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Questions and Answers
What is the primary characteristic of a dynamic programming algorithm?
What type of algorithm solves a problem by breaking it down into smaller instances of the same problem?
What is the purpose of Big O Notation in algorithm analysis?
What is the name of the algorithm design technique that breaks down a problem into smaller subproblems and solves each subproblem recursively?
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What is the name of the sorting algorithm that compares adjacent elements and swaps them if they are in the wrong order?
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What is the application of algorithms in which they are used to secure data and ensure confidentiality?
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What type of algorithm makes the locally optimal choice at each step, hoping to find a global optimum?
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What is the type of complexity that measures the amount of memory an algorithm uses?
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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
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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.
Algorithm Analysis
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.
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.
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Description
Learn about the definition of algorithms, and types of algorithms including recursive, dynamic programming, and backtracking algorithms.
