Algorithmic COMP108 Foundations Tutorial 1
25 January 2008
1. Simplify the following mathematical expressions (a) (x - 2)(x + 1) + x + 2 (b) x2 + 2x + 1 (d) 2 + log2 (x/4) 2. Give the trace table and the output of the following algorithm for m = 16. input m count = 0 x=1 while x < m do begin x = x2 count = count + 1 end output count What is the output for general m that is a positive power of 2 (i.e., m = 2, 4, 8, 16, 32, . . .)? 3. Rewrite the following for-loop into a while loop. input m x=0 for i = 1 to m do begin x=x+i end output x 4. Rewrite the above for-loop into a repeat loop. 5. Write a pseudo code using a while-loop to (1) input two numbers x and y; (2) output all multiples of 3 between x y and inclusively. For example, if x = 1 and y = 100, then your pseduo code should output 3 6 9 ... 99. 6. [Puzzle] A farmer is standing on the left side of the river and with him are a wolf, a goat and a box of cabbages. In the river there is a small boat. The farmer wants to cross the river with all the three items that are with him. There are no bridges and in the boat there is only room for the farmer and one item. If...