Suppose that an engineer excitedly runs up to you and claims that they've implemented an algorithm that can sort n elements (e.g., numbers) in fewer than n steps. Give some thought as to why that's simply not possible and politely explain

The summary including its given problem is outlined in the following section on the interpretation.

Explanation:

That's not entirely feasible, since at least n similarities have to be made to order n quantities. Find the finest representation where the numbers of 1 to 10 have already been arranged.

⇒ 1 2 3 4 5 6 7 8 9 10

Let's say that we identify one figure as the key then compared it towards the numbers across the left. Whether the correct number is greater, therefore, left number, are doing nothing to switch the location elsewhere.

Because although the numbers have already been categorized 2 has always been compared to 1 which would be perfect, 3 becomes especially in comparison to 2 and so much more. This should essentially take 9 moves, or nearly O(n) moves.

If we switch that little bit already

⇒ 1 3 2 4 5 6 7 8 9 10

3 Is contrasted with 1. 2 will indeed be matched against 3 as well as 2. Since 2 has indeed been exchanged, it must, therefore, be matched with 1 as there might be a case whereby each number z exchanged is greater than the number Y as well as the quantity X < Y.

X = 1, Y = 3, and Z = 2.

Only one adjustment expanded the steps which culminated in n+1.

We can use our shortcuts to test if 4221462 is divisible or not by a certain number:
All integers are divisible by 1.
This is even, so it is divisible by 2.
The sum of the digits of this number is divisible by 3, so the whole number is divisible by 3.
The last two digits of this number are not divisible by 4, so it is not divisible by 8 either.
This number is not divisible by 5 or 10, because it doesn't end with a 5 or 0.
This number is divisible by 6, because it is divisible by two and three.
This number is divisible by 7.
The sum of the digits of this number is not divisible by 9, so the whole number is not divisible by 9.
We get 1 + 2 + 3 + 6 + 7 = 19.
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Hope this helps!