Can you explain the concept of Big O notation and its significance in algorithm analysis?

Big O notation is a way of describing the asymptotic complexity of an algorithm, that is, how the execution time or memory consumption grows depending on the size of the input data. It helps evaluate the efficiency of an algorithm and compare different solutions.

For example, if an algorithm has a complexity of O(n), it means that the execution time grows linearly with the increase in input size. If it is O(n²), then the time grows quadratically.

This is important for understanding how an algorithm will behave on large data sets and for choosing optimal solutions.

Example:

# Linear search for an element in a list — O(n)
def linear_search(arr, target):
    for i in arr:
        if i == target:
            return True
    return False

# Bubble sort — O(n^2)
def bubble_sort(arr):
    n = len(arr)
    for i in range(n):
        for j in range(0, n-i-1):
            if arr[j] > arr[j+1]:
                arr[j], arr[j+1] = arr[j+1], arr[j]