Podcast
Questions and Answers
Which of the following represents the fundamental relationship in program design?
Which of the following represents the fundamental relationship in program design?
- Program = Algorithm - Data Structure
- Data Structure = Program + Algorithm
- Program = Algorithm + Data Structure (correct)
- Algorithm = Program + Data Structure
Why is it important to analyze algorithms based on time and space complexity?
Why is it important to analyze algorithms based on time and space complexity?
- To know which algorithm is more efficient under given constraints. (correct)
- To decide the order in which to write code.
- To determine which programming language to use.
- To ensure the algorithm is written in natural language.
What is the primary difference between an algorithm and a program regarding the phase in which they are required?
What is the primary difference between an algorithm and a program regarding the phase in which they are required?
- An algorithm is required during the testing phase, while a program is required during the design phase.
- A program is needed for design, while an algorithm is for maintenance.
- An algorithm is required during the implementation phase, while a program is required during the design phase.
- An algorithm is required during the design phase, while a program is required during the implementation phase. (correct)
In the context of algorithm development, why is domain knowledge considered important for the person writing the algorithm?
In the context of algorithm development, why is domain knowledge considered important for the person writing the algorithm?
Which of the following is NOT considered a rule for constructing an algorithm?
Which of the following is NOT considered a rule for constructing an algorithm?
Which of the following is NOT a way to represent an algorithm?
Which of the following is NOT a way to represent an algorithm?
Which statement accurately describes the relationship between time complexity and computational complexity?
Which statement accurately describes the relationship between time complexity and computational complexity?
What does Big O notation primarily describe?
What does Big O notation primarily describe?
If $f(n) = O(g(n))$, what does this imply about the growth rate of $f(n)$ compared to $g(n)$?
If $f(n) = O(g(n))$, what does this imply about the growth rate of $f(n)$ compared to $g(n)$?
What does Theta notation, denoted as $(g(n))$, describe about a function $f(n)$?
What does Theta notation, denoted as $(g(n))$, describe about a function $f(n)$?
If $f(n) = (g(n))$, what can be said about the relationship between $f(n)$ and $g(n)$?
If $f(n) = (g(n))$, what can be said about the relationship between $f(n)$ and $g(n)$?
What does Big Omega notation, denoted as $(g(n))$, primarily indicate about a function $f(n)$?
What does Big Omega notation, denoted as $(g(n))$, primarily indicate about a function $f(n)$?
What are the two key measures used in the performance analysis of an algorithm?
What are the two key measures used in the performance analysis of an algorithm?
What is the term for the memory space required by an algorithm during its execution?
What is the term for the memory space required by an algorithm during its execution?
What is the aim of the 'Divide and Conquer' approach in algorithm design?
What is the aim of the 'Divide and Conquer' approach in algorithm design?
Flashcards
What is a Program?
What is a Program?
Program = Algorithm + Data Structure, provides shorter path solutions to problems.
What is an Algorithm?
What is an Algorithm?
A set of steps or instructions to solve a problem or accomplish a task.
Algorithm vs. Program
Algorithm vs. Program
Algorithms are required to design a better program and are written before programs.
Algorithm vs. Program - Testing
Algorithm vs. Program - Testing
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Algorithm Construction Rules?
Algorithm Construction Rules?
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Ways to represent an algorithm?
Ways to represent an algorithm?
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Algorithm Analysis Factors?
Algorithm Analysis Factors?
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Big O Notation?
Big O Notation?
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Theta Notation?
Theta Notation?
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Omega Notation?
Omega Notation?
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Space Complexity?
Space Complexity?
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Time Complexity?
Time Complexity?
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Constant Space Complexity
Constant Space Complexity
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Linear Space Complexity?
Linear Space Complexity?
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Divide and Conquer?
Divide and Conquer?
