Algorithm Design Fundamentals

Definition: An algorithm is a step-by-step procedure for solving a problem or achieving a specific goal.
Characteristics:
- Finiteness: An algorithm must have a finite number of steps.
- Definiteness: Each step must be precisely defined.
- Effectiveness: An algorithm must be able to solve the problem in a reasonable amount of time.
- Efficiency: An algorithm should use minimal resources (time, space, etc.).
Types of algorithms:
- Brute Force: Try all possible solutions until the correct one is found.
- Divide and Conquer: Break down the problem into smaller sub-problems and solve each recursively.
- Dynamic Programming: Break down the problem into smaller sub-problems and solve each only once.
Algorithm design strategies:
- Top-down: Start with a general solution and break it down into smaller steps.
- Bottom-up: Start with individual steps and combine them to form a solution.

Definition: A data structure is a way to organize and store data in a computer.
Types of data structures:
- Arrays: A collection of elements of the same data type stored in contiguous memory locations.
- Linked Lists: A collection of elements where each element points to the next element.
- Stacks: A last-in, first-out (LIFO) data structure.
- Queues: A first-in, first-out (FIFO) data structure.
- Trees: A hierarchical data structure with nodes and edges.
- Graphs: A non-hierarchical data structure with nodes and edges.
Data structure operations:
- Insertion: Adding a new element to the data structure.
- Deletion: Removing an element from the data structure.
- Traversal: Iterating over the elements of the data structure.
- Search: Finding a specific element in the data structure.

Definition: Logic is the systematic study of the principles of valid inference and reasoning.
Types of logic:
- Propositional Logic: Deals with statements that can be either true or false.
- Predicate Logic: Deals with statements that contain variables and predicates.
Logical operators:
- NOT (negation): Reverses the truth value of a statement.
- AND (conjunction): Combines two statements into one that is true only if both are true.
- OR (disjunction): Combines two statements into one that is true if at least one is true.
- IF-THEN (implication): States that if one statement is true, then another statement must also be true.
Reasoning techniques:
- Deductive reasoning: Drawing a conclusion based on given premises.
- Inductive reasoning: Drawing a conclusion based on patterns or trends.
- Abductive reasoning: Drawing a conclusion based on incomplete information.

An algorithm is a step-by-step procedure for solving a problem or achieving a specific goal, and it must have a finite number of steps, be precisely defined, and be able to solve the problem in a reasonable amount of time.
Characteristics of an algorithm include finiteness, definiteness, effectiveness, and efficiency.
There are several types of algorithms, including Brute Force, Divide and Conquer, and Dynamic Programming.
Brute Force algorithms try all possible solutions until the correct one is found.
Divide and Conquer algorithms break down the problem into smaller sub-problems and solve each recursively.
Dynamic Programming algorithms break down the problem into smaller sub-problems and solve each only once.
Algorithm design strategies include Top-down and Bottom-up approaches.
Top-down approach starts with a general solution and breaks it down into smaller steps.
Bottom-up approach starts with individual steps and combines them to form a solution.

A data structure is a way to organize and store data in a computer.
Types of data structures include Arrays, Linked Lists, Stacks, Queues, Trees, and Graphs.
Arrays are a collection of elements of the same data type stored in contiguous memory locations.
Linked Lists are a collection of elements where each element points to the next element.
Stacks are a last-in, first-out (LIFO) data structure.
Queues are a first-in, first-out (FIFO) data structure.
Trees are a hierarchical data structure with nodes and edges.
Graphs are a non-hierarchical data structure with nodes and edges.
Data structure operations include Insertion, Deletion, Traversal, and Search.
Insertion operation adds a new element to the data structure.
Deletion operation removes an element from the data structure.
Traversal operation iterates over the elements of the data structure.
Search operation finds a specific element in the data structure.

Logic is the systematic study of the principles of valid inference and reasoning.
Types of logic include Propositional Logic and Predicate Logic.
Propositional Logic deals with statements that can be either true or false.
Predicate Logic deals with statements that contain variables and predicates.
Logical operators include NOT, AND, OR, and IF-THEN.
NOT operator reverses the truth value of a statement.
AND operator combines two statements into one that is true only if both are true.
OR operator combines two statements into one that is true if at least one is true.
IF-THEN operator states that if one statement is true, then another statement must also be true.
Reasoning techniques include Deductive, Inductive, and Abductive reasoning.
Deductive reasoning draws a conclusion based on given premises.
Inductive reasoning draws a conclusion based on patterns or trends.
Abductive reasoning draws a conclusion based on incomplete information.