A Practical Introduction to Data Structures and Algorithm Analysis

Sec. 9.4 Hashing 335For example, because the ASCII value for “A” is 65 and “Z” is 90, sum willalways be in the range 650 to 900 for a string of ten upper case letters. Fora hash table of size 100 or less, a good distribution results with all slots inthe table accepting either two or three of the values in the key range. For ahash table of size 1000, the distribution is terrible because only slots 650 to900 can possibly be the home slot for some key value.Example 9.8 Here is a much better hash function for strings.long sfold(String s, int M) {int intLength = s.length() / 4;long sum = 0;for (int j = 0; j < intLength; j++) {char c[] = s.substring(j * 4, (j * 4) + 4).toCharArray();long mult = 1;for (int k = 0; k < c.length; k++) {sum += c[k] * mult;mult *= 256;}}char c[] = s.substring(intLength * 4).toCharArray();long mult = 1;for (int k = 0; k < c.length; k++) {sum += c[k] * mult;mult *= 256;}}return(Math.abs(sum) % M);This function takes a string as input. It processes the string four bytesat a time, and interprets each of the four-byte chunks as a single (unsigned)long integer value. The integer values for the four-byte chunks are addedtogether. In the end, the resulting sum is converted to the range 0 to M − 1using the modulus operator. 2For example, if the string “aaaabbbb” is passed to sfold, then the firstfour bytes (“aaaa”) will be interpreted as the integer value 1,633,771,8732 Recall from Section 2.2 that the implementation for n mod m on many C ++ and Java compilerswill yield a negative number if n is negative. Implementors for hash functions need to be careful thattheir hash function does not generate a negative number. This can be avoided either by insuringthat n is positive when computing n mod m, or adding m to the result if n mod m is negative.All computation in sfold is done using unsigned long values in part to protect against taking themodulus of an negative number.