5.10: Maximum and Minimum Loops

To find the largest value in a list or sequence, we construct the following loop:

Code 5.9.1 (Python)

%%python3

largest = None
print('Before:', largest)
for itervar in [3, 41, 12, 9, 74, 15]:
    if largest is None or itervar > largest :
        largest = itervar
    print('Loop:', itervar, largest)
print('Largest:', largest)

When the program executes, the output is as follows:

Before: None
Loop: 3 3
Loop: 41 41
Loop: 12 41
Loop: 9 41
Loop: 74 74
Loop: 15 74
Largest: 74

The variable largest is best thought of as the "largest value we have seen so far". Before the loop, we set largest to the constant None. None is a special constant value which we can store in a variable to mark the variable as "empty".

Before the loop starts, the largest value we have seen so far is None since we have not yet seen any values. While the loop is executing, if largest is None then we take the first value we see as the largest so far. You can see in the first iteration when the value of itervar is 3, since largest is None, we immediately set largest to be 3.

After the first iteration, largest is no longer None, so the second part of the compound logical expression that checks itervar > largest triggers only when we see a value that is larger than the "largest so far". When we see a new "even larger" value we take that new value for largest. You can see in the program output that largest progresses from 3 to 41 to 74.

At the end of the loop, we have scanned all of the values and the variable largest now does contain the largest value in the list.

To compute the smallest number, the code is very similar with one small change:

Code 5.9.1 (Python)

%%python3

smallest = None
print('Before:', smallest)
for itervar in [3, 41, 12, 9, 74, 15]:
    if smallest is None or itervar < smallest:
        smallest = itervar
    print('Loop:', itervar, smallest)
print('Smallest:', smallest)

Again, smallest is the "smallest so far" before, during, and after the loop executes. When the loop has completed, smallest contains the minimum value in the list.

Again as in counting and summing, the built-in functions max() and min() make writing these exact loops unnecessary.

The following is a simple version of the Python built-in min() function:

def min(values):
    smallest = None
    for value in values:
        if smallest is None or value < smallest:
            smallest = value
    return smallest

In the function version of the smallest code, we removed all of the print statements so as to be equivalent to the min function which is already built in to Python.