8.4. Looping When We Don’t Know When We’ll Stop

While loops are typically used when you don’t know how many times the loop needs to repeat. The body of the loop will repeat while the condition is true. The logical expression will be evaluated just before the body of the loop is repeated.

Let’s say that we want to find the square root of a number. For some square roots, you’re never going to be exact. Let’s say that we want to find a square root that, when multiplied by itself, is within 0.01 of the square we want. How do we do it? There’s a really old process that we can apply here.

1. Start by guessing 2.

2. Compute the guess squared.

3. Is the guess squared close to the target number? If it’s within 0.01, we’re done. We’ll take the absolute value of the difference, in case we overshoot. (In Python, abs is the absolute value function.)

4. If it’s not close enough, we divide the target number by our guess, then average that value with our guess.

5. That’s our new guess. Square it, and go back to Step #3.

Here’s a program that does exactly that. Try different target values, and see how good it is at computing square roots.

target = 6 guess = 2 guessSquared = guess * guess while abs(target-guessSquared) > 0.01: closer = target / guess guess = (guess + closer) / 2.0 guessSquared = guess * guess print("Square root of", target,"is", guess)

What would happen if we didn’t compute guessSquared before the while loop?

• No error, since we compute it inside the loop.
• We have to compute it before, or abs(target-guessSquared) > 0.01 would be an error.
• We would get an error.
• A variable has to be declared (created) before it is used.
• We need the one before the while loop, but not the one afterward.
• We need both. The one before sets up the test. The one inside the loop lets us update guessSquared.

Let’s say that you wanted to figure out the square root of 6. How many times would the body of the while loop be executed? We could figure it out by tracing the program.

How many times do we execute the test abs(target-guessSquared) > 0.01 when target = 6 (in the video)?

• Just once.
• The first time we do the test, guess is 2, and 2 * 2 is 4, and 6 - 4 is 2 which is greater than 0.01.
• Twice.
• The second time we do the test, guess is 2.5 (average of 3 and 2). But, 2.5 * 2.5 = 6.25 which is still more than 0.01 away from 6.
• Three times.
• The third time we do the test, guess is 2.45 which is 6.0025 when squared. This is less than 0.01 away from 6. So test executes 3 times.
• Four times
• We don't get to a fourth time. Guess is 2, then 2.5, then 2.45 at which point the test fails and and the loop stops.

How about the square root of 25? How about 2,356? It’s difficult to know ahead of time how many times the loop will execute. That’s where the while loop really shines, when you can specify an end condition (or rather, a continue condition).

What are the values of var1 and var2 that are printed when the following code executes?

var1 = -2
var2 = 0
while var1 != 0:
    var1 = var1 + 1
    var2 = var2 - 1
print("var1: " + str(var1) + " var2 " + str(var2))

• var1 = -2, var2 = 0
• These are the initial value, but they change during the loop
• var1 = 0, var2 = -2
• This loop will execute two times so var1 will be 0 and var2 will be -2 after the loop finishes.
• var1 = 0, var2 = -1
• This would be true if the loop stopped executing as soon as var1 was equal to 0, but that isn't what happens. The body of the loop will finish executing before the value of var1 is tested again.
• This is an infinite loop so it will never print anything.
• This would be true if it was var1 = var1 - 1

Note

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