A binary tree is a hierarchical data structure in computer science that consists of nodes connected by edges. Each node in a binary tree has at most two children, referred to as the left child and the right child. The topmost node in a binary tree is called the root. Here are some key terms and concepts associated with binary trees: Root: The topmost node in the tree, from which all other nodes are descended. Node: A fundamental unit of a binary tree that contains data and may have zero, one, or two children nodes. Parent: A node in the tree that has one or more child nodes. Child: Nodes that are descendants of a parent node. In a binary tree, a node can have at most two children. Leaf: A node in the tree that has no children, i.e., it is at the bottom of the tree. Subtree: A tree formed by a node and its descendants. Height: The length of the longest path from the root to a leaf. The height of an empty tree is typically defined as -1. Depth: The length of the path from the root to a particular node. Binary trees are commonly used in various applications, such as expression trees, binary search trees, and Huffman coding trees. They provide an efficient way to organize and search data, and their recursive nature makes them well-suited for certain algorithms and data manipulations. Understanding binary trees is fundamental to many aspects of computer science and programming.

1. Search Algorithm
Joseph C. Lorilla

2. Linear Search - O(n)

3. Linear Search Code

4. Advantages of Linear Search
• Linear search can be used irrespective of whether the array is sorted
or not. It can be used on arrays of any data type.
• Does not require any additional memory.
• It is a well-suited algorithm for small datasets.

5. Drawbacks of Linear Search
• Linear search has a time complexity of O(N), which in turn makes it
slow for large datasets.
• Not suitable for large arrays.

6. Binary Search – O(log n)

7. Binary Search – O(log n)

8. Binary Search – O(log n)

9. Binary Search – O(log n)

10. Binary Search – O(log n)

11. Binary Search – O(log n)

12. Binary Search – O(log n)

13. Binary Search Code

14. Advantage of Binary Search
• Binary search is faster than linear search, especially for large arrays.
• More efficient than other searching algorithms with a similar time
complexity, such as interpolation search or exponential search.
• Binary search is well-suited for searching large datasets that are
stored in external memory, such as on a hard drive or in the cloud.

15. Disadvantage of Binary Search
• The array should be sorted.
• Binary search requires that the data structure being searched be
stored in contiguous memory locations.
• Binary search requires that the elements of the array be comparable,
meaning that they must be able to be ordered.

16. Application of Binary Search
• Binary search can be used as a building block for more complex
algorithms used in machine learning, such as algorithms for training
neural networks or finding the optimal hyperparameters for a model.
• It can be used for searching in computer graphics such as algorithms
for ray tracing or texture mapping.
• It can be used for searching a database.

17. Sorting Algorithm

18. Sorting Algorithm

19. Different Sorting Algorithms
• Bubble Sort
• Selection Sort
• Insertion Sort
• Merge Sort
• Quicksort
• Counting Sort
• Radix Sort
• Bucket Sort
• Heap Sort
• Shell Sort

20. Time Complexity of Sorting Algorithms

21. Stability of Sorting Algorithm

22. Stability of Sorting Algorithm

23. Stability of Sorting Algorithms

24. Bubble Sort
• Bubble sort is a sorting algorithm that compares two adjacent
elements and swaps them until they are in the intended order.
• Just like the movement of air bubbles in the water that rise up to the
surface, each element of the array move to the end in each iteration.
Therefore, it is called a bubble sort.

25. Bubble Sort Process
1. Starting from the first index, compare
the first and the second elements.
2. If the first element is greater than the
second element, they are swapped.
3. Now, compare the second and the
third elements. Swap them if they are
not in order
• The above process goes on until the last
element.

26. Bubble Sort