Binary Search First Occurrence

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

Algorithm

Basic Implementation

basic.sh

#!/usr/bin/env bash
set -euo pipefail
arr=(1 2 4 4 4 7 9)
target=4
lo=0
hi=$((${#arr[@]} - 1))
result=-1
while [ "$lo" -le "$hi" ]; do
	mid=$((lo + (hi - lo) / 2))
	if [ "${arr[mid]}" -eq "$target" ]; then
		result=$mid
		hi=$((mid - 1))
	elif [ "${arr[mid]}" -lt "$target" ]; then
		lo=$((mid + 1))
	else
		hi=$((mid - 1))
	fi
done
echo "$result"

Complexity

Time: O(log n)
Space: O(1)

Implementation notes

arr=(1 2 4 4 4 7 9) is a Bash indexed array, and this lesson uses zero-based positions.
hi=$((${#arr[@]} - 1)) reads the array length with ${#arr[@]} and sets the initial upper bound to index 6.
lo=0, hi=6, and result=-1 seed the search window and the not-found sentinel.
mid=$((lo + (hi - lo) / 2)) computes the midpoint with Bash arithmetic expansion.
[ "${arr[mid]}" -eq "$target" ] tests for a numeric match, and [ "${arr[mid]}" -lt "$target" ] tests whether the current value is too small.
On a match, result=$mid records the current index, then hi=$((mid - 1)) keeps searching left for the first duplicate.
When the value is too small, lo=$((mid + 1)) moves the lower bound right.

Replay steps

start: lo=0, hi=6, result=-1
mid=3: arr[3]=4 matches -> result=3, hi=2
mid=1: arr[1]=2 is too small -> lo=2
mid=2: arr[2]=4 matches -> result=2, hi=1
stop:  lo=2, hi=1 -> print 2

echo "$result" prints exactly 2.

execution replay The checked-in replay follows the language-neutral state table for `search-binary-first`.

cross-language comparison This Bash DSA version keeps the same data and final output as every other DSA book in this wave.