What a List Is, and the Indexing Gap

A list stores many values under one name. Instead of a, b, c, and d, you keep four related values in one ordered collection and reach any of them by its position, called an index. Lists are how a program manages a group of data whose size you may not know in advance.

Here is the single most tested idea in this topic, and it trips up students on every exam: the two notations you will see count from different starting points. Python lists are 0-indexed, so the first element is at index 0 and the last is at index len(list) - 1. AP pseudocode lists are 1-indexed, so the first element is at index 1 and the last is at index LENGTH(list). Same list, same values, different index numbers.

nums = [10, 20, 30, 40]
print(nums[0])
print(nums[3])

nums <- [10, 20, 30, 40]
DISPLAY(nums[1])
DISPLAY(nums[4])

Look closely: both panels print 10 and then 40, the first and last values. But Python reaches the first value with nums[0] and the last with nums[3], while AP pseudocode reaches the exact same values with nums[1] and nums[4]. Read every index question by first asking which notation you are in.

data = [4, 8, 15, 16]
print(data[2])

Updating, Appending, and Length

Once a list exists you can change an element in place by assigning to its index: nums[1] = 99 replaces whatever was at index 1. You can grow the list from the end with append, which always adds one new element after the current last one. And len(nums) reports how many elements the list currently holds, a value that changes every time you add or remove.

nums = [10, 20, 30]
nums[1] = 99
nums.append(40)
print(nums)
print(len(nums))

nums <- [10, 20, 30]
nums[2] <- 99
APPEND(nums, 40)
DISPLAY(LENGTH(nums))

Trace it: the list starts as three values, nums[1] = 99 overwrites the middle one, and append(40) tacks a fourth on the end, giving [10, 99, 30, 40]. Because there are now four elements, len(nums) is 4. In AP pseudocode the same edit uses nums[2] <- 99 (index 2 is the middle element when counting from 1) and APPEND, and LENGTH(nums) returns 4.

Insert and Remove: Everything Shifts

Inserting or removing an element in the middle of a list does more than change one spot. Every element after the change shifts to a new index to keep the list packed with no gaps. This shifting is where index bugs are born, because a position you were pointing at a moment ago may now hold a different value.

letters = ["a", "b", "c"]
letters.insert(1, "x")
letters.pop(0)
print(letters)

letters <- ["a", "b", "c"]
INSERT(letters, 2, "x")
REMOVE(letters, 1)
DISPLAY(letters)

Start with ["a", "b", "c"]. In Python, insert(1, "x") drops "x" at index 1 and pushes "b" and "c" right, giving ["a", "x", "b", "c"]. Then pop(0) removes the element at index 0, and everything shifts left, leaving ["x", "b", "c"]. The pseudocode reaches the identical result, but its INSERT uses index 2 and its REMOVE uses index 1 because it counts from 1.

t = [1, 2, 3]
t.insert(1, 9)
print(t[2])

Traversing a List with a Loop

A traversal visits every element of a list one at a time, usually with a loop. Traversal is how you sum values, search for a target, or count how many match a rule, no matter how long the list is. The most common Python form is for element in list, which hands you each value in order without you managing an index at all.

You can also traverse by index with for i in range(len(list)). That form is powerful, but it is exactly where the bounds trap lives: the valid indices are 0 through len(list) - 1, so you loop range(len(list)). If you loop one step too far, you index past the end and the program crashes.

scores = [8, 5, 9, 7]
total = 0
for s in scores:
    total = total + s
print(total)

scores <- [8, 5, 9, 7]
total <- 0
FOR EACH s IN scores
{
    total <- total + s
}
DISPLAY(total)

This traversal starts a running total at 0, then adds each score as the loop visits it: 0, then 8, then 13, then 22, then 29. After the last element it prints 29. The pseudocode FOR EACH loop does the same thing, visiting every element in order.

vals = [3, 6, 1]
n = 0
for v in vals:
    n = n + v
print(n)

Key Vocabulary