Lower Bound - Code

Here is the implementation of lower bound:

function lowerBound(arr, target):
    low = 0
    high = arr.length

    while low < high:
        mid = low + (high - low) / 2
        if arr[mid] < target:
            low = mid + 1
        else:
            high = mid

    return low

Key differences from exact-match: $1.$ high = arr.length (not arr.length - 1) because the answer can be past the end.

$2.$ while low < high (not <=) because we narrow to a single point.

$3.$ When arr[mid] >= target, set high = mid (not mid - 1) because mid might be the answer.

Result: low is the first index where arr[low] >= target. If all elements are smaller, low == arr.length.