Algorithm question. Please answer all questions, and show work or explain when necessary!
Consider the following algorithm. ALGORITHM Mystery(n)//Input: A nonnegative integer n
Sir- 0 for i leftarrow1 to n do S leftarrow S + i * i return S What does the algorithm compute?
What is its basic operation? How many times is the basic operation executed? What is the
efficiency class of this algorithm?
Solution
a} What does the algorithm compute?
----The algorithm computes the sum of squares of n numbers.
S <--- 0 The sum is iitialized to 0
for i <---1 to n This is a loop which will execute n times. n is a non negative integer.
S<----S + i * i  This statement in the loop computes the square of numbers 1 to n ie 1 2 +
2 2+
...............+ n 2
return S
b}. The basic operations are sum comparison and assignment .
c}.The basic operation sum will be executed n times.Assignment and comparisons will also be
executed n times each.
d} The efficiency class of this algorithm is cubic ( n 3
)as formula is n(n+1)(2n +1)/6