The following sequence of keys is to be inserted into an initially empty hash table of size 8 that employs open addressing:

cat, goat, dog, bird, bison, ant, flea, bat, duck 

The hash function assigns to each key the number of characters in the key. For example,h("cat")is 3, because"cat"has 3 characters.

1. Assume thatlinear probingis used to insert the keys. Determine which key causes overflow, and show the table at that point by copying the following template into your text file and adding the keys at the appropriate positions:

0:  1:  2:  3:  4:  5:  6:  7: 

1. Now assume thatquadratic probingis used. Determine which key causes overflow, and show the table at that point.
2. Finally, assume thatdouble hashingis used, with the value of the second hash function based on the first character in the key: a = 1, b = 2, c = 3, d = 4, e = 5, f = 6, g = 7, etc. Determine which key causes the table to overflow, and show the table at the point at which it does so.