Q.Program 6-9: Program to print the multiples of 10 for numbers in a given range.

Iteration With Condition

Imagine you're searching for a lost key in a dark room. You don't know how many steps you'll need — you just keep moving your hand along the floor until you feel the metal. You're repeating the same action (searching), but you stop only when a specific condition is met (you touch the key).

That's iteration with a condition. It's the idea of repeating a process not a fixed number of times, but while something remains true, or until something becomes true.

The Intuition

Most everyday loops are conditional. You don't say "I will stir the tea exactly 47 times." You say "I will stir the tea until the sugar dissolves." The number of stirs depends on when the condition (sugar dissolved) is satisfied.

In programming and mathematics, this is far more natural than a fixed-count loop. You often don't know in advance how many repetitions you'll need — you only know the rule that should keep you going, or the rule that should stop you.

The Precise Statement

An iteration with condition is a control structure that repeatedly executes a block of statements as long as a given Boolean condition evaluates to true. The condition is checked before (or after) each execution of the block.

The two standard forms are:

1. While loop (entry-controlled)

while (condition):
    statement(s)

The condition is tested first. If it's true, the block runs; then the condition is tested again. If it's false from the start, the block never runs.

2. Do-while loop (exit-controlled)

do:
    statement(s)
while (condition)

The block runs once unconditionally, then the condition is tested. If true, it repeats; if false, it stops. This guarantees at least one execution.

A Concrete Example

Suppose you want to find the smallest power of 2 greater than 1000. You don't know the answer in advance — you need to keep doubling until you cross the threshold.

n = 1
while (n <= 1000):
    n = n * 2

Trace it:

• Start: n = 1. Is 1 <= 1000? Yes → n = 2
• n = 2. Is 2 <= 1000? Yes → n = 4 …