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An algorithm is a finite sequence of well-defined instructions aimed at solving a specific problem, expressed in various forms such as natural language, pseudocode, flowcharts, or programming code. Key properties of algorithms include finiteness, definiteness, input/output requirements, effectiveness, correctness, generality, and optimization. An example of an algorithm is provided for calculating the sum of two numbers and another for finding the GCD of two numbers using a specific iterative method.

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11 views2 pages

Ia 1 QB

An algorithm is a finite sequence of well-defined instructions aimed at solving a specific problem, expressed in various forms such as natural language, pseudocode, flowcharts, or programming code. Key properties of algorithms include finiteness, definiteness, input/output requirements, effectiveness, correctness, generality, and optimization. An example of an algorithm is provided for calculating the sum of two numbers and another for finding the GCD of two numbers using a specific iterative method.

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1. Define Algorithm? Explain the notion of an algorithm and list out its important properties.

Definition of an Algorithm

An algorithm is a finite sequence of well-defined instructions designed to perform a specific task or


solve a particular problem. These instructions are executed in a logical order to transform input into a
desired output. Algorithms are fundamental in computer science and mathematics, as they form the
backbone of programming and problem-solving.

Notion of an Algorithm

The notion of an algorithm revolves around step-by-step computation to achieve a goal. It can be
expressed in different forms, such as:

 Natural Language (human-readable steps)

 Pseudocode (structured description of logic)

 Flowcharts (graphical representation)

 Programming Code (implementation in languages like Python, C, etc.)

Algorithms must be precise, unambiguous, and effective, ensuring they solve a problem in a finite
amount of time.

Important Properties of an Algorithm

A well-defined algorithm must possess the following key properties:

1. Finiteness

o The algorithm must terminate after a finite number of steps. It should not run
indefinitely.

2. Definiteness (Unambiguity)

o Each step of the algorithm must be clear and precisely defined. There should be no
ambiguity in instructions.

3. Input

o An algorithm must take zero or more inputs from a well-defined domain.

4. Output

o It must produce at least one output, which is the result after execution.

5. Effectiveness

o Every step should be basic and executable within a finite amount of time, without
requiring infinite resources.
6. Correctness

o The algorithm must produce the correct result for all valid inputs.

7. Generality

o It should be applicable to a range of inputs, not just a specific case.

8. Optimization (Efficiency)

o A good algorithm should be optimized in terms of time complexity (speed) and space
complexity (memory usage).

Example of a Simple Algorithm

Algorithm to find the sum of two numbers:

1. Start

2. Take two numbers as input

3. Add the numbers

4. Display the result

5. Stop

2. Discuss various algorithms to calculate GCD of 2 numbers.

Algorithm GCD(a, b)

1. While b ≠ 0 do:
2. a ← a mod b
3. Swap a and b
4. Return a as the GCD

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