Algorithms

What is an algorithm

• It is the step by step solution to the given problem.
• It is clear and specific, include all steps and has correct order.
• The algorithm can be expressed in plain spoken language and/or series of calculations, or charts such as flow charts.
• Sometimes there are different solutions or algorithms to solve the same problems.
• Some algorithms are faster and more efficient than others.
• There are many ways to solve the same problem.

Example-1

List all even numbers from 1 to 1000 2, 4, 6, 8, 10, 12....998, 1000

          
         assign 0 to x.      (x = 0)  
         for number i = 1 to 500   (i = 500)  
          increase x by 2        	(x = 1000)  
          Display x 
          next i 
     
     

Example-2

Find the maximum number in the following list: 1, 3, 5, 6, 2, 8, 9, 10, 11, 2, 4

          
         maxNumber = The first number
         for every number in the list
	         if the number is greater than maxNumber 
		        assign number to the maxNumber
         next number
         print maxNumber
      
     

Example-3

Find all even numbers in the following list: 1, 3, 5, 6, 2, 8, 9, 10, 11, 2, 4

           
         for every number in the list
             divide the number by 2 
             get the remainder of the division 
             if the remainder = 0
	            the number is even, print it 
             else
	            the number is odd, do nothing
         next number
     
     

Algorithm in computer terms

• An algorithm is a step-by-step process producing a solution for a problem which can be translated into computer code.
• There are four main components of an algorithm: data acquisition, sequence, selection and iteration.
• Writing an algorithm to solve a simple problem may not require all these components.
• An algorithm is usually written in plain (simple) human language, and then translated to a high-level programming language such as Python.

Example-4

• Assume that you are required to develop an algorithm to draw the shape as below.
• 
• How can you apply computational thinking to this problem?
• Develop the solution/algorithm, and later use a computer language called Python to draw this shape.

Solution

• If you divide the shape into four parts, examining each part carefully, you will notice that the shape is made up of squares.
• Each square is rotated slightly by a small angle.
• This process of discovery is called decomposition.
• If you draw one square, then change the angle slightly, draw the next square, and repeat this multiple times, you will get the shape.
• 
• There are other lines in this shape that are created by having many squares drawn at different angles.
• If you spend too much time at this stage trying to understand how they have been created, you might get confused.
• Focusing on the big picture and finding the most important part of the problem is called abstraction.
• The next step is writing the solution step-by-step using simple language. This is called algorithm.

         from 1 to the number of boxes 
	          draw a box
	          change drawing angle by 5 degrees 
         next box