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Grade 10 · lesson 1 of 4

Trace a Linear Search

Count comparisons and handle an absent target in an unsorted list.

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Supplied materials

  • Paper and pencil; an adult may read aloud. No device, account or purchase is needed.

Learn the idea

Linear search checks items one at a time and can work on an unsorted list. State its stopping rule: return the first matching zero-based position; if the list ends without a match, return not found. We count item inspections rather than elapsed time, so our result describes this algorithm on the supplied data.

Pseudocode: for i = 0 through n−1, inspect values[i]; if values[i] equals target, return i; after the loop return not found. Use unsorted fictional codes [8, 3, 11, 5, 2]. For target 5, the algorithm inspects 8, 3, 11 and 5 and stops before inspecting 2.

  1. Write zero-based positions 0..4 over the supplied list.
  2. Trace target 5 and mark every inspected item.
  3. Record returned position and inspection count separately.
  4. Trace absent target 7 and confirm all five items are checked.
Worked example

See the method in action

Target 5: inspected values 8 → 3 → 11 → 5; return position 3 after 4 inspections. Target 7: inspect all 5 items, return not found. A position and a count differ by one in this first-match case.

Your turn

Check your reasoning

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For target 11 in the supplied list, what are returned position and inspections?

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See the answer and explanation

Position 2; 3 inspections

The target is at zero-based position 2, after inspecting positions 0, 1 and 2: three inspections.

Take it further

Move target 5 to the front by using [5, 8, 3, 11, 2]. Expected result: position 0 after 1 inspection. The search rule stays the same.

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These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.