Question

Consider the following pseudo-code:

// Assume i, j, k are integers

for i = 1 to n do

for j = n-i+1 to n {

k = 1;

while (k*k <= j)

{ perform <op>;

k = k + 1; } }

Find an expression for f(n), the number of times is performed. Find g(n) so that f(n) is Θ(g(n)). Prove your answer.

Answer 1

First loop is running for n times.
Second loop is running for (i-1) times.
Max value of i is n.
So, Second loop runs max of n times.
Third loop is running for sqrt(n) times.