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Study Notes
- Program = Algorithm + Data Structure, programs use algorithms
- Many real-life problems and daily tasks involve algorithms such as preparing for an exam or a meal
- To choose the optimal algorithm, analyze each algorithm based on factors, including time and space complexity
Algorithm Definition
- An algorithm is a set of steps to accomplish a task
- Formally, it is a finite sequence of instructions to solve a computational problem
- Algorithms should be written before programs
Algorithm vs Program
| Algorithm | Program |
|---|---|
| Required at the design phase | Required at the implementation phase |
| Requires domain knowledge | Implementation requires the use of appropriate data structures |
| Written in natural language like English | Written in a programming language |
| Algorithm is analysed | Program is tested |
Algorithm Construction Rules
- Input necessary
- Output needed
- Definiteness required
- Finiteness present
- Effectiveness
- Use Comment session
Algorithm Representation
- Natural Language
- Programming language
- Flowchart
- Pseudocode
Computational Complexity
- Computational Complexity includes time complexity and space complexity
- Space complexity considers the Turing machines of Turing
Theorem and Sorting Algorithms
- Theorem 1.1
- Sorting algorithms include selection sort, exchange sort, and insertion sort
Big O Notation
- Deals with two differentiable functions, f(n) and g(n)
- Defines asymptotic upper bound for the growth rate of algorithms
f(n) ≤ C * g(n)forn ≥ n0, whereC > 0andn0 ≥ 1- Showing that
f(n) = O(g(n)) g(n)is an asymptotic upper bound forf(n)
Big Theta Notation
- Given two differentiable functions, f(n) and g(n)
- Both functions have the same growth rate
- Expressed formally as
f(n) = Θ(g(n)) - Holds when
C1 * g(n) ≤ f(n) ≤ C2 * g(n)andC1, C2 > 0
Big Omega Notation
- Given differentiable functions f(n) and g(n)
- f(n) grows at the rate faster than g(n)
- Represented as: f(n) ≥ C * g(n), where n ≥ n0, C > 0, n0 ≥ 1
- Denoted as: f(n) = Ω(g(n))
- Formula to calculate time complexity with the big omega notation: f(n) = Ω(g(n))
Performance Analysis
- Measured in terms of space complexity and time complexity
- Time complexity is how much time it takes to complete a program
- Space complexity refers to the amount of memory space required by an algorithm during its execution
- An efficient algorithm executes quickly and consumes less memory
Space Complexity
- Space complexity is how much memory space is needed by an algorithm
- Includes instruction space, data space, and environment space
- Instruction space depends on the number of lines of code
- Data space is for storing constants and variables
- Environment space is for storing environment information needed to resume suspended functions
- Space complexity calculations include two types of programs: Constant and Linear
Constant Space Complexity
- Fixed space is used
- Example usage contains one variable, and only 1 Input.
- The algorithm requires a fixed amount of space for all input values
Linear Space Complexity
- Space used varies, usually on one variable
- Calculated by (n + 3) words
Memory Purposes:
- To store program instructions
- To store constant values
- To store variable values
- Function calls + jumping statements
Auxiliary Space
- The temporary space allocated by the algorithm (excludes the input size)
- Problem solving is done with respect to input size
- Space complexity includes auxiliary space + the space used by the input
- Formula for overall space complexity: input size + auxiliary space
Time Complexity
- Is total amount of time required by an algorithm to complete its execution
- Constant time complexity is when a program requires a fixed amount of time for all input values
- Linear time complexity is when the time complexity increases with input values
Divide and Conquer
- Step 1: Divide problems into smaller parts
- Step 2: Solve the parts independently
- Step 3: Combine these solutions to get the overall solution
Divide and Conquer Ideas
- Divide array into two halves and recursively solve left and right halves
- Merge the two halves
- This technique represents a merge sort
- Partition array into small items and large items, recursively sort the two sets, representing a quick sort
Divide and Conquer Examples
- Searching uses Binary search
- Includes Sorting e.g Merge sort, and Quick sort
- Tree Transversal
- Does Matrix Multiplication
- Strassen's algorithm
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