Concepts / Understanding Lists and Their Properties

Understanding Lists and Their Properties

List indexing uses the bracket operator with zero-based indices: the first element is at index 0, the second at index 1, and so on.

  • Programming
Interactive lab

Try it: Indexing and Slicing

How Python indexes a sequence from 0 (or from the end with negative numbers) and how a slice start:stop:step picks positions — with the exact CPython rules for omitted and out-of-range bounds.

How it works

  1. Positions run 0 … len−1; negative positions count back from the end (−1 is the last).
  2. An index outside the string raises IndexError.
  3. A slice resolves start and stop (omitted → the ends; out of range → clamped), then walks by step, stopping before stop.
  4. A negative step walks backwards; a step of 0 is a ValueError.

Default run (7 steps): 'PYTHONIC'[1:6:2]: a slice copies characters from start up to (not including) stop, moving by step. … 'PYTHONIC'[1:6:2] → 'YHN' (positions 1, 3, 5).

Simplified: Works on a short string (up to 16 printable ASCII characters); lists slice by exactly the same rules.

Educational simulation

Loading the simulation…

Finding the First Element

A list stores elements in an ordered sequence. To retrieve one element, write the list name followed by brackets containing an index. The important starting point is that Python counts list positions from zero: the first element has index 0, the second has index 1, and later elements continue in the same pattern.

Cheddarindex 0Goudaindex 1Mozzarellaindex 2later elementindex 3next positionnext positionnext position
How do list positions map to zero-based indices when retrieving the first, second, and later elements?

Reading Positions with Brackets

The bracket operator selects an element by position. For the source example, cheeses[0] retrieves the first element, and cheeses[2] retrieves the third element. The number inside the brackets is not a human-style position number; it is a zero-based index. Therefore, an index of 2 means the third element because counting begins at 0.

Worked example

Selecting a Known Element

Determine which element is selected by cheeses[2].

  1. 1
    Start at zero

    The first element is at index 0, so the indices advance as 0, 1, and 2.

  2. 2
    Locate index 2

    Index 2 identifies the third element in the list.

  3. 3
    Retrieve the element

    cheeses[2] retrieves the third element.

Result

The expression selects the third element of cheeses.

Evaluating an Index Expression

The index does not have to be a literal integer written directly inside the brackets. Any integer expression can be used. This includes a variable, an arithmetic expression, or a function call that evaluates to an integer. Python evaluates that expression first, then uses the resulting integer to select the list element.

index + 1index is 12evaluated indexelement at index 2third elementevaluateselect
How is an integer expression evaluated before its result is used to select a list element?
Worked example

Using a Variable and Arithmetic

Determine the index used by cheeses[index + 1] when index is 1.

  1. 1
    Read the variable

    The variable index has the integer value 1.

  2. 2
    Evaluate the expression

    The expression index + 1 becomes 1 + 1, which evaluates to 2.

  3. 3
    Use the result

    The list access therefore uses index 2.

Result

cheeses[index + 1] retrieves the element at index 2, which is the third element.

Counting Backward

Negative indices provide a second way to locate elements. They count backward from the end of the list: -1 selects the last element, -2 selects the second-to-last element, and the count continues toward the beginning. In the source example, cheeses[-1] selects Mozzarella, cheeses[-2] selects Gouda, and cheeses[-4] selects Cheddar.

Cheddarindex 0, negative index -4Goudanegative index -2Mozzarellanegative index -1fourth elementnegative index -1count backwardcount backwardcount backward
How do negative indices count backward from the end of a list, and which element does each one select?
Worked example

Reading from the End

Identify the elements selected by cheeses[-1], cheeses[-2], and cheeses[-4].

  1. 1
    Use -1

    -1 means the last element, which is Mozzarella in the source example.

  2. 2
    Use -2

    -2 means the second-to-last element, which is Gouda.

  3. 3
    Use -4

    The list has four elements, so -4 reaches the first element, Cheddar.

Result

The expressions select Mozzarella, Gouda, and Cheddar respectively.

When an Index Fails

A list can only be accessed through its valid index range. The source example has four elements, so its non-negative indices are 0, 1, 2, and 3. Attempting to access index 4 goes beyond the available elements and raises an IndexError. The same problem occurs when an index is too negative: cheeses[-5] is invalid for a four-element list because it goes beyond the beginning.

index 4requested accessvalid range 0 to 3four-element listIndexErrorindex outside rangecheck indexoutside range
What happens when an index points beyond the available list elements, and how does execution flow to the error?
  • Common mistake

    Treating index 1 as the first element

    What it looks like

    Using index 1 when the intended element is the first item

    Why it fails

    List indices begin at 0, so index 1 identifies the second element.

    Do this instead

    Use index 0 for the first element, index 1 for the second, and index 2 for the third.

  • Common mistake

    Assuming the last index equals the number of elements

    What it looks like

    Accessing index 4 in a list with four elements

    Why it fails

    A four-element list uses non-negative indices 0 through 3. Index 4 is outside the valid range and raises IndexError.

    Do this instead

    For a four-element list, the final non-negative index is 3.

  • Common mistake

    Counting too far backward

    What it looks like

    Using cheeses[-5] for the four-element source list

    Why it fails

    The valid negative indices for that list range from -1 through -4.

    Do this instead

    Keep the negative index within the available backward range.

Practice and Review

MEDIUM

For the source list cheeses, identify the selected position for cheeses[0], cheeses[2], cheeses[index] when index is 1, cheeses[index + 1] when index is 1, cheeses[-1], and cheeses[-2]. Then determine which two accesses would raise IndexError: cheeses[4] or cheeses[-5].

Hints
  • Translate non-negative indices from zero: 0 is first, 1 is second, and 2 is third.
  • Evaluate index + 1 before using it as the list index.
  • For a four-element list, the valid negative indices range from -1 through -4.
  1. 1
    List elements are retrieved with the bracket operator. Python uses zero-based indexing, so index 0 identifies the first element. The expression inside the brackets can be any expression that evaluates to an integer, including a variable or arithmetic expression. Negative indices count backward from the end, with -1 selecting the last element. An index outside the valid range raises IndexError.

Key Takeaways

  • Use brackets to retrieve a list element by index.
  • The first element is at index 0, not index 1.
  • Integer expressions are evaluated before their results are used as indices.
  • Negative indices count backward, with -1 selecting the last element.
  • An index outside the available range raises IndexError.

Related Topics

Related concepts

More concepts starting with U