Lists

Lists are a way of storing several values in one variable. Here is an example, with data from here

earnings = [91, 87, 115, 108]

The values are separated by commas, and enclosed in square brackets. We can access the individual elements as follows:

earnings[0]

91

earnings[1]

87

earnings[3]

108

The numbers 0, 1, and 3 are called indices (the singular is index). Note that we start from 0. The list earnings is of length 4 (since it has four elements), so the last possible index will be 3.

We can get the length of a list using the len() function:

len(earnings)

4

Looping over lists

We have all the tools in order to print every element of a list in turn. For example, suppose we need to print, in turn, earnings[0], earnings[1], ... earnings[3]. In other words, suppose we need to print earnings[i] for every i between 0 and 3 inclusive. The way to do this is to use a for-loop:

for i in range(4):
    print("You make", earnings[i], "thousand dollars a year!")

You make 91 thousand dollars a year!
You make 87 thousand dollars a year!
You make 115 thousand dollars a year!
You make 108 thousand dollars a year!

We can make this a little nicer. We used for i in range(4) because we know that we need the index i to range from 0 to 3 because we know that earnings contains 4 elements. But we can use len(earnings) instead of 4 to get the same results:

for i in range(len(earnings)):
    print(earnings[i])

91
87
115
108

If all we want to do is to print (or use somehow) the elements of the list earnings, there is a nicer way to do this using for. Note that the following is a new way of using for:

for amt in earnings:
    print(amt)

91
87
115
108

for <elem> in <list> puts the elements of <list> into the variable <elem>, in turn.

When using indices is necessary

Suppose we want to convert the amounts from US dollars to Canadian dollars. Here is how you might try to do this:

USD_TO_CAD = 1.3
for amt in earnings:
    amt *= USD_TO_CAD
    print('amt is now', amt)
print('earnings is now', earnings)

amt is now 118.3
amt is now 113.10000000000001
amt is now 149.5
amt is now 140.4
earnings is now [91, 87, 115, 108]

The value of amt changed every time, but earnings never did! What happenned? You can think of for amt in earnings variant as:

for i in range(len(earnings)):
    amt = earnings[i]
    amt *= USD_TO_CAD

It's clear why this wouldn't change earnings: what's changed is the variable amt, but not earnings[i]. It's the same situation as a = 42 b = a b = 43

b changes, but a would still be 42.

How can we change earnings? Just loop over all the indices.

USD_TO_CAD = 1.3
for i in range(len(earnings)):
    earnings[i] *= USD_TO_CAD
    
print(earnings)    

[118.3, 113.10000000000001, 149.5, 140.4]

is_non_decreasing

A list L is non-decreasing if for every i, $L[i] \geq L[i-1]$. For example, [1, 2, 3, 3, 5, 100, 200] is non-decreasing, but [1, 0, 5, 6] is not, since its second element is smaller than its first element.

Let's write the function is_non_decreasing(L) that returns True iff L is non-decreasing.

def is_non_decreasing(L):
    '''Return True iff L is non-decreasing
    
    Arguments:
    L -- a list of integers
    '''
    
    for i in range(1, len(L)): #start at i = 1, since it makes no sense to compare L[0] and L[-1]
        if L[i] < L[i-1]:
            return False #L is definitely not non-decreasing
    
    #Checked for every i, and didn't return False, so we can return True
    return True