Lab 4 Fall 2009

This lab is to review parts of Chapter 2 of Das Gupta et al's text book. Please go to your lab, do the problems to get your full credit for the lab.

You are welcome to try this problem ahead of time.
  1. Please plot n, vs T(n), Q(n), R(n), X(n),Y(n),Z(n) for the follwoing functions, by using a C++ program to produce comma separated values and the exporting this file into a spreadsheet program to produce a plot.
    1. T(n)= T(n-1) +1, T(0)=0
    2. Q(n) = Q(n-1) + n , Q(0) =0
    3. R(n) = 2*R(n-1)+1, R(0)=0
    4. X(n) = 2*X(n/2)+1, X(0) =0
    5. Y(N) = 2*Y(n/2)+n, Y(0) =0
    6. Z(n) = Z(sqrt(n)) + 1, Z(1)= 0 
    
int main(void)
{
  int n;

  for (n = 10; n <=1000; n=n+10)
    cout << n<<","<< T(n) <<","<< Q(n) << "," << X(n) <<"," << Y(n) <<","<< Z(n) << "\n";
   exit(1);
}
  2. Write the first 15 values of R and guess what function it is.
  3. Solve any three of the above recurrence equations in any of the methods (using telescpoping (by series summation), or guess and checking or by using Master Theorem)
  4. Optional - Descibe algorithms whose running times are describe by the above recurrence relations.