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Questions and Answers
What is a set of instructions to solve a specific problem or perform a particular task?
What is a set of instructions to solve a specific problem or perform a particular task?
Which characteristic of algorithms ensures that they terminate after a finite number of steps?
Which characteristic of algorithms ensures that they terminate after a finite number of steps?
Which type of algorithm solves a problem by breaking it down into smaller instances of the same problem?
Which type of algorithm solves a problem by breaking it down into smaller instances of the same problem?
What is the main goal of the Greedy Method in algorithm design?
What is the main goal of the Greedy Method in algorithm design?
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What is the term for the amount of time an algorithm takes to complete?
What is the term for the amount of time an algorithm takes to complete?
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What is the main difference between Divide and Conquer and Dynamic Programming techniques?
What is the main difference between Divide and Conquer and Dynamic Programming techniques?
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What is the term for the amount of memory an algorithm uses?
What is the term for the amount of memory an algorithm uses?
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What is often a trade-off in algorithm design?
What is often a trade-off in algorithm design?
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Study Notes
Algorithms
Definition
- A set of instructions to solve a specific problem or perform a particular task
- A well-defined procedure that takes some input and produces a corresponding output
Characteristics
- Finiteness: Algorithms must terminate after a finite number of steps
- Definiteness: Each step of the algorithm must be precisely defined
- Effectiveness: The algorithm must be capable of being performed exactly and in a finite amount of time
- Generality: The algorithm should be applicable to a wide range of inputs
Types of Algorithms
- Recursive algorithms: Solve a problem by breaking it down into smaller instances of the same problem
- Dynamic programming algorithms: Break down a problem into smaller sub-problems and solve each only once
- Greedy algorithms: Make the locally optimal choice at each step, hoping to find a global optimum
- Backtracking algorithms: Explore all possible solutions and backtrack when a dead end is reached
Algorithm Design Techniques
- Divide and Conquer: Divide the problem into smaller sub-problems, solve each, and combine the solutions
- Dynamic Programming: Break down the problem into smaller sub-problems, solve each, and store the solutions
- Greedy Method: Make the locally optimal choice at each step
- Brute Force: Try all possible solutions and select the best one
Algorithm Analysis
- Time complexity: The amount of time an algorithm takes to complete, usually measured in Big O notation
- Space complexity: The amount of memory an algorithm uses, usually measured in Big O notation
- Trade-offs: Often, there is a trade-off between time and space complexity in algorithm design
Algorithms
Definition and Characteristics
- An algorithm is a set of instructions to solve a specific problem or perform a particular task, with a well-defined procedure that takes input and produces output
- Algorithms have four main characteristics:
- Finiteness: They must terminate after a finite number of steps
- Definiteness: Each step is precisely defined
- Effectiveness: They can be performed exactly and in a finite amount of time
- Generality: They are applicable to a wide range of inputs
Algorithm Classification
Recursive Algorithms
- Solve a problem by breaking it down into smaller instances of the same problem
Dynamic Programming Algorithms
- Break down a problem into smaller sub-problems and solve each only once
Greedy Algorithms
- Make the locally optimal choice at each step, hoping to find a global optimum
Backtracking Algorithms
- Explore all possible solutions and backtrack when a dead end is reached
Algorithm Design Techniques
Divide and Conquer
- Divide the problem into smaller sub-problems, solve each, and combine the solutions
Dynamic Programming
- Break down the problem into smaller sub-problems, solve each, and store the solutions
Greedy Method
- Make the locally optimal choice at each step
Brute Force
- Try all possible solutions and select the best one
Algorithm Analysis
Time and Space Complexity
- Time complexity: The amount of time an algorithm takes to complete, usually measured in Big O notation
- Space complexity: The amount of memory an algorithm uses, usually measured in Big O notation
Trade-offs
- Often, there is a trade-off between time and space complexity in algorithm design
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Description
Learn about the definition and characteristics of algorithms, including finiteness, definiteness, effectiveness, and generality.
