F1.5 · LESSON 5 OF 6

Loops and accumulation

Write a small program that transforms data using conditions, loops and functions.

THE IDEA

Doing something once per item

A for loop visits the items of a sequence one at a time. On each pass the loop variable is bound to the next item and the indented body runs once. You write the body one time; Python repeats it.

The most useful pattern is the accumulator: a name you set up before the loop and update inside it, so information carries from one pass to the next. A total starts at 0, a biggest-so-far starts at the first item.

nums

Pass 1 of 5

nums = [3, 8, 1, 9]total = 0for n in nums: total = total + n

Before the loop: total is set to 0.

pass	n	total after
start	-	0

Pick a program, edit the numbers, and press the arrows to go pass by pass. The table keeps the history.

range: counting without writing the numbers out

range(n) produces 0, 1, ..., n-1: n values starting at zero. range(a, b) starts at a and stops before b, and a third number sets the step. As with slices, the stop value is never included.

start stop step

range(0, 4) produces 4 values

01234 (stop, not included)

One argument means range(stop) starting from 0. Try start 1, stop 6 and then step 2, then start 5, stop 0, step -1.

Change start, stop and step. The dashed chip is the stop value, which is never produced.

Predict first. What is the sum of the values produced by range(4)?

while: repeat until a condition fails

When you do not know in advance how many passes you need, use while condition:. The body repeats as long as the condition is true, so the body must change something that the condition looks at. Otherwise the loop never ends.

Halving 100 until it is 1 or less

value = 100
steps = 0
while value > 1:
    value = value // 2     # 50, 25, 12, 6, 3, 1
    steps = steps + 1
print(steps)               # 6

The classic mistake: resetting the accumulator

Looks fine, gives the wrong answer

total = 0
for n in [3, 8, 1, 9]:
    total = 0            # reset on every pass!
    total = total + n
print(total)             # 9, not 21: only the last item survives

Set the accumulator up above the loop. Inside the loop it should only be updated. The trace above shows the correct version: the "total after" column keeps growing.

Chapter context

A program is a precise sequence of state changes. Python names refer to objects; reading a program means tracking the values those names refer to, rather than guessing from how the code sounds.

TRY IT YOURSELF

Exercise 1: an accumulator loop

Write one for loop over numbers. Each pass adds the number to total, adds 1 to count and updates biggest when the number is larger.
After the loop, set mean to total / count. Your program is re-run on other lists, including one with only negative numbers.

numbers = [3, 8, 1, 9]

total = 0
count = 0
biggest = None   # TODO: start from numbers[0], NOT from 0 (what if every number is negative?)

# TODO: write a for loop over numbers. Inside the loop:
#   - add the number to total
#   - add 1 to count
#   - if the number is bigger than biggest, store it in biggest

mean = None      # TODO: after the loop, mean = total / count

print(total, count, biggest, mean)

Ctrl/⌘ + Enter runs it

Exercise 2: range and while

range(1, 6) gives 1, 2, 3, 4, 5. The stop value is never included.
Fill multiples with the first five multiples of n using a for loop over a range and append.
Then use a while loop that halves value with // until it is no longer greater than 1, counting the halvings in steps.

n = 7

multiples = []
# TODO 1: for each i in range(1, 6), append i * n to multiples.
# For n = 7 this must give [7, 14, 21, 28, 35].

value = 100
steps = 0
# TODO 2: while value is greater than 1:
#     halve it with value = value // 2
#     and count the step with steps = steps + 1
# Make sure the loop body changes value, or the loop never ends.

print(multiples, value, steps)

Ctrl/⌘ + Enter runs it

Both exercises must be solved to finish this lesson.

Stuck, or something not working? You can come back to it any time.

CHECK YOUR UNDERSTANDING

Sum the values emitted by range(4).

AThe sum is 6, because range(4) produces 0, 1, 2 and 3 and stops before 4.BThe sum is 10, because range(4) produces 1, 2, 3 and 4.CThe sum is 4, because range(4) produces only the single value 4.

Chapter reference: math, worked example & code

This section belongs to the whole chapter, so it is the same on every lesson in it and may cover a different lesson's topic. The code for the experiment you just ran is inside the experiment itself.

Math and notation

For an accumulator over numbers $x_1,\ldots,x_n$ :

s_0=0,\qquad s_i=s_{i-1}+x_i.

The subscript denotes a step, not a Python index. After the last step, $s_n$ is the sum. For a mean, divide by the number of items, and define what should happen for an empty list.

Worked example

Trace a robot's forward distances [2, 1, 3]. Position starts at zero and changes to 2, then 3, then 6. Replacing three copy-pasted moves with a loop preserves the order and final state. A mean distance is 6/3 = 2; the count is 3, not the last list index 2.

Reference code

The following example uses the Python standard library and does not call a remote service.

moves = [2, 1, 3]
position = 0
for distance in moves:
    position += distance
assert position == 6
assert sum(moves) / len(moves) == 2

Python examples are provided for study and local execution; this page does not execute Python.

Common mistakes

Assignment does not copy a mutable object. A loop stop value is exclusive. A function can return None even when its print output looks correct.