Problem 1. 

a. bad
Most English words have no more than 15 letters. Hence
only 15*26<400 entries are used. Those English words whose
sum of letters equal would hash to the same location.
Most entries of hash table are not used.

b. bad
Since the position of first letter of key is between
0 and 255. Hence only 256 entries are used. Those
strings which have the same first letter would hash to
the same location. Most enties of hash table are not
used.

c. bad
In this case, the keys are uniformly distributed in Hash
Table. However, since the hash function h(x) is a random
function. It is hard to locate a key. One has to locate
the key sequentially. There is no general rule to predict
the entry of a key.

d. bad
In this case, the keys are uniformly distributed in Hash
table. And we can uniquely locate the entry of a key by h(x). 
However, this hash function is a time consuming function, since 
there are 1000000 iterations to get h(x).

Problem 2.

The key to implement a symbol table that uses hashing in 
this problem is to implement the hash function using Horner's
rule.

int char_to_int(char c) // convert character to integer
{
	if(c>='a' && c<='z') return c-'a'+1;
	else if(c>='A' && c<='Z') return c-'A'+1;
	else {
	     cout<<"error"<<endl;
		exit(1);
		}
}

int hash(char str[])
{
	int l=strlen(str);
	int a[100];    // a[] stores the corresponding integer 
	           // for each character of str[].     
		   int i;
		   int h;
		   
		   for(i=0;i<l;i++) {a[i]=char_to_int(str[i]);cout<<a[i]<<"  ";}
		   h=0;
		   for(i=0;i<l-1;i++){
			h+=a[i];
				h*=32;
					h=h%TableSize;
					}		
					h+=a[l=1];
					h=h%TableSize;
					return h;
}

The time required for an insertion only increases a little, since
we don't have to access the entries sequentially. We can use
hash function to compute the exact position of a key.