Chapter 7.2. More Complex Loops – Exam Problems

We already learned how to execute a block of commands more than once using a for loop. In the previous chapter, we reviewed some loop structures that would help us solve more complex problems like:

• loops with a step
• nested loops
• while loops
• do-while loops
• infinite loops and breaking out of the loop (break operator)
• try-except construction

Exam Problems

Let's start work on solving the following practical exam problems.

Problem: Stupid Password Generator

Write a program that enters two integers n and l and generates in alphabetical order all possible "dumb” passwords", that consist of the following 5 characters:

• Character 1: digit from 1 to n.
• Character 2: digit from 1 to n.
• Character 3: small letter among the first l letters of the Latin alphabet.
• Character 4: small letter among the first l letters of the Latin alphabet.
• Character 5: digit from 1 to n, bigger than first 2 digits.

Input Data

The input is read from the console and consists of two integers: n and l within the range [1 … 9], one per line.

Output Data

Print on the console all "dumb" passwords in alphabetical order, separated by space.

Sample Input and Output

Hints and Guidelines

We can split the solution of the problem into 3 parts:

• Reading the input – in the current problem, this includes reading two numbers n and l, each on a separate line.
• Processing The Input Data – using nested loops to iterate through every possible symbol for each of the five password symbols.
• Printing the output – printing every "dumb" password that meets the requirements.

Reading and Processing The Input Data

For reading of input data, we will declare two integer variables int: n and l.

Printing Output

One of the ways to find a solution for this problem is to create five for nested loops, one for each variable. To ensure that the last digit is greater than the first two, we will use the built-in method max(…):

Do you know that…?

• For convenience we can use the ASCII value of the symbol "a" directly in the declarations of the loops - 97:

• If we are not sure about a given value of a symbol or we want to take the values of dynamically generated symbols, we can use the built-in function ord(char), which returns the integer representation of the character:

• Or the opposite, we can generate a character from a given integer, using a built-in function in Python chr(number):

• Python has a wide range of built-in functions and methods for working with strings. Look for more information on the following functions: str(number), .lower(), `.format(*args, kwargs)**, **.swapcase()**, **.upper()`**.

Testing in The Judge System

Test your solution here: https://judge.softuni.org/Contests/Practice/Index/1058#0.

Problem: Magic Numbers

Write a program that enters a single integer magic number and produces all possible 6-digit numbers for which the product of their digits is equal to the magical number.

Example: "Magic number" → 2

• 111112 → 1 * 1 * 1 * 1 * 1 * 2 = 2
• 111121 → 1 * 1 * 1 * 1 * 2 * 1 = 2
• 111211 → 1 * 1 * 1 * 2 * 1 * 1 = 2
• 112111 → 1 * 1 * 2 * 1 * 1 * 1 = 2
• 121111 → 1 * 2 * 1 * 1 * 1 * 1 = 2
• 211111 → 2 * 1 * 1 * 1 * 1 * 1 = 2

Input Data

The input is from the console and consists of one integer within the range [1 … 600 000].

Output Data

Print on the console all magic numbers, separated by space.

Sample Input and Output

Hints and Guidelines

The solution of this problem follows the same conception (we have to generate all n combinations of the element). Follow the steps and try to solve the problem on your own:

• Declare and initialize an integer type variable int and read the input from the console.
• Nest six for loops one for each digit.
• In the last loop, using an if statement checks if the product of the six digits is equal to the magic number.

Here is an example implementation of the idea:

In the previous chapter, we reviewed other loop constructions. Let's look at the sample solution of the same problem using the while loop. First, we need to store the input magical number in a suitable variable:

Then we will start writing while loops.

• We will initialize the first digit: a = 1.
• We will set a condition for each loop: the digit will be less than or equal to 9.
• At the beginning of each loop, we set a value of the next digit, in this case: b = 1. In the nested for loops, we initialize the variables in the inner loops at each increment of the outer ones. We want to do the same here.
• At the end of each loop, we will increase the digit by one: a += 1, b += 1, c += 1 etc.
• In the innermost loop, we will make the check and if necessary, we will print on the console.

