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Binary Search First Occurrence

Find the first copy of a duplicated target by recording matches and continuing to search the left half.

Algorithm

execution replay The checked-in replay follows the language-neutral state table for `search-binary-first`.
cross-language comparison This Python DSA version keeps the same data and final output as every other DSA book in this wave.

Basic Implementation

basic.py
Replay: real traced execution (multi-file project)
arr = [1, 2, 4, 4, 4, 7, 9]
target = 4
lo = 0
hi = len(arr) - 1
result = -1
while lo <= hi:
    mid = lo + (hi - lo) // 2
    if arr[mid] == target:
        result = mid
        hi = mid - 1
    elif arr[mid] < target:
        lo = mid + 1
    else:
        hi = mid - 1
print(result)

  1. arr ← [1, 2, 4, 4, 4, 7, 9], target ← 4, result ← -1

    1arr = [1, 2, 4, 4, 4, 7, 9]2target = 4
    values this step[1, 2, 4, 4, 4, 7, 9]arr4target-1result

  2. hi ← 2, mid ← 3, result ← 3

    6while lo <= hi:7    mid = lo + (hi - lo) // 28    if arr[mid] == target:
    values this step6 → 2hi3mid3result0lo

  3. lo ← 2, mid ← 1

    6while lo <= hi:7    mid = lo + (hi - lo) // 28    if arr[mid] == target:
    values this step0 → 2lo1mid2hi3result

  4. hi ← 1, result ← 2, mid ← 2

    6while lo <= hi:7    mid = lo + (hi - lo) // 28    if arr[mid] == target:
    values this step2 → 1hi3 → 2result2mid2lo

  5. stdout ← 2

    14        hi = mid - 115print(result)
    values this step2stdout2result

Complexity

  • Time: O(log n)
  • Space: O(1)

Implementation notes

  • Python stores arr as a list of references to immutable int objects. The search only reads arr[mid]; it never mutates the list or allocates a replacement container.
  • lo, hi, mid, and result are local integer bindings. The midpoint uses lo + (hi - lo) // 2, and the while lo <= hi guard keeps every arr[mid] access inside the current bounds.
  • On equality, the code records result = mid and then sets hi = mid - 1 to keep searching left. GC is not part of the visible loop state; the trace shows result move from -1 to 3, then to the first occurrence at 2.