Sorting Arrays Chapter 10

Agenda Review of Arrays  Sorting Arrays Bubble Sort Selection Sort Finding the smallest element in array Multidimensional arrays

Review Arrays You know how to declare, initialize, process arrays with loops, and pass them to functions: float stuff[10]={3, 4, 6, 8, 2, 1, 0}; for (int k=0; k<9; k++) stuff[k]=stuff[k+1]; Display(stuff, 10);

You can also pass one (or more) individual cells of an array to a function: int scores[8]={33, 54, 65, 84, 42, 61, 100, 53}; swap(scores[4], scores[1]); swap(scores[2], scores[7]); Notice a Pattern? void swap(int& x, int& y) { // exchanges the values of x , y: float temp = x; x = y; y = temp; }

Agenda Review of Arrays Sorting Arrays  Bubble Sort Selection Sort Finding the smallest element in array Multidimensional arrays

Sorting Arrays Computer scientists often need to sort arrays –Why? Because it’s easier to find things in the array when it is sorted Most data looks better displayed in sorted form (phone books, employee records, Lacrosse games) How can we sort an array? What is the algorithm? A: There are several!!

Bubble Sort Bubble sort is one of the simplest sorting algorithms It proceeds through a sequence of iterations, each time moving the next largest item into its correct position On each iteration, it compares each pair of consecutive elements, moving the larger element up

Bubble Sort 55 22 99 66 55

Bubble Sort 55 22 99 66 > 55 ?

Bubble Sort 55 22 99 66 swap

Bubble Sort 22 55 99 66 55

Bubble Sort 22 55 99 66 > 55 ?

Bubble Sort 22 55 99 66 99

Bubble Sort 22 55 99 66 > 99 ?

Bubble Sort 22 55 99 66 swap

Bubble Sort 22 55 66 99 Notice how the data “bubbles up” through the array moving slowly, one bin at a time After N-1 “Passes” or “Sweeps”, the final array is guaranteed to be sorted in ascending order, no matter what input data

Bubble Sort #include <iostream.h> void print(float a[], int n); //Prints array a void sort(float a[], int n);//Sorts array a void swap(float& , float&);//Swaps a[j] and a[j+1] void main() { float a[] = {55.5, 22.5, 99.9, 66.6, 44.4, 88.8, 33.3, 77.7}; print(a,8); sort(a,8); } void print(float a[], int n) for (int i=0; i<n-1; i++) cout<< a[i] << ", "; cout << a[n-1] << endl;

Bubble Sort (contd) void sort(float a[], int n) { for (int i=1; i<n; i++) for ( int j=0; j<n-1; j++) if(a[j] > a[j+1]) swap(a[j],a[j+1]); } void swap(float& x, float& y) float temp; temp=y; y=x; x=temp;

Selection Sort Another way of sorting is the selection sort The main idea is to keep finding the smallest (and next smallest) items in the array And move them into correct position (swap)

Selection Sort 1 2 3 55 22 99 66 data smallest small_pos 55 k 1 2 3 data 55 22 99 66 smallest small_pos 55 k 55 < smallest? F

Selection Sort 1 2 3 55 22 99 66 data smallest small_pos 55 k 1 2 3 data 55 22 99 66 smallest small_pos 55 k 22 < smallest? T

Selection Sort 1 2 3 55 22 99 66 data smallest small_pos 22 1 k 1 2 3 data 55 22 99 66 smallest small_pos 22 1 k 22 < smallest? T

Selection Sort 1 2 3 55 22 99 66 data smallest small_pos 22 1 k 1 2 3 data 55 22 99 66 smallest small_pos 22 1 k 99 < smallest? F

Selection Sort 1 2 3 55 22 99 66 data smallest small_pos 22 1 k 1 2 3 data 55 22 99 66 smallest small_pos 22 1 k 66 < smallest? F

Selection Sort—SWAP 1 2 3 55 22 99 66 Swap(data[k], data[small_pos]); 1 2 3 data 55 22 99 66 smallest small_pos 22 1 k Swap(data[k], data[small_pos]);

Selection Sort—Repeat 1 2 3 22 55 99 66 smallest small_pos 55 1 k 1 55 < smallest ? F

Selection Sort—Finding Smallest After (SIZE-1) iterations of the above, array is sorted The heart of this algorithm is finding the smallest element of the array (and it’s position or index small_pos): smallest=data[0]; // assume 0th cell small_pos=0; // is smallest for (n=0; n<SIZE; n++) // go thru array if (data[n]<smallest) // if smaller { small_pos=n; //save position smallest=data[n]; // and value }

Selection Sort—the whole function void Sort(int data[], int size) { int n, k, small_pos, smallest; for (k=0; k<size-1; k++) { smallest=data[k]; // assume kth cell small_pos=k; // is smallest for (n=k; n<SIZE; n++) if (data[n]<smallest)// if smaller { small_pos=n; //save position smallest=data[n]; // and value } Swap(data[k], data[small_pos]);

Agenda Review of Arrays Sorting Arrays Bubble Sort Selection Sort Finding the smallest element in array Multidimensional arrays 

Multidimensional Arrays The arrays we have looked at till now have been one-dimensional They are linear (or sequential) An array of arrays is called a multidimensional array A one-dimensional array of one-dimensional arrays is called a two-dimensional array

Multidimensional Arrays 1 2 3 4 An array

Multidimensional Arrays 0 1 2 3 4 5 COLUMNS 1 2 3 An array of arrays ROWS

Multidimensional Array Simplest way to define a multi-dimensional array is int matrix[4][6]; This would create a two-dimensional array of type int with 4 rows and 6 columns int matrix[4][6]={0};

Multidimensional Arrays 0 1 2 3 4 5 matrix COLUMNS 1 2 3 An array of arrays ROWS

Accessing a 2D Array matrix[2][3]=22; matrix[0][5]=44; 44 22 0 1 2 3 4 5 matrix 44 22 1 2 3

Processing a 2D Array w/Loop for(k=0; k<6; k++) matrix[3][k]=k; 0 1 2 3 4 5 matrix 44 22 1 2 3 4 5 1 2 3

2D Array Read/Print Example #include<iostream.h> void read(int a[][5]); //Read the input into two dimen array a void print(const int a[][5]);//Print array a void main() { int a[3][5]; read(a); print(a); } void read(int a[][5]) { cout << "Enter 15 integers, 5 per row:\n"; for (int i=0; i<3; i++) { for (int j=0; j<5; j++) cin >> a[i][j];

2D Array Example (contd) void print(const int a[][5]) { for (int i=0; i<3; i++) { cout << "Row " << i << ": "; for (int j=0; j<5; j++) cout << " " << a[i][j]; cout << endl; }

That’s a wrap ! What we learned today: Sorting Arrays Bubble Sort Selection Sort Multidimensional arrays

Go back home proud ! You’re brighter than Ar’ray’ !