Problem Solving with Python 🐍

A public bus company in one district announces these fares:

• Ordinary passengers pay 10 baht each, for any distance.
• Children under 3 years old ride free.
• Elders aged 60 or over pay half price.
• A group of at most 30 people whose total fare is 200 baht or more gets a further 10% discount.

You want to take people from your village on a field trip. How would you design an algorithm to work out the bus fare?

To solve it, consider these sub-problems:

Putting the sub-problems in order gives this pseudocode (รหัสลำลอง):

1. all ← number of passengers
2. children ← number of children under 3
3. elders ← number of elders (aged 60 or over)
4. regular ← (all − children − elders)
5. fare_elders ← elders × (10/2)
6. fare_regular ← regular × 10
7. total ← fare_elders + fare_regular
8. show all, children, elders, regular
9. show total
10. if all <= 30 and total >= 200
    1. total_discounted ← total − (total × 0.1)
    2. show total_discounted

Step 10 needs two conditions to be true at the same time. That is exactly what the Boolean operator and in 2.2 is for. (One small slip in the book: sub-problem 1 says elders are “over 60”, but the fare rule and the pseudocode both use “60 or over”. We use 60 or over.)

Write a program that reads a set of positive whole numbers (you do not know in advance how many there will be), then finds their sum and the largest value.

Example 2.4 explained

1. Line 1 reads the first positive integer into x. The user types 0 when there is no more data. Because we only want positive numbers, 0 can be the signal that the data has run out.
2. Lines 2–4 set starting values for the variables that keep the sum (sum), the largest value (max) and the number of values (n).
3. Line 5 is the while statement. Its condition is that x must be a positive number.
4. Lines 6–10 are the block inside the loop: line 6 counts the values in n, line 7 adds to sum, lines 8–9 keep the largest value so far, and line 10 reads the next value.
5. Lines 11–12: if at least one value was entered, print the results.

Teacher’s note: the book names two variables sum and max. That works, but those are also Python’s built-in sum() and max() functions, which you then can’t use in that program. In your own code, names like total and biggest are safer.

Write a Python program that tells a passenger the bus fare. The normal fare is 6.50 baht, elders pay half, and children no more than 3 years old ride free.

Example 2.5 explained

1. Line 1 stores the fare 6.50 in fare.
2. Line 2 reads the age into age.
3. Line 3 checks the condition: if the age is 60 or over, the fare is halved and stored in fare, so it becomes fare/2 baht.
4. Line 5 is the case of someone under 60 who is no more than 3 years old. elif creates this choice.
5. Line 7 covers every other case: an ordinary passenger. if-elif-else keeps the program short and easy to check.

Write a Python program where the user chooses whether to find the area of a circle, a triangle or a rectangle.

Example 2.6 explained

1. Line 3 reads a letter from the user into shape, to say which shape’s area is wanted.
2. Lines 4, 7 and 11 compare that letter, to choose the circle, triangle or rectangle formula.

Try typing x as the shape: the program still asks for a width and length, because everything that is not c or t falls into else. Activity 2.1 asks you to fix that.

Watch line 1 being worked out, innermost function first. Type an age, then press Next.

Example 2.7 explained

1. Line 1 calls int() and input(), one inside the other. When functions are nested, Python works out the innermost one first. So input() is called first: Python passes it the string "Your age: ", and input() shows that on screen and waits. When the user types something and presses Enter, input() returns what was typed as a string. If the user types 20, then int(input("Your age: ")) becomes int('20').
2. Next Python works out int('20'): it sends '20' to int(), which converts the string to the integer 20 and returns it. So age=int(input("Your age: ")) becomes age=int('20'), which is age=20.
3. Line 8 calls print() with 2 values, the string "Your fare is" and the variable fare, and print() shows them in order.

Type this into a cell:

Result:

Hello Prawit

Example 2.8 explained

1. Line 1 creates a new function. The Python keyword def starts the definition. The function is named hello1 and has 1 parameter, the variable name, written inside the brackets after the name, then a colon : after the closing bracket. When the function is called, the statements inside it can use the value passed in through name.
2. Line 2 is the function’s block. It has only one statement, print('Hello', name), which prints Hello followed by the value of name.
3. Line 4 calls hello1() with the single string argument 'Prawit'. The statements of hello1() defined in lines 1–2 run, and the result is “Hello Prawit”.

The book’s program prints the Thai greeting สวัสดี (“sawasdee”) and the name ประวิทย์; we use English here.

In Example 2.9, lines 1–2 create a new function. After the keyword def comes the name hello2, with 2 parameters, the variables fname and lname, inside the brackets. The arguments are matched to the parameters in order: the first argument goes to fname, the second to lname.

The house-drawing program from Example 1.1 in Chapter 1 can be written with functions in Python. Type this in script mode, then run the program to check the result.

Example 2.10 explained

1. Line 1 loads the turtle module, so you can call its drawing functions.
2. Lines 3–8 create a function that draws a square, with 1 parameter, size, for the length of a side.
3. Lines 10–15 create a function that draws an equilateral triangle, with 1 parameter, size, for the length of a side.
4. Lines 17–22 create a function that draws a house, by calling the square function and the triangle function.
5. Lines 24–29 are the main program. Line 24 makes the pen look like a turtle, line 25 sets how thick the line is, line 26 sets how fast the turtle moves, line 27 calls the function that draws a house of size 50, line 28 hides the turtle when the drawing is finished, and line 29 keeps the drawing window open until the user clicks anywhere in it.

This program uses a function that takes the radius of a sphere and returns the sphere’s volume. Type it in script mode and run it to check.

Example 2.11 explained

1. Line 3 starts defining sphere_volume(), with 1 parameter, the sphere’s radius, stored in r.
2. Lines 4 and 5 are the function’s block. Line 4 calculates the volume into vol, and line 5 returns that volume to whichever program called the function.
3. From line 7 on is the main program, which calls sphere_volume(). Line 7 reads the radius typed by the user into radius.
4. Line 8 calls sphere_volume() with radius as its argument. When sphere_volume() finishes and returns a value, the string 'Volume is' and the returned value are passed as arguments to print().