2. [0][1][2][3][4][5][6][7][8][9] Bing David Ina Abhinav Erik Hyun Jim Fiona Gheeta Chelsea I can easily loop through all the student records by using a for loop. But if I want to access Jims record only, I have to start at 0 and loop through the array until I find it. With a big array this could be rather inefficient. Is there a better way? Sequential access good Arrays Direct access bad Remember! The array elements just hold references to the objects, not the objects themselves! Consider this array of Student records

3. Sequential access bad Hash tables Direct access good Bing David Ina Abhinav Erik Hyun Jim Fiona Gheeta Chelsea [0] [1] [2] [3] [4] [5] [6] [7] [8] [9] Hashing Function Jims student ID no. 6 The student records are stored in an array. The place in the array that a particular student is held is determined by the hashing function. The hashing function takes some value, e.g. a name, or, as here, a student id number, and translates it into an array index. So if we want to find Jims record we just give his id number to the hashing function and it tells us where his record is located.

4. Collisions What happens if the hashing function gives the same array index for two different students? This happens and it is called a collision. There are a number of ways of dealing with collisions, the details of which you dont need to know. But what you do need to know is that the performance of hash tables degrades over time because of multiple collisions. Bing David Ina Abhinav Erik Hyun Jim Fiona Gheeta Chelsea [0] [1] [2] [3] [4] [5] [6] [7] [8] [9] Hashing Function Hiros student ID no. 6 Collision!

5. Collisions [0] [1] [2] [3] [4] [5] [6] [7] [8] [9] Hashing Function Eriks student ID no. 4 Erik Davids student ID no. 1 David Hyuns student ID no. 4 Collision! Hyun goes into next available index Hyun If there had already been a lot of records in the array when the collision happened, Hyun may have been pushed a long way down the array. Later, when we try to access Hyuns record, the hashing function still gives us 4 as the place to find him. But hes not there! So we have to do a sequential search from index number 4, through the array to find him. This is the reason that hash table performance degrades over time.

6. The Hashing Algorithm The simplest way to translate the Student ID into an array index is to use the modulo operator (% in Java). The modulo operator returns the remainder of a division operation, for example 11 % 4 = 3. Question: If we have an array of 10 elements, what do we need to mod our Student IDs by to be sure of getting some value from 0 to 10? Answer: 11 Question: Lets say we have an array of size N. Now what to we need to mod our Student IDs by? Answer: N+1