what to do with fraction as index number?

fraction as index number?

• given these inputs x = 4, S = [1 2 3 4 5 6 7 8 9 10], and n = 10 search (x,S,n) { i = 1 j = n while i < j { m = [(i+j)/2] if x > Sm then i=n+1 else j = m end if x = Si then location = i else location = 0 This algorithm is from my discrete math hw. I'm confused as to what Sm would equal on the first iteration because m would be $\frac{11}{2}$. If i use a fraction as the index do I round down? Is there a general rule for this? Am I making any sense? Help pls

• Answer:

  Yes, you should round down (or in other words, take only the integer part). $$[11/2]=[5.5]=5$$ This is known as the http://en.wikipedia.org/wiki/Floor_and_ceiling_functions in mathematics (usually there is a floor(x) function in programming languages).