Exercise 1: Tracing Binary Search for Target 23 — Possible Solution
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GIVEN
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arr = [3, 7, 11, 15, 19, 23, 27, 31] (indices 0-7)
target = 23

STEP-BY-STEP TRACE
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Step 1: lo=0, hi=7, mid=(0+7)//2=3, arr[3]=15
        15 < 23, so search the right half: lo becomes 4

Step 2: lo=4, hi=7, mid=(4+7)//2=5, arr[5]=23
        arr[5] equals the target - found!

TOTAL COMPARISONS
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2 comparisons were needed to find the target among 8 elements -
consistent with this chapter's own Theta(log n) bound: log2(8) = 3,
and 2 comparisons is within that bound (the exact count depends on
where the target happens to fall, per Chapter 4's own best/worst-case
distinction).

WHY THIS WORKS AS AN ANSWER
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Each step is traced following exactly this chapter's own trace format
- showing lo, hi, mid, and the value found at mid before making the
next decision - and the final comparison count is checked against the
chapter's own Theta(log n) bound for an array of this size, rather
than left unverified.