ProgrammingIntroduction to ProgrammingHigh school

Control Flow

Conditionals and loops; tracing code by hand.

Control flow is the order in which a program's statements run. By default, statements run top to bottom. Conditionals (`if`, `else if`, `else`) choose between branches based on a Boolean test, and loops (`for`, `while`) repeat a block until a condition changes.

Tracing code by hand, keeping a table of each variable's value after every step, is the most reliable way to predict what a program does and to find bugs. Most loop bugs are off-by-one errors at the boundaries or conditions that never become false, which create infinite loops.

Key ideas

A `for` loop suits a known number of repetitions; a `while` loop suits repeat-until-done.
Check boundary cases: zero iterations, one iteration and the last iteration.
Combine conditions with and, or and not; watch operator precedence.
Nested loops multiply: an outer loop of $n$ with an inner loop of $m$ runs $nm$ times.

Worked example

What does this print? `total = 0; for i in 1..4: total = total + i * i; print(total)`

$i = 1$ : total $= 1$ .
$i = 2$ : total $= 1 + 4 = 5$ .
$i = 3$ : total $= 5 + 9 = 14$ .
$i = 4$ : total $= 14 + 16 = 30$ , which is printed.

Answer: $30$

Common mistakes

Off-by-one errors: using `<` where `<=` is needed or starting at 1 instead of 0.
Forgetting to update the loop variable in a `while` loop.
Using `=` (assignment) where `==` (comparison) is meant.

Practice questions

Try each one, then open the answer. Numerical answers on this page are verified by an automated calculation check.

1.How many times does a loop from $i = 0$ while $i < 10$ , step 2, run?
Show answer
$5$
2.A loop adds $i$ for $i = 1$ to $10$ . Final total?
Show answer
$55$
3.An outer loop runs 6 times and an inner loop 4 times per outer pass. How many inner executions?
Show answer
$24$

Key ideas

Worked example

Common mistakes

Practice questions

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