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# Algorithms Definition and Types

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@AppreciatedIodine

## Questions and Answers

### What is the primary characteristic of a dynamic programming algorithm?

It breaks down a complex problem into smaller subproblems and solves each subproblem only once.

### What type of algorithm solves a problem by breaking it down into smaller instances of the same problem?

Recursive algorithm

### What is the purpose of Big O Notation in algorithm analysis?

To provide an upper bound on the number of steps an algorithm takes

### What is the name of the algorithm design technique that breaks down a problem into smaller subproblems and solves each subproblem recursively?

<p>Divide and Conquer</p> Signup and view all the answers

### What is the name of the sorting algorithm that compares adjacent elements and swaps them if they are in the wrong order?

<p>Bubble sort</p> Signup and view all the answers

### What is the application of algorithms in which they are used to secure data and ensure confidentiality?

<p>Cryptography</p> Signup and view all the answers

### What type of algorithm makes the locally optimal choice at each step, hoping to find a global optimum?

<p>Greedy algorithm</p> Signup and view all the answers

### What is the type of complexity that measures the amount of memory an algorithm uses?

<p>Space complexity</p> Signup and view all the answers

## Study Notes

### Algorithms

#### Definition

• An algorithm is a well-defined procedure that takes some input and produces a corresponding output
• It is a step-by-step procedure to solve a computational problem

#### Types of Algorithms

• Recursive Algorithm: solves a problem by breaking it down into smaller instances of the same problem
• Dynamic Programming Algorithm: breaks down a complex problem into smaller subproblems and solves each subproblem only once
• Backtracking Algorithm: finds a solution by recursively exploring all possible solutions
• Greedy Algorithm: makes the locally optimal choice at each step, hoping to find a global optimum

#### Algorithm Analysis

• Time Complexity: measures the amount of time an algorithm takes to complete
• Big O Notation: upper bound on the number of steps an algorithm takes
• Omega Notation: lower bound on the number of steps an algorithm takes
• Theta Notation: exact bound on the number of steps an algorithm takes
• Space Complexity: measures the amount of memory an algorithm uses
• Auxiliary Space Complexity: measures the amount of extra memory used by an algorithm

#### Algorithm Design Techniques

• Divide and Conquer: breaks down a problem into smaller subproblems and solves each subproblem recursively
• Dynamic Programming: breaks down a complex problem into smaller subproblems and solves each subproblem only once
• Greedy Method: makes the locally optimal choice at each step, hoping to find a global optimum

#### Famous Algorithms

• Sorting Algorithms:
• Bubble Sort: compares adjacent elements and swaps them if they are in the wrong order
• Selection Sort: selects the smallest element from the unsorted portion of the array and swaps it with the first element
• Merge Sort: divides the array into smaller subarrays and merges them in sorted order
• Searching Algorithms:
• Linear Search: checks each element of the array in sequence until a match is found
• Binary Search: searches for an element in a sorted array by repeatedly dividing the search interval in half

#### Algorithm Applications

• Cryptography: uses algorithms to secure data and ensure confidentiality
• Data Compression: uses algorithms to reduce the size of data
• Machine Learning: uses algorithms to make predictions and classify data
• Network Flow: uses algorithms to optimize the flow of data through a network

### Algorithms

#### Definition

• An algorithm is a well-defined procedure that takes input and produces a corresponding output.
• It is a step-by-step procedure to solve a computational problem.

#### Types of Algorithms

• Recursive Algorithm: breaks down a problem into smaller instances of the same problem to solve it.
• Dynamic Programming Algorithm: breaks down a complex problem into smaller subproblems, solves each subproblem only once, and stores the solutions to subproblems to avoid redundant computation.
• Backtracking Algorithm: finds a solution by recursively exploring all possible solutions.
• Greedy Algorithm: makes the locally optimal choice at each step, hoping to find a global optimum.

### Time Complexity

• Measures the amount of time an algorithm takes to complete.
• Big O Notation: represents the upper bound on the number of steps an algorithm takes.
• Omega Notation: represents the lower bound on the number of steps an algorithm takes.
• Theta Notation: represents the exact bound on the number of steps an algorithm takes.

### Space Complexity

• Measures the amount of memory an algorithm uses.
• Auxiliary Space Complexity: measures the amount of extra memory used by an algorithm.

#### Algorithm Design Techniques

• Divide and Conquer: breaks down a problem into smaller subproblems and solves each subproblem recursively.
• Dynamic Programming: breaks down a complex problem into smaller subproblems, solves each subproblem only once, and stores the solutions to subproblems to avoid redundant computation.
• Greedy Method: makes the locally optimal choice at each step, hoping to find a global optimum.

### Sorting Algorithms

• Bubble Sort: compares adjacent elements and swaps them if they are in the wrong order.
• Selection Sort: selects the smallest element from the unsorted portion of the array and swaps it with the first element.
• Merge Sort: divides the array into smaller subarrays and merges them in sorted order.

### Searching Algorithms

• Linear Search: checks each element of the array in sequence until a match is found.
• Binary Search: searches for an element in a sorted array by repeatedly dividing the search interval in half.

#### Algorithm Applications

• Cryptography: uses algorithms to secure data and ensure confidentiality.
• Data Compression: uses algorithms to reduce the size of data.
• Machine Learning: uses algorithms to make predictions and classify data.
• Network Flow: uses algorithms to optimize the flow of data through a network.

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## Description

Learn about the definition of algorithms, and types of algorithms including recursive, dynamic programming, and backtracking algorithms.

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