Algorithms

Write an algorithm to add two numbers \( a \), \( b\) and \( c\).

Solution.

This algorithm will have three parts. The input, the process for addition, and the output. Here, there are two inputs \( a\) and \( b\). Below is the algorithm.

Step 1 - Place \( a \), \( b\) and \( c\) on top of each other according to their place values forming columns.

Step 2 - Add the numbers from the right taking note of their place values.

Step 3 - If you add the numbers in the right column and the number exceeds \( 9\), carry over the tens unit of the number to the next column.

Step 4 - Write the sum of the numbers.

This algorithm is correct because it satisfies the properties of an algorithm. It has an input and output, it has a finite number of steps, each step of the algorithm is complete and easy to understand and the algorithm is able to perform the task that it is written for.

Write an algorithm to find out if a number is an odd number.

Solution.

Step 1 - Divide the number by \( 2\)

Step 2 - If after division there is a remainder, then the number is odd. Otherwise, it is not.

This algorithm is clear and complete. It has a finite number of steps and can give the desired result. It posses the properties of a good algorithm

Write an algorithm to calculate the area of a triangle.

Solution.

When calculating the area of a triangle, you consider the base and the height. Having this in mind, let's write the algorithm.

Step 1 - Note the value of the base \( b\) of the triangle.

Step 2 - Note the value of the height \( h\) of the triangle.

Step 3 - Multiply the value for the base and height of the triangle (\( b \cdot h \)).

Step 4 - Divide the result from the multiplication by \( 2\) to get the area \( \left( \frac {b \cdot h} {2} \right) \).

The algorithm above is a good one. You can identify the inputs as \(b\) and \(h\), and the output as the area of the triangle. It has a finite number of steps and each step is complete and precise. The algorithm can do what its meant to do.

Which of these is the correct algorithm for finding the perimeter of the shape below.

Fig. 1. Polygon with irregular sides.

1. Step 1 - Add \( a\) and \( b\).

Step 2 - Add \( c\), \( d\) and \( e\) .

Step 3 - The sum is the perimeter.

B. Step 1 - Count the number of sides of the shape.

Step 2 - Add.

Step 3 - The sum is the perimeter.

C. Step 1 - Note the value of the sides of the shape - \( a\), \( b\), \( c\), \( d\) and \( e\).

Step 2 - Add the values \( a\), \( b\), \( c\), \( d\) and \( e\) to get the perimeter.

D. Step 1 - Note the value of the sides of the shape - \( a\), \( b\), \( c\), \( d\) and \( e\).

Step 2 - Add the values \( a\), \( b\), \( c\), \( d\) and \( e\).

Step 3 - Divide the sum by \( 5\) to get the perimeter.

Solution

The answer is option C. All other options do not possess the properties of an algorithm. They are ineffective and ambiguous.

Here's why the other options are wrong.

Option A is not effective. Following those steps will not give you the perimeter of the shape.

Option B is ineffective and ambiguous. You will not get the perimeter following the steps and the second step has no meaning.

Option D is a wrong algorithm. Its Step 3 says to divide by 5. You do not get the perimeter of a shape by dividing by anything. It is ineffective.

A friend has given you the following algorithm to look over. Explain why or why not this is an algorithm.

The Algorithm

Step 1 - Pick it up.

Step 2 - Walk to the bin.

Step 3 - Throw it away.

Solution

You should first examine each step of the algorithm to see what is wrong and what is write.

Step 1 says to ''pick it up''. What exactly should be picked up? It doesn't say what to pick up or where to pick it up from. There is no clarity and it doesn't make much sense. This goes against the definiteness property of an algorithm.

Step 2 says to ''walk to the bin''. It is an instruction to take an action. It makes sense on its own but because you do not know what step 1 is communicating, step 2 won't make as much sense as it should. This also goes against the definiteness property of an algorithm.

Step 3 says to ''Throw it away''. Again, throw what away? We do not know what we are to throw away. So this goes against the definiteness property of an algorithm.

The problem with this algorithm is that it doesn't have a clear meaning. It is incomplete and not easy to understand. That means you can go ahead to let your friend know that this is not an algorithm.

Which of the following is the correct sequence for an algorithm for brushing your teeth.

1. Brush your teeth.
2. Open your mouth.
3. Open the toothpaste.
4. Put tooth paste on the toothbrush.
5. Rinse your mouth with water.

1. 4, 3, 1, 2, 5
2. 3, 2, 1, 4, 5
3. 4, 2, 5, 1, 3
4. 3, 4, 2, 1, 5

Solution

The correct option is D. It is the correct order of steps for brushing your teeth.

Write an algorithm to solve \( 2 + 5 \times 4 \).

Solution

To write the correct algorithm for this, you need to have know about BODMAS. (To know more about BODMAS, check out the article on Structure and Calculation)

The algorithm is as follows.

Step 1 - Multiply 5 and 4

Step 2 - Add the result from the previous step to 2 to get the answer.

This algorithm can give the result it is supposed to give, The steps are clear and complete and it has a finite number of steps. Hence, it is a good algorithm.