Exercises from Chapter 9
                  
9.3
9.9
9.13
9.14
9.16

                                   Solutions

9.3 During interpolation i, the size of the jumps is n^(1/2^i).
(I'm using a^b to mean a to the power b.) So the number of
interpolations is the smallest number m such that n^(1/2^m) <= 1.
Solving n^(1/2^m) <= 1 for m, m >= log log n. Since each interpolation
costs on average O(1), the total average cost is O(log log n).

9.9
template <class Elem>
void MoveTo Front(Elem A[]) {
  int n = 0;
// GETNEXT is a function that returns the next item.
// DONE is a user-defined value indicating end of items.
  while ((Elem val = GETNEXT()) != DONE) {
    for (i=0; i<n; i++)
      if (A[i] == val) break;
    while (i > 0) {
      A[i] = A[i-1];
      i--;
    }
    A[0] = val;
  }
}

9.13 (a) NO: hash value will be greater than largest index in HT when k > n^2.

(b) It would work correctly, but it is a very bad hash function because any two
items will have a collision.

(c) NO: a hash function must return the same value each time.

(d) YES: In fact, this is often used in practice if not much is known about
the distribution of key values.

9.14 Table index   Value
          0
          1
          2           9
          3           3
          4           2
          5          12
          6
Slots 0 and 1 each have probability 1/7 of being filled next.
Slot 6 has probability 5/7 of being filled next.

9.16 Here are the two hash values for each item:
   Key     H1     H2
     2      2      3
     8      8      9
    31      5      1
    20      7      1
    19      6      2
    18      5      3
    53      1      1
    27      1      5
This shows the probing that results from inserting each item:
   Key     Slots probed (including initial slot)
     2      2
     8      8
    31      5
    20      7
    19      6
    18      5, 8, 11
    53      1
    27      1, 6, 11, 3
The final table is:
     Table index   Value
          0
          1          53
          2           2
          3          27
          4           
          5          31
          6          19
          7          20
          8           8
          9
         10
         11          18
         12