Gain insights into connecting discrete mathematics with programming. Explore variables, expressions, data structures, and algorithm design to enhance your problem-solving and implementation skills.

Discrete Mathematical Algorithms and Data Structures-02-02.png

momoexp4.tar.gz

java and C++

OnlyPython

OnlyJava

OnlyCplusplus

OnlyC

JavaLang3

Discrete mathematics is the basis of several popular algorithms. This course shows the discreteness of data structures and algorithms. It can benefit programmers with a non-CS background looking to strengthen their foundations by connecting theoretical concepts with practical programming scenarios.

The course starts with discussing relating discrete mathematics with algorithms and data structures. You will have examples demonstrating variables, conditional expressions, and arrays as basic building blocks of programming. Then, you will use classes and objects to define and implement linear data structures. You will also learn about the binary tree traversals and templates and the topics of time complexity, set difference, and rearranging the values in a string.

By the end of the course, you will have a strong grasp of algorithm design, data structure implementation, and overall problem-solving.

Programming Discrete Math Concepts for Beginners

# Introduction to binary trees

The main reason we’re studying data structures is to organize data most efficiently. A binary tree is a specialized representation of data structure. A binary tree is used for data storage purposes. A tree is represented by nodes that are connected by edges or pointers. 

A binary tree has a unique condition, making it very special among other data storage mechanisms. A node of a binary tree can have a maximum of two children. When it has one or two children, we call it a **subtree**. Each node of a subtree can have more subtrees. 

When a tree node or subtree node doesn’t have children, it’s called a **leaf node**. 

While traversing a tree, we always take the leaf node as our ending point or base case for recursion. We can search a binary tree as an ordered array. We can also insert and delete data in any binary tree like we do in a linked list. 

A binary tree’s sequence of nodes is known as a **path**. This path starts at the top of the node, referred to as the **root**. There’s always only one root and one path to the other node. It has no duplicate path. The nodes placed below are **children**; these children nodes always have nodes above them, known as **parent nodes**. 


If we consider a root node as the parent node, then this node is on level one. The node just below is placed at level two.  

# Tree traversal algorithms

Trees can be traversed in a few different ways: **preorder**, **postorder**, and **inorder**. There are different algorithms for each kind of tree traversal. In this lesson, we’ll briefly examine tree traversal algorithms.






As we learned in the previous lesson, in some cases, recursions are essential. Most tree-based algorithms can be easily implemented using recursion because a binary tree is a recursive data structure. Although learning to solve the same problems with recursion is wise, we can also solve tree-based algorithms using iteration.


Course Introduction

Programming Language and Boolean Algebra

Logical Expressions and Algorithms

Arrays and Discrete Mathematics

Classes, Objects, and Methods

Linear Data Structures

Tree, Algorithms, and Templates

Time Complexity

Propositional Logic

Combinatorics

Wrapping Up

Solving Sudoku and the 8-Queens Puzzle as Constraint Satisfaction

Binary Tree

Introduction to binary trees