Data Structures Arrays Array Most commonly used data

Data Structures Arrays

Array �Most commonly used data structure �Ordered array, in which the data is stored in ascending (or descending) key order. This arrangement makes possible a fast way of searching for a data item: the binary search.

Example �Attendance monitoring program for cricket team --- using Array. ◦ Insert player at arrival ◦ Search player ◦ Delete player after departure �Imagine that each player has been issued a team shirt with the player’s number on the back. �To make things visually interesting, the shirts come in a variety of colors --- number and color stored in array �Create an applet viewer for it --- insert player and randomly choose color NO DUPLICATION

Insertion / Searching �Each button press in a Workshop applet corresponds to a step that an algorithm carries out. The more steps required, the longer the algorithm takes. �Insertion taking One step because no empty cell in array ---- sequence (assume not doing dup) �Searching will take more steps ◦ Average is half of steps like N/2 ◦ Worst case scenario is N �The time an algorithm takes to execute is proportional to the number of steps, so searching takes much longer on the average (N/2 steps) than insertion (one step).

Deletion � 2 step procedure ◦ Search required item + Clear cell ◦ Fill holes/empty cell � A deletion requires (assuming no duplicates are allowed) searching through an average of N/2 elements and then moving the remaining elements (an average of N/2 moves) to fill up the resulting hole. This is N steps in all.

Duplicate Issues �Primary �Human key cannot duplicate error chance so check all data items before insertion. �Searching with duplicates ◦ N moves required (whole array search) �Insertion with duplicates �Deletion with duplicates ◦ N moves to search duplicates ◦ 1 step insertion ◦ N moves to search and N/2 moves to shift cells ◦ Average will be based on how many duplicates

Average moves for 3 operations Create program for this example Manage it with classes so that class can be used for some other purpose. E. g separate array insertion separately. Like store serial # of travelers cheque Apply abstraction

Ordered Array �Useful when more searching ◦ Linear Search ◦ Binary Search

Example

Logarithms & Equation