Array Algorithms

1. Array Algorithms CS0007: Introduction to Computer Programming

2. Review • Arraysare… • complex variables that can hold multiple values of the same data type. • The size declarator indicates… • the number of elements the array can hold. • Individual values inside of an array are called… • elements. • An element’s index (or subscript) is… • a uniquely identifying number that is used to pinpoint its position in the array. • The enhanced forloop is… • a special loop that iterates through the elements in a collection (in this case array) and allows access to each element.

3. Comparing Arrays • Sometimes you want to know if two arrays contain all of the same elements. • What would be the output? int[] firstArray = {1, 2, 3, 4, 5}; int[] secondArray= {1, 2, 3, 4, 5}; if(firstArray== secondArray) System.out.print("The arrays are the same!"); else System.out.print("The arrays are NOT the same!"); • Answer: “The arrays are NOT the same” • Why? • Because the == operator compares the references in the array variables and they point to two different objects • How do we fix it? • We iterate through each the arrays and compare them element by element • Example: ArrayComparison.java

4. Sum, Average, and Minimum and Maximum • Four common algorithms used with arrays: • Sum of all the elements in the array (ArraySum.java) • Average of all the elements in the array (ArrayAverage.java) • Minimum element in the array (ArrayMin.java) • Max element in the array (ArrayMax.java)

5. Partially Filled Arrays • Sometimes you need to stores a series of items in an array, but you don’t know the number of items there are. • Solutions? • One solution is to create and array with the size being equal to the maximum number of possible items. • Problem? • If you do not fill the entire array, the array will only be partially filled. • If you go to process the items in the array, you need to only process valid items. • Solution? • You must keep track of the number of items you have currently in the array, as well. • Example: PartialArray.java

6. The Sequential Search Algorithm • Arrays are known as a data structures. • A Data Structure is a particular way of storing and organizing data in a computer so that it can be used efficiently. • There are many, many data structures and many are provided by the Java API. • The array is one of the more simple ones. • Although arrays are very useful, they may not be the most efficient structure depending on the situation you want to use them. • For instance, if you need to find an element with a specific value in an array, what can you do? • Simplest answer: look at every element in the array starting from the begining and see if it is the one we are looking for. • This is called the Sequential Search Algorithm (SequentialSearch.java).

7. The Sequential Search Algorithm • If we are talking about speed in terms of number of comparisons, what is the worst case scenario for the Sequential Search Algorithm? • The element we are looking for is the last element of the array. • If there are n elements, that means we have to check n elements in the worst case. • If there are n elements in the array what is the average case? • n+1/2 comparisons. • There are data structures that can theoretically perform better in the worst case • There are search algorithms that can perform better in the average case • We will revisit this in a bit.

8. The Selection Sort Algorithm • Another thing we often want do to with data, besides search it, is to sort it. • Names, grades, scores, etc. • Probably the most simple sorting algorithm is the Selection Sort Algorithm. • The Selection Sort Algorithm works as follows: • Search the array for the smallest element • Swap the first element with the smallest element • The first element is holding the correct value, so no longer consider it in the sort • Repeat previous steps for rest of array until the array is completely sorted. • Example: SelectionSort.java • There are many, many more sorting algorithms, most of which are more efficient than Selection Sort.

9. Binary Search • Sequential Search does not scale well to arrays with a large number of elements. • As stated before, there are many, many searching algorithms. One of which is the Binary Search Algorithm. • The general idea of Binary Search assumes that the array is sorted in ascending order, and it uses this knowledge to incrementally eliminate half of the elements from the array. • The algorithm is as follows: • Compare the target value to the element in the middle of the sorted array • If they are the same, the search ends • If the target value is larger than the element, then you know every element to the left of the middle is also not the element. • Eliminate all values to the left of the middle and repeat step 1 with the elements left in the array. • If the target value is smaller that the element, then you know every element to the right of the middle is also not the element. • Eliminate all values to the right of the middle and repeat step 1 with the elements left in the array. • If there is no more elements to eliminate in the array, the target value is not in the array.