Lab 3 Fall 2011

1. Please plot n, vs T(n), Q(n), X(n),Y(n),Z(n) for the following functions, by using a C++ program to produce comma separated values and the exporting this file into a spreadsheet program to produce a plot. Always round off the arguments to integers.
   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. Solve any two of the above recurrence equations in any of the methods (using telescoping (by series summation), or guess and checking or by using Master Theorem)
3. Implement linear time algorithm for the maximumsubarray problem and test with the input given in Benley's paper first page.{31,-41,59,26,-53,58,97,-93,-23,84} answer is 2 and 6 as the index starts from 0. (From Home work 3, read Section 4.1 of CLRS (third edition) - Wikipedia Article on Maximum subarray problem - You need not submit the solution for this problem when you submit your homework solution. Here is a nice write up by Bentley Dr. Bentley )