgrind ./101-lvl
==23445== Memcheck, a memory error detector
==23445== Copyright (C) 2002-2013, and GNU GPL'd, by Julian Seward et al.
==23445== Using Valgrind-3.10.1 and LibVEX; rerun with -h for copyright info
==23445== Command: ./101-lvl
==23445== 
       .-------(098)-------.
  .--(012)--.         .--(402)--.
(006)     (056)     (256)     (512)
98
12
402
6
56
256
512
==23445== 
==23445== HEAP SUMMARY:
==23445==     in use at exit: 0 bytes in 0 blocks
==23445==   total heap usage: 19 allocs, 19 frees, 1,197 bytes allocated
==23445== 
==23445== All heap blocks were freed -- no leaks are possible
==23445== 
==23445== For counts of detected and suppressed errors, rerun with: -v
==23445== ERROR SUMMARY: 0 errors from 0 contexts (suppressed: 0 from 0)
alex@/tmp/binary_trees$

29. Big O #BST

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

35. Big O #AVL Tree

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

41. Big O #Binary Heap

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

• Inserting the value n
• Extracting the root node
• Searching for a node in a binary heap of size n