As we can see, we can solve a problem using different types of loops. Of course, each task has its most appropriate choice. To practice each type of loop – try to solve each of the following problems with all the learned loops.

Testing in The Judge System

Test your solution here: https://judge.softuni.org/Contests/Practice/Index/1058#1.

Problem: Stop Number

Write a program that prints on the console all numbers from N to M, that are divisible by 2 and 3 without remainder, in reversed order. We will read one more "stop" number from the console – S. If any of the numbers divisible by 2 and 3 is equal to the stop number, it should not be printed and the program should end. Otherwise print all numbers up to N, that meet the condition.

Input Data

Read from the console 3 numbers, each on a single line:

• N - integer number: 0 ≤ N < M.
• M - integer number: N < M ≤ 10000.
• S - integer number: N ≤ S ≤ M.

Output Data

Print on the console on a single line all numbers, that meet the condition, separated by space.

Sample Input and Output

Hints and Guidelines

The problem can be divided into four logical parts:

• Reading the input from the console.
• Checking all numbers in the given range, and then running a loop.
• Checking the conditions of the problem according to every number in the given range.
• Printing the numbers.

The first part is ordinary - we read three integer numbers from the console

We have already seen examples of the second part – initialization of the for loop. It is a bit tricky - the explanation mentions that the numbers have to be printed in reversed order. This means that the initial value of the variable i will be bigger, and from the examples, we can see that it is M. Thus, the final value of i should be N. The fact that we will print the results in reversed order and the values of i suggest that the step would be decreased by 1:

After we have initialized the for loop, it is time for the third part of the problem - checking the condition if the given number is divisible both by 2 and 3 without remainder. We will do this using one simple if condition that we will leave to the reader to do by themselves.

Another tricky part of this problem is that apart from the above check we need to do another one – whether the number is equal to the "stop" number, entered from the console on the third line. To do this check, the previous one has to be passed. For this reason, we will add another if statement that we will nest in the previous one. If the condition is true, we need to stop the program from printing. We can do this using a break, operator, and it will lead us out of the for loop.

If the condition that checks whether the number is equal with the "stop" number returns a false, result, our program should continue to print. This covers the fourth and last part of our program.

Testing in The Judge System

Test your solution here: https://judge.softuni.org/Contests/Practice/Index/1058#2.

Problem: Special Numbers

Write a program that reads one integer number N and generates all possible "special numbers from 1111 to 9999. To be considered "special" a number must correspond to the following condition:

• N to be divisible by each of its digits without remainder.

Example: upon N = 16, 2418 is a special number:

• 16 / 2 = 8 without remainder
• 16 / 4 = 4 without remainder
• 16 / 1 = 16 without remainder
• 16 / 8 = 2 without remainder

Input Data

The input is read from the program and consists of one integer within the range [1 … 600 000].

Output Data

Print on the console all special numbers, separated by space.

Sample Input and Output

Hints and Guidelines

Solve the problem by yourself using what you learned from the previous two problems. Keep in mind the difference between operators for integer division // and division with remainder % in Python.

Testing in The Judge System

Test your solution here: https://judge.softuni.org/Contests/Practice/Index/1058#3.

Problem: Digits

Write a program that reads from the console 1 integer within the range [100 … 999], and then prints it a predefined number of times – modifying it before each print, as follows:

• If the number is divisible by 5 without remainder, subtract from it its first digit.
• If the number is divisible by 3 without remainder, subtract from it its second digit.
• If none of the above-mentioned conditions is valid, add to it its third digit.

Print on the console N lines, and each line has M numbers, that are the result of the above actions. Let:

• N = sum of the first and second digits of the number.
• M = sum of the first and third digits of the number.

Input Data

The input is read from the console and is an integer within the range [100 … 999].

Output Data

Print on the console all integer numbers, that is the result of the above-mentioned calculations in the respective number of rows and columns as in the examples.

Sample Input and Output

Hints and Guidelines

Solve the problem by yourself, using what you learned from the previous ones. Remember that you will need to define different variables for each digit of the input number.

Testing in The Judge System

Test your solution here: https://judge.softuni.org/Contests/Practice/Index/1058#4.