Lecture 9 Iterations

1. The 'while' statement
Computers are often used to automate repetitive tasks. Repeating identical or similar tasks without making errors is something that computers do well and people do poorly
Here is what countdown looks like with a while statement:


2. Tables
One of the things loops are good for is generating tabular data.


We can test if 'math.log()' is calculating the natural log: we put 'math.e' there as the natural log constant, and we got all the '1's in the results.
Don't forget to import the 'math' package if you did do this before.


Note that, 'math.e' is the constant, 'math.exp()' is the function which allows you to choose the power.

If you want to find the log for base 2:


Or an alternative way:
Since we know:


So the alternative way to get log base 2 is:


This is verified when x=2, the result is 1.

3. The 'for loop'
Using an index to traverse a set of values is so common that Python provides an alternative, simpler syntax - the for loop:


Traverse a range:


One more example:
To print out all the letters in 'fruit' one by one, you can use a 'while loop':


Or a 'for loop':

The 'for loop' in Python has the index running on the back-end.

Multiple indices:
Copy the following data:
students = [ ("John", ["CompSci", "Physics"]), ("Vusi", ["Maths", "CompSci", "Stats"]), ("Jess", ["CompSci", "Accounting", "Economics", "Management"]), ("Sarah", ["InfSys", "Accounting", "Economics", "CommLaw"]), ("Zuki", ["Sociology", "Economics", "Law", "Stats", "Music"])]



4. Looping and counting
The following program counts the number of times the letter 'a' appears in a string:


5. Break and Continue
'Break' will quit the loop.





Istead of quiting the loop, Continue will skip it and continue traversing other elements. :



6. Exercise:
Loop through and print out all even numbers from the numbers list in the same order they are received. Don't print any numbers that come after 237 in the sequence.
numbers = [
    951, 402, 984, 651, 360, 69, 408, 319, 601, 485, 980, 507, 725, 547, 544,
    615, 83, 165, 141, 501, 263, 617, 865, 575, 219, 390, 984, 592, 236, 105, 942, 941,
    386, 462, 47, 418, 907, 344, 236, 375, 823, 566, 597, 978, 328, 615, 953, 345,
    399, 162, 758, 219, 918, 237, 412, 566, 826, 248, 866, 950, 626, 949, 687, 217,
    815, 67, 104, 58, 512, 24, 892, 894, 767, 553, 81, 379, 843, 831, 445, 742, 717,
    958, 609, 842, 451, 688, 753, 854, 685, 93, 857, 440, 380, 126, 721, 328, 753, 470,
    743, 527
]

Solution:

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Tasks:

1. The value of pi can be approximated by:

Wriet a script (must use the 'while loop') with a user-defined function which asks the user to input the number of iterations (n), then computes the expression. The larger the number of iterations, the closer the result should be to pi. Print out the final result by calling the function. (You may want to force the input into an 'int' varable)

2. Repeat the task above using the 'for loop' instead of the 'while loop'.

3. Given that the square root of a number 'n' can be calculated by the following equation:

Better = (approx + n/approx)/2

"Better' means a better/closer result to the real square root. 'approx' means the previous approximated value, maybe from the last iteration or from the initial assigned value.

Design a function that uses this method to calculate the square root of a given number. The relative error, abs((approx-better)/approx),should be smaller than 0.001.

Make sure it'll also return the number of iterations to reach this accuracy. (Do not use math.sqrt() or any other embedded sqrt() functions)

(Hint, you can start approx with n/2 or something like that)

4. As the last example in the 'For Loop' section, we have the same student information data set:
students = [ ("John", ["CompSci", "Physics"]), ("Vusi", ["Maths", "CompSci", "Stats"]), ("Jess", ["CompSci", "Accounting", "Economics", "Management"]), ("Sarah", ["InfSys", "Accounting", "Economics", "CommLaw"]), ("Zuki", ["Sociology", "Economics", "Law", "Stats", "Music"])]

How many students are taking CompSci? This needs a counter, and for each student we need a second loop that tests each of the subjects in turn.