Spring 2001 CS100M    Solutions to Exercise E10

+ here are how many people chose each answer;
  solutions are marked with an arrow $-->$.

+ see also the $e10maple$ script

+ see also the $e10plot$ script

1. x = [n];

--> 154: $length(x)$ is O(1)
     22: $length(x)$ is O(n)
      4: $length(x)$ is none of the above

2. x = 1:n;

     21: $length(x)$ is O(1)
--> 151: $length(x)$ is O(n)
      2: $length(x)$ is O(n^2)
      6: $length(x)$ is none of the above

3. x = [2]; for j = (n-5):(n+5), x = [x 2]; end     $length(x)$ is O(1)  

-->  73: $length(x)$ is O(1)
     24: $length(x)$ is O(n)
      2: $length(x)$ is O(n^.5)
      6: $length(x)$ is O(n^2)
     75: $length(x)$ is none of the above

4. O(100 n^2 + 5n + 1) = O(n^2 + 5n + 100)

     27: $O(100 n^2 + 5n + 1)$ is bigger
      2: $O(n^2 + 5n + 100)$ is bigger
--> 151: they are the same

5. O(10 n^2) < O(2 n^10)

      3: $O(10 n^2)$ is bigger
--> 176: $O(2 n^10)$ is bigger
      1: they are the same

6. O(10) = O(1)

      1: $O(1)$ is bigger
     26: $O(10)$ is bigger
--> 153: they are the same

7. O(1 + 1/n) = O(2)

     17: $O(1 + 1/n)$ is bigger
     69: $O(2)$ is bigger
-->  94: they are the same

8. O(n+log(n)) = O(n)

      2: $O(n)$ is bigger
     48: $O(n+log(n))$ is bigger
--> 130: they are the same

Histogram of number of correct replies

     34	number of correct answers: 8
     45	number of correct answers: 7
     42	number of correct answers: 6
     25	number of correct answers: 5
     11	number of correct answers: 4
     14	number of correct answers: 3
      5	number of correct answers: 2
      1	number of correct answers: 1