hi, im trying to do the dominant behaviour, which will compute the total run time, but im not sure if im on the right track. heres what i have:

Function mystery(n)
r = 0
for i = 1 to n -1 do
for j = i + 1 to n do
for k = 1 to j do
r = r + 1
return r
END

first thought
the function sets the value of r to 1 (one operation). then it tests the second loop to loop 1 to n- 1 times...(it runs the body of the for loop exactly n - 1 times. the body performs two other for loops; ' j, which is i + 1 to n ' and ' k which runs 1 to j times.'

other thought
the outer most loop executes n-1 times (worst case?). the next innermost one on the order exectures i + n-1 times (loops based on first for loop?).
the addition is based on two for loops....


any suggestions, id appreciate it...

couldnt have said it better ...

need explanation on finding order of growth of a recusive function example what is the order of growth given that T(1)=1 and T(n)=2T(n/4) + 1 for n>0
what are the steps to find ORDER OF GROWTH OF ANY function.

steps or methods of order og growth of a function

For any function?

Here's a tip: For any function f, f(n) = O(f(n)). It's true! He he he.

Now, given T(1) = 1 and T(n) = 2T(n/4) + 1, you can find the order of growth using the Master theorem.

One way, though, to think about the above problem intuitively, is to ask what the statement "T(n) = 2T(n/4)+1" really means. Another way of writing it is to say, "T(4n) = 2T(n) + 1". That is, every time you multiply n by four, the value of T(n) multiplies by 2. (For large values of n, adding 1 has a negligible effect.)

What function has that property, where multiplying the input by four results in the output being multiplied by 2? We know the function is sublinear, because if it were linear, we would find that T(4n) is approximately 4T(n), for large n. But it's only 2T(n)

We know it's bigger than logarithmic, because we know that for logarithmic functions, multiplying a constant by the input results in a mere constant being added to the output.

So, what function has the property that T(4n) is 2T(n)? Make some guesses. And this will be the function that conveniently represents your order of growth.

some one help me please...
how will i compute the time complexity of these algo...


do{
h=h-1
}while(h!=n);

Very carefully, I hope! Why don't you start by learning how to compute time complexity for algorithms, in general.