Which is faster: linear or logarithmic complexity?

Logarithmic.

Comparison of complexities:

Complexity	Description	Example algorithm
$O(\log n)$	Execution time grows slowly with increasing $n$.	Binary search
$O(n)$	Execution time grows proportionally with $n$.	Linear scan

For $ n > 2 $, $ \log n < n $.

Example comparison at $ n = 1000 $:

• $ \log_2 1000 \approx 10 $
• $ 1000 $

# Function with logarithmic complexity (binary search)
def binary_search(arr, target):
    low = 0
    high = len(arr) - 1

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

    return -1

# Function with linear complexity (linear search)
def linear_search(arr, target):
    for i in range(len(arr)):
        if arr[i] == target:
            return i
    return -1