# SI204 Class 27: Sorting and Searching

None.

Lecture

## Indices rather than elements

Often with arrays it's more powerful to return the index of an element with a certain property, rather than the value of the element. For example, if `string *name` is an array of names of contest participants, and ``` int *score``` is an array of scores, such that participant `name[i]` has score `score[i]`, then knowing the value of the largest element in `score` won't tell me who the winner is, but knowing the index (i) of the largest element in `score` will.

So, with this in mind, let's consider writing a function `maxIndex` that will return the index of the element with the maximum value in array arrayIn of ``` sizeIn``` objects of type ``` int```.

`int maxIndex(int *arrayIn, int sizeIn)`
`{`
`  int iMax = 0;`
`  for(int i = 1; i < sizeIn; i++)`
`    if (arrayIn[iMax] < arrayIn[i])`
`      iMax = i;`
`  return iMax;`
`}`

Very simple function! Now, using our above example, the winner of our contest is `NAME[maxindex(SCORE,N)]`.

## Sorting using Selection Sort (Selection Sort code)

Consider the following function that uses our `maxIndex` function:

`void mystery(int *arrayIn, int sizeIn)`
`{`
`  for(int size = sizeIn; size > 1; size--)`
`  {`
`    int k = maxIndex(arrayIn,size);`
`    int temp = arrayIn[size-1];`
`    arrayIn[size-1] = arrayIn[k];`
`    arrayIn[k] = temp;`
`  }`
`}`
`    `

What does the `mystery` function do? Well, it starts by swapping the largest element in the array with the last element of the array, and then pretends the last array slot isn't there any more. Hopefully, you see that this puts the largest at the back of the array, the next largest in the second to last spot, etc. until the array is in sorted order! This sorting algorithm is known as Selection Sort, because it selects the largest of the remaining elements and puts it in its proper spot in the sorted array. If you define the ``` swap``` function (as in Class 18), you can write a particularly succinct version of this function:

`void selectionSort(int *arrayIn, int sizeIn)`
`{`
`  for(int size = sizeIn; size > 1; size--)`
`    swap(arrayIn[maxindex(arrayIn,size)],arrayIn[size-1]);`
`}`

This is actually a subtle and important function for the way it uses pass-by-reference on array elements. Make sure you understand how it works!

## Search

Searching for values in arrays is another fundamental operation. The basic format is ``` search(A,N,x)```, where we search for value `x` in the array `A` of `N` elements, and return the index of an element of `A` that matches the value `x`. If no such element is found, an index of `N` may be returned and, since it is not a valid index, the caller of the function can determine that no match was found. For example, to search in an array of objects of type `string`, I'd define the following function:

`int search(string *arrayIn, int sizeIn, string target)`
`{`
`  int i = 0;`
`  while(i < sizeIn && arrayIn[i] != target)`
`    i++;`
`  return i;`
`}`
`    `

## Problems

1.      Write a program that reads in a list of 10 names (first name followed by last name) and prints them out in the usual order - i.e. alphabetically by last name, using first names to break ties.

Assoc Prof Christopher Brown