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Grade 10 · unit review

Review: Prepare and Compare Searches

Sort data, count search inspections and trace a first-match binary-search variant.

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Bring the unit skills together

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Unit review questions
1. Sorted list [2, 6, 10, 14, 18, 22, 26], target 22. What is the second inspected value under middle-item binary search?
2. Linear first-match search on [9, 1, 7, 4], target 7: what are returned position and inspections?
3. Insertion sort starts with [5, 3, 4]. After inserting the first key 3, what is the full list?
4. Lower-bound search uses sorted [1, 3, 3, 6], target 3. Which zero-based position is returned?

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Prepare fictional codes [8, 2, 5, 2] for first-match searching. Trace insertion-sort passes, then lower-bound search for 2 on the sorted list. Also trace linear first-match search for 5 on the original list and middle-item binary search for 8 on the sorted list, choosing floor((lo+hi)/2) for inclusive binary bounds. Compare inspected-item counts without counting sorting as free.

Work on paper or in your own document. Explain the choices you made.

  • Sort with passes [2,8,5,2], [2,5,8,2], [2,2,5,8].
  • Find the first 2 at sorted position 0 using lower-bound, inspecting positions 2,1,0.
  • Linear search for 5 on original list returns position 2 after 3 inspections.
  • Inclusive-bound binary search for 8 inspects values 2,5,8: 3 inspections; state sorting preparation has additional work.
Compare with a model response

Insertion-sort passes: [2,8,5,2] → [2,5,8,2] → [2,2,5,8]. Lower-bound target 2: range [0,4), mid 2 value 5; then [0,2), mid 1 value 2; then [0,1), mid 0 value 2; return 0 after 3 inspections. Linear target 5 on [8,2,5,2] inspects 8,2,5 and returns position 2 after 3 inspections. Binary target 8 with inclusive bounds 0..3 inspects positions 1,2,3, values 2,5,8, also 3 inspections. These small examples do not establish a universal winner, and sorting adds preparation work.

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