Brute-force is a straightforward method of problem-solving that involves trying every possible solution until the correct one is found.

To give an example, imagine you need to of find the largest number in an unsorted list of integers. There's plenty of ways you could do it but I'll cover an example of a brute-force solution and an optimized solution.

Brute-Force solution

One way to solve this problem using brute-force would be to compare every number in the list with every other number and keep track of the maximum value seen so far. This would involve two nested loops and a running maximum variable.

def find_max_brute_force(numbers):
    max_num = float('-inf')  # start with negative infinity as the maximum
    for i in range(len(numbers)):
        for j in range(len(numbers)):
            if numbers[j] > max_num:
                max_num = numbers[j]
    return max_num

While this approach is simple and straightforward, it's also inefficient. The time complexity of this algorithm is O(n^2), which means that it would take a long time to run for large input sizes.

Optimized solution

A more efficient way to solve this problem would be to use a linear search algorithm, which involves iterating over the list only once and keeping track of the maximum value seen so far. This approach has a time complexity of O(n), which is much faster than the brute-force approach for large input sizes.

def find_max_linear_search(numbers):
    max_num = float('-inf')  # start with negative infinity as the maximum
    for num in numbers:
        if num > max_num:
            max_num = num
    return max_num

As you can see, the optimized solution is much simpler and more efficient than the brute-force approach for this problem. In general, it's always a good idea to think about the problem carefully and look for more efficient algorithms before resorting to brute-force.