Loops and common algorithms

while and for loops

while repeats a block while its condition is true. The condition is checked before each iteration, so the body may never run. You must ensure a state change that leads to termination. If a counter is not incremented, the condition may remain true forever.

for iterates over the elements of a sequence. For an integer range, use range(start, stop, step). The stop endpoint is excluded. The step cannot be zero. range(5) specifies 0, 1, 2, 3, 4, while range(5, 0, -2) specifies 5, 3, 1. The range object itself does not create a list of all these numbers in memory.

total = 0
for number in range(1, 6):
    total += number
print("Sum:", total)

number = 5
while number > 0:
    print(number, end=" ")
    number -= 2
print()

The output is Sum: 15 and the line 5 3 1. Notice the final print(): it ends the line after several calls with end=" ". A nested loop completes an entire inner pass for each iteration of the outer loop.

break, continue, and loop else

break ends the nearest loop, while continue moves to the next iteration. In a while loop, you often need to update the counter before continue; otherwise, the program will repeat the same check. In a for loop, the loop itself retrieves the next element.

A loop's else block runs after a for loop normally exhausts its elements or a while condition becomes false. It is skipped after break. This does not mean “the loop ran at least once”: else also runs for an empty range. Exiting through an exception or return does not run this block either. Figure 2.6 shows an ordinary for loop.

Figure 2.6. Execution paths through a loop, continue, break, and else

Example. Guess the number

The computer chooses an integer from 1 to 20. The user has five attempts; an invalid format or an out-of-range number does not use an attempt. For automated checking, you can replace the selection below with secret = 7.

import random

secret = random.randint(1, 20)
attempts = 0
while attempts < 5:
    text = input("Number 1..20: ").strip()
    if not (1 <= len(text) <= 2 and text.isascii()
            and text.isdecimal()):
        print("Enter one or two digits")
        continue
    guess = int(text)
    if not 1 <= guess <= 20:
        print("Number out of range")
        continue
    attempts += 1
    if guess == secret:
        print(f"Guessed on attempt {attempts}")
        break
    print("Higher" if guess < secret else "Lower")
else:
    print(f"No attempts left. Number: {secret}")

For the reference secret 7 and inputs 5, 10, 7, the messages are Higher, Lower, and Guessed on attempt 3. Five unsuccessful valid attempts execute else. During a normal game, the specific number and sequence of hints may differ.

Common loop algorithms

An accumulator starts with an identity element: 0 for a sum, 1 for a product. A counter increases only when the required condition holds. A flag stores a yes/no answer, such as whether a violation was found. Variable names should reflect these roles.

Do not initialize a minimum to zero without justification: all entered numbers may be positive. Use the first value or None. The complete example below reads three correctly formatted integers without storing the entire series in a collection.

minimum = None
total = 0
positive_count = 0
for index in range(3):
    value = int(input(f"Number {index + 1}: "))
    total += value
    if minimum is None or value < minimum:
        minimum = value
    if value > 0:
        positive_count += 1
print("Minimum:", minimum)
print("Mean:", total / 3)
print("Positive:", positive_count)

For 4, -2, 7, the minimum is -2, the mean is 3.0, and there are two positive numbers. In the minimum check, short-circuit evaluation of or prevents comparing a number with None on the first iteration.

Euclid's algorithm

For nonnegative integers a and b, the GCD does not change when the pair is replaced with b and a % b. The second component decreases until it reaches zero. Multiple assignment first evaluates the right side using the old values, then binds the names to the new ones.

a = 84
b = 30
while b != 0:
    a, b = b, a % b
print("GCD:", a)

The output is GCD: 6. The sequence of pairs is (84, 30), (30, 24), (24, 6), (6, 0). For negative inputs, first take abs. If the LCM is needed, for nonzero numbers it is convenient to calculate abs(a // gcd * b). Handle the zero case separately before division.

Prime numbers and nested loops

A prime number is an integer greater than 1 with exactly two positive divisors. The number 1 is not prime. To test a number n, it is enough to look for a divisor up to and including its square root: a larger divisor would have a smaller paired divisor. math.isqrt(n) returns the exact integer square root for a nonnegative integer, avoiding float errors.

In nested loops, break exits only the inner loop. This lets you stop checking one composite number while continuing to iterate over the entire range. A complete example is given in the lab. Control flow description: https://docs.python.org/3.14/tutorial/controlflow.html.

Checking a program and common mistakes

Checking means comparing the actual result with the expected one. Process finished with exit code 0 means normal termination, but does not prove that a formula is correct. For each branch, choose an example that executes it. For a loop, test zero, one, and several iterations, as well as exiting through break and completing with else.

In PyCharm, Ctrl+Alt+L formats code. Inspections highlight suspicious code and style violations; Alt+Enter opens suggested actions. Do not apply fixes mechanically: read which construct they change. An inspection does not replace running the program with data.

Screenshot

Editor: MyVar=5 and if MyVar==1 : followed by an indented print. Show inspection tooltip and Problems.

Figure 2.7. Spacing and naming suggestions in PyCharm

Table 2.2. Errors and ways to check them

Problem	How to fix it
Getting 55 instead of 10	Convert the result of input to a number before adding
A branch never runs	Check the order of thresholds and the difference between if and elif
A loop does not terminate	Check that the counter changes before continue
The last number is missing	Account for the exclusive endpoint of range
Incorrect minimum	Initialize with the first value or None
Equal numbers give False	Distinguish is, ==, and approximate comparison
Indentation error	Four spaces, with statements in a block at the same level

Before the defense, make an “input – expected – actual result” table. Check both sides of rate and grade boundaries, zero values, and impossible geometric data. Test random programs using a reference state or a fixed secret, then restore normal mode. Do not include random object addresses or machine-dependent identifiers in tests.