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Hash Tables

Hash Functions

Problems

Problems

As mentioned briefly in the previous section, there are multiple ways for constructing a hash function. Remember that hash function takes the data as input (often a string), and return s an integer in the range of possible indices into the hash table. Every hash function must do that, including the bad ones. So what makes for a good hash function?

Characteristics of a Good Hash Function

There are four main characteristics of a good hash function: 1) The hash value is fully determined by the data being hashed. 2) The hash function uses all the input data. 3) The hash function "uniformly" distributes the data across the entire set of possible hash values. 4) The hash function generates very different hash values for similar strings.

Let's examine why each of these is important: Rule 1: If something else besides the input data is used to determine the hash, then the hash value is not as dependent upon the input data, thus allowing for a worse distribution of the hash values. Rule 2: If the hash function doesn't use all the input data, then slight variations to the input data would cause an inappropriate number of similar hash values resulting in too many collisions. Rule 3: If the hash function does not uniformly distribute the data across the entire set of possible hash values, a large number of collisions will result, cutting down on the efficiency of the hash table. Rule 4: In real world applications, many data sets contain very similar data elements. We would like these data elements to still be distributable over a hash table.

So let's take as an example the hash function used in the last section:


int hash(char *str, int table_size)
{
	int sum;

	// Make sure a valid string passed in
	if (str==NULL) return -1;

	// Sum up all the characters in the string
	for( ; *str; str++) sum += *str;

	// Return the sum mod the table size
	return sum % table_size;
}

Which rules does it break and satisfy? Rule 1: Satisfies. The hash value is fully determined by the data being hashed. The hash value is just the sum of all the input characters. Rule 2: Satisfies. Every character is summed. Rule 3: Breaks. From looking at it, it isn't obvious that it doesn't uniformly distribute the strings, but if you were to analyze this function for a large input you would see certain statistical properties bad for a hash function. Rule 4: Breaks. Hash the string "bog". Now hash the string "gob". They're the same. Slight variations in the string should result in different hash values, but with this function they often don't.

So this hash function isn't so good. It's a good introductory example but not so good in the long run.

There are many possible ways to construct a better hash function (doing a web search will turn up hundreds) so we won't cover too many here except to present a few decent examples of hash functions:


/* Peter Weinberger's */
int hashpjw(char *s)
{
	char *p;
	unsigned int h, g;
	h = 0;
	for(p=s; *p!='\0'; p++){
		h = (h<<4) + *p;
		if (g = h&0xF0000000) {
			h ^= g>>24;
			h ^= g;
		}
	}
	return h % 211;
}

Another one:


/* UNIX ELF hash
 * Published hash algorithm used in the UNIX ELF format for object files
 */
unsigned long hash(char *name)
{
	unsigned long h = 0, g;

	while ( *name ) {
		h = ( h << 4 ) + *name++;
		if ( g = h & 0xF0000000 )
		h ^= g >> 24;
		h &= ~g;
	}

	return h;
}

or possibly:


/* This algorithm was created for the sdbm (a reimplementation of ndbm) 
 * database library and seems to work relatively well in scrambling bits
 */
static unsigned long sdbm(unsigned char *str)
{
	unsigned long hash = 0;
	int c; 
	while (c = *str++) hash = c + (hash << 6) + (hash << 16) - hash;
	return hash;
}

or possibly:


/* djb2
 * This algorithm was first reported by Dan Bernstein
 * many years ago in comp.lang.c
 */
unsigned long hash(unsigned char *str)
{
	unsigned long hash = 5381;
	int c; 
	while (c = *str++) hash = ((hash << 5) + hash) + c; // hash*33 + c
	return hash;
}

or another:


char XORhash( char *key, int len)
{
	char hash;
	int  i;
	for (hash=0, i=0; i<len; ++i) hash=hash^key[i];
	return (hash%101);           /* 101 is prime */
}

You get the idea... there are many possible hash functions. For coding up a hash function quickly, djb2 is usually a good candidate as it is easily implemented and has relatively good statistical properties.

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