Hi there!

So, we have made it to Chapter 7.

In case you have not noticed, I have not worked on the exercises from chapter 5 to chapter 7 yet. My goal is to speed up with the theory and then practice for a week. I will organize a session of “Code til you drop” with exercises from Chapter 5 to 8. I hope you can join. This will help us consolidate our knowledge before we tackle Chapter 9’s case study.

The title of chapter 7 is Iteration.

Here is a quick definition in order for us to start:

Iterationis the act of repeating a process with the aim of approaching a desired goal, target or result. Each repetition of the process is also called an “iteration”, and the results of one iteration are used as the starting point for the next iteration.

Source: Wikipedia/Iteration

**7.1 Multiple assignment**

Let us recall the notion of assignment from Chapter 3 – Functions (Part II):

>>> *x* = 3 # Read, variable *x* gets the value of 3.

>>>* x* = *x* + 1 # Read, variable *x* gets the value of itself plus 1.

In addition, we were introduced to Boolean expressions on Chapter 5 / Section 5.1.

>>> 5 == 5 # Read, verify if 5 equals 5.

[…] With multiple assignment it is especially important to distinguish between an assignment operation [ “=” ] and a statement of equality [ “==” ].

Here is the definition that Professor Downey provides for** multiple assignment**.

Multiple assignment: Making more than one assignment to the same variable during the execution of a program [or code block]

**7.2 Updating variables**

Do you remember when we first saw this assignment statement “*x* = *x* + 1″ in Chapter 3? Today we learn that it is called an assignment **update**, since the new value of the variable *x* depends on the old value of *x*.

>>>* x* = *x* + 1 # Read, “get the current value of *x*, add one (1), and then update *x* with the new value”.

In order to update a variable, you must **initialize** the variable first. Otherwise, Python will not recognize the variable.

Python evaluates the right side before it assigns a value to

x.

>>>* x* = 0 # Read, variable *x* gets the value of zero (0). This assignments is also considered as the initialization of variable *x*.

>>>* x* = *x* + 1 #”Updating a variable by adding one (1) is called an **increment**“.

>>>* x* = *x* 1 1 #”Updating a variable by subtracting one (1) is called an **decrement**“.

**7.3 The while statement**

Iteration: Repeated execution of a set of statements using either a recursive function call or a loop.

Python statements that make recursion easier are:

*for*statement : ”*for*i in range ( n ): “*while*statement : ”*while*Boolean expression : “

NOTE: I was looking for a way to improve the “*countdown*” function with a *for* loop, and I found inspiration in PythonicProse and Docs/Python.

Here is the flow of execution for the *while* loop:

- Evaluate the condition, yielding
TrueorFalse.- If the condition is false, exit the
whilestatement and continue execution at the next statement.- If the condition is true, execute the body and loop back to step 1.

The loop’s body should aim to prove the condition false, so that the loop terminates. The body may do so by changing the value of one or more variables.

The objective is to avoid **infinite loops**.

Infinite loop: A loop in which terminating condition is never satisfied.

>>> def sequence (n):

… while n != 1:

… print n,

… if n%2 == 0: # n is even

… n = n/2

… else: #n is odd

… n = n * 3 + 1

…

>>> sequence (16)

16, 8, 4, 2

>>> sequence (3)

3, 10, 5, 16, 8, 4, 2

>>>

**7.4 Break**

The ** break** statement can be used to exit a loop. To illustrate this notion, Professor Downey provides this example:

>>> while True:

… line = raw_input (‘> ‘)

… if line == ‘done’:

… break # The condition (*if line == ‘done’*) allows us to stop the condition affirmatively (“stop when this happens”).

… print line

…

> Hi there!

Hi there!

> done

>>>

The loop condition is

True, which is always true, so the loop runs until it hits thebreakstatement.Each time through, it prompts the user with an angle bracket. If the user types

done, thebreakstatement exits the loop.

**Exercise 7.1**

Re-write the function *print_n* from Section 5.8 using iteration instead of recursion.

I tried a couple of times to re-write the *print_n* function using a *while* statement. This helped me get it right :

- First, it is useful to remind ourselves that the
*while*statement will execute as long as the conditional is*True*.- So, we can include in the
*while*-block whatever we want to do or display while the function is*True*. - In the
*print_n*function from exercise 7.1, we want to print the variable*s*as long that the conditional ”*n > 0*” is*True*.

- So, we can include in the
- Second, a great quality of the
*while*statement is that whenever the conditional is*False*it ends. Isn’t this great?

**7.5 Square roots**

For instance, if we were to write a program that computes numerical results, we could use loops in order to start with approximate answers and iteratively improving it.

The book (*Think Python*) demonstrates this by working with the Newton’s method for computing a square root.

*y*= (

*x + a/x*)/2

*float*equality since “floating-point values are only approximately right”.

*float*.

*Moonwalking with Einstein: the Art and Science of Remembering Everything*mentions that there are people that have memorized hundreds of digits from pi. This give us a sense of how the

*float*3.1416 is a rough approximation.

Rather than checking whether

xandyare exactly equal, it is safer to use the built-in functionabsto compute the absolute value, or magnitude, of the difference between them:if abs (y – x) < epsilon:breakWhereepsilonhas a value like 0.0000001 that determines how close is close enough.

**Exercise 7.2)** Encapsulate this loop in a function called *square_root* that takes *a* as a parameter, chooses a reasonable value of *x*, and returns an estimate of the square root of *a*.

>>> x = 3.0

>>> while True:

… print x

… y = (x + a/x)/2

… if abs (y-x) < epsilon:

… break

… x = y

>>>

File “<stdin>”, line 4, in <module>

NameError: name ‘epsilon’ is not defined

>>>

*math*module.

Here is the code block in script mode (using Sublime Text):

EPSILON = 0.0000001

a = 4.0

x = 3.0

while True:

print x

y = (x + a/x)/2

if abs (y-x) < EPSILON:

break

x = y

*sqroot_epsilon*

*.py*) via the Terminal. Here is the outcome!

3.0

2.16666666667

2.00641025641

2.00001024003

2.00000000003

MacBook-Air-xxxx:Desktop xxxx$

*epsilon*had to be set before hand. So, the code block can perfectly work in script or interactive mode.

**7.6 Algorithms**

**algorithm**notion. I asked countless times what was an

**algorithm**. The best answer I got was that it was like a recipe. Fair enough. However, I could not understand why a simple recipe was so fascinating in the programming world.

For example, to find the product of n and 9, you can write n – 1 as the first digit and 10 – n as the second digit. This trick is a general solution for multiplying any single-digit number by 9. That’s an algorithm!

**7.7 Debugging**

The bigger the program is, the greater the possibility of making errors. Thus, we can say that a program’s length and the possibility of making an error are positively correlated.

**incremental development**technique we learned in Chapter 6 and use the

***

### Acknowledgments :

These notes represent my understanding from the book *Think Python: How to Think Like a Computer Scientist* written by Allen B. Downey.

Part of the chapter is transcribed and all the quotes unless specified otherwise come directly from his book.

Thank you Professor Downey for making this knowledge available.

Also, I would like to thank the open source community for their valuable contribution in making resources on programming available.

Thank you

interesting site you have here! I started this book last week as an intro to coding, and got caught out with ‘epsilon’. Your info on here helped a lot (either I missed the point entirely or the book doesn’t explain the use of epsilon so well). Thanks, Alan