"A short and knowledgeable concept about Algorithm "
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This document discusses algorithms and their properties. It defines an algorithm as a finite set of well-defined instructions to solve a problem. There are five criteria for writing algorithms: they must have inputs and outputs, be definite, finite, and effective. Algorithms use notation like step numbers, comments, and termination statements. Common algorithm types are dynamic programming, greedy, brute force, and divide and conquer. An example algorithm calculates the average of four numbers by reading inputs, computing the sum, calculating the average, and writing the output. Key patterns in algorithms are sequences, decisions, and repetitions.
![Solution
Algorithm: Average of four numbers.
Step 1: [Read the value of four numbers]
Read num1, num2, num3, num4
Step 2: [Compute the sum of numbers]
sum=num1+num2+num3+num4
Step 3: [Compute average]
average=sum/4
Step 4: [Print the value of average]
Write average
Step 5: [End of algorithm]
END/STOP](https://image.slidesharecdn.com/algorithm-180908092619/85/A-short-and-knowledgeable-concept-about-Algorithm-7-320.jpg)
"A short and knowledgeable concept about Algorithm "
- 1. ALGORITHM Dr. Chandan Kumar Assistant Professor, Computer Science & Engineering Department Invertis University, Bareilly
- 2. Definition An algorithm is an effective manner for solving a problem using finite set of instructions. Algorithms are used for calculation, data processing and automated reasoning. Each algorithm is a list of well defined instructions for computing a task starting from an initial step, the instruction describe a computation that process through a well defined series of successive steps, termination in a final step.
- 3. Criteria of algorithm There are five important criteria of writing algorithm. Input- It may accept Zero (0) or more inputs. Output- It should produce at least one output. Definiteness- Each instruction must be clear, well defined and precise. Finiteness- It should be a sequence of finite instructions. Effectiveness- This means that the operation must be simple and carried out in a finite time at one or more levels of complexity.
- 4. Notation for Algorithm Name of the algorithm- It specify the problem to be solved. Step number- Identification tag of an instruction and it is an unsigned positive number. Comment- It follows the step number and describes the operation. It should be written within a pair of square brackets. It is optional. Termination- It specifies end of algorithm. It is generally a STOP statement and the last instruction in the algorithm.
- 5. Types of Algorithms Dynamic Programming Algorithm- This algorithm remembers older results and attempts to use this to speed the process of finding new results. Greedy Algorithm- This algorithm attempts not only to find a solution but to find the ideal solution to any given problem. Brute Force Algorithm- This approach starts at some random point and iterates through every possibility until it finds the solution. Divide and Conquer Algorithm- This algorithm is similar to a branch and bound algorithm but the difference is to uses the back tracking method.
- 6. Problem statement Find the average of four numbers. Solution: To solve this problem you need to follow these steps: Identify the inputs and outputs. Identify any other data and constants required to solve the problem. Identify what needs to be computed Write an algorithm to depict the logic.
- 7. Solution Algorithm: Average of four numbers. Step 1: [Read the value of four numbers] Read num1, num2, num3, num4 Step 2: [Compute the sum of numbers] sum=num1+num2+num3+num4 Step 3: [Compute average] average=sum/4 Step 4: [Print the value of average] Write average Step 5: [End of algorithm] END/STOP
- 8. Let us analyse this algorithm Read” and “Write” are input and output operations. Num1, num2, num3 and num4 are the input to the algorithm. Average is the output of the algorithm. Other than inputs and outputs, ‘sum’ and constant ‘4’ are also used.
- 10. Patterns in Algorithms Computer scientists have defined three constructs for a structured program or algorithm. The idea is that a program must be made of a combination of only these three constructs: sequence decision (selection) repetition It has been proven there is no need for any other constructs. Using only these constructs makes a program or an algorithm easy to understand, debug or change.
- 11. Patterns in Algorithms Sequence: The first construct is called the sequence. An algorithm, and eventually a program, is a sequence of instructions, which can be a simple instruction or either of the other two constructs. Decision: Some problems cannot be solved with only a sequence of simple instructions. Sometimes we need to test a condition. If the result of testing is true, we follow a sequence of instructions: if it is false, we follow a different sequence of instructions. This is called the decision (selection) construct.
- 12. Patterns in Algorithms Repetition: In some problems, the same sequence of instructions must be repeated. We handle this with the repetition or loop construct. Finding the largest integer among a set of integers can use a construct of this kind.
- 13. Algorithm