Assistant System Engineer

You have an integer ‘N’. Now let’s define a function ‘f(x)’ equal to the number of integers not more than ‘x+1’ and greater than equal to ‘1’ and are coprime to integer ‘x’.

Let’s say there is a number ‘X’ divided by ‘K’ different prime numbers, and let array ‘P’ of length ‘K’ be the array of prime numbers dividing the number ‘X’.

So ‘g(X)’ is equal to the sum of ∑f(X/Pi) ‘i’ in the range ‘[0, K-1]’ both inclusive.

Construct an array ‘Y’ of length ‘N’ where ‘Y[i]’= ‘g(i+1)’ for ‘i’ in the range ‘[0, N-1]’.

Determine the array ‘Y’.

Example:

'N' = 3
First calculate ‘f(1)’, ‘f(2)’ and ‘f(3)’.
‘f(1)’ = ‘2’ as ‘1’ and ‘2’ are co-prime to ‘1’.
‘f(2)’ = ‘2’ as ‘1’ and ‘3’ are co-prime to ‘2’.
‘f(3)’ = ‘3’ as ‘1’, ‘2’  and ‘4’ are co-prime to ‘3’.
Now calculate ‘g(1)’ , ‘g(2)’, ‘g(3)’.
‘g(1)’ as no prime number divides 1, so ‘g(1) = 0’.
‘g(2)’ = ‘f(2/2)’ = ‘f(1) = 2’ as ‘2’ is the only prime number that divides ‘2’.
‘g(3) = ‘f(3/3)’ = ‘f(1) = 2’ as ‘3’ is the only prime number that divides ‘3’.

An ant is at the bottom of the wall 35 feet down. It climbs up 2 feet each hour, but later it slips down 1 feet. How long will it take to reach the top of the wall?

You are given an array of integers. You need to sort the array in ascending order using quick sort.

Quick sort is a divide and conquer algorithm in which we choose a pivot point and partition the array into two parts i.e, left and right. The left part contains the numbers smaller than the pivot element and the right part contains the numbers larger than the pivot element. Then we recursively sort the left and right parts of the array.

Example:

Let the array = [ 4, 2, 1, 5, 3 ]
Let pivot to be the rightmost number.

After the 1st level partitioning the array will be { 2, 1, 3, 4, 5 } as 3 was the pivot. After 2nd level partitioning the array will be { 1, 2, 3, 4, 5 } as 1 was the pivot for the left part and 5 was the pivot for the right part. Now our array is sorted and there is no need to divide it again.

What do you understand by Caching

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What is AJAX ?

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