Sorting Algorithms. Selection Sort Algorithm

Transcription

1 Sorting Algorithms Kirkuk Common problem: sort a list of values, starting from lowest to highest. List of exam scores, Words of dictionary in alphabetical order, Students names listed alphabetically, Student records sorted by ID#. Main types of sorting algorithms: Selection sort, Insertion sort, Bubble sort. Selection Sort Algorithm Depends on finding the smallest item and swap it with the first item of the unsorted side. Example: we are given an array of six integers that we want to sort from smallest to largest. Start by finding the smallest entry. 1

2 Kirkuk Swap the smallest entry with the first entry. Part of the array is now sorted. Find the smallest element in the unsorted side.

3 Kirkuk Swap with the front of the unsorted side. Swap with the front of the unsorted side. We have increased the size of the sorted side by one element. 3

4 Kirkuk The process continues... The process continues... The process continues... 4

5 Kirkuk The process keeps adding one more number to the sorted side, which has the smallest numbers, arranged from small to large. We can stop when the unsorted side has just one number, since that number must be the largest number. The array is now sorted, We repeatedly selected the smallest element, and moved this element to the front of the unsorted side. 5

6 Kirkuk Example 1: Write a C++ program to apply the selection sorting algorithm on a 10-element 1D array. #include<iostream.h> #include<conio.h> #define size 10 int i,j,temp,smallest; void selection_sort(int array[size]) for(i=0;i<size-1;i++) smallest=i; for(j=i+1;j<size;j++) if(array[smallest]>array[j]) smallest=j; if(smallest!=i) temp=array[i]; array[i]=array[smallest]; array[smallest]=temp; void main() int a[size]; cout<<"enter elements of array[10]"<<endl; for(i=0;i<size;i++) //reading array cout<<"enter element NO."<<i+1<<": "; cin>>a[i]; cout<<"\nthe array before sorting:\n"; for(i=0;i<size;i++) //printing array cout<<a[i]<<"\t"; selection_sort(a); cout<<"\n\nthe array after sorting:\n"; for(i=0;i<size;i++) cout<<a[i]<<"\t"; getch(); 6

7 Bubble Sort Algorithm Kirkuk The Bubble Sort algorithm looks at pairs of entries in the array, and swaps their order if needed. The same process is repeated till the loop ends and the array is sorted completely. Example: we are given an array of six integers that we want to sort from smallest to largest. 7

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10 Kirkuk Repeat till the end 10

11 Kirkuk Example : Write a C++ program to apply the bubble sorting algorithm on a 10-element 1D array. #include<iostream.h> #include<conio.h> #define size 10 int i,j,k,temp; void bubble_sort(int array[size]) for(k=0;k<size-1;k++) for(i=0;i<size-1;i++) for(j=i+1;j<size;j++) if(array[i]>array[j]) temp=array[i]; array[i]=array[j]; array[j]=temp; void main() int a[size]; cout<<"enter elements of array[10]"<<endl; for(i=0;i<size;i++) //reading array cout<<"enter element NO."<<i+1<<": "; cin>>a[i]; cout<<"\nthe array before sorting:\n"; for(i=0;i<size;i++) //printing array cout<<a[i]<<"\t"; bubble_sort(a); cout<<"\n\nthe array after sorting:\n"; for(i=0;i<size;i++) cout<<a[i]<<"\t"; getch(); 11

12 Searching Algorithms Kirkuk A search algorithm is a method of locating a specific item of information in a larger collection of data. We are going to discuss two algorithms for searching the contents of an array. Linear Search This is a very simple algorithm. It uses a loop to sequentially step through an array, starting with the first element. It compares each element with the value being searched for and stops when that value is found or the end of the array is reached. Advantages and Disadvantages: The advantage is its simplicity. It is easy to understand Easy to implement Does not require the array to be in order The disadvantage is its inefficiency If there are 0,000 items in the array and what you are looking for is in the 19,999 th element, you need to search through the entire list. 1

13 Kirkuk Example 3: write a C++ program to search an item in a 10-element 1D array using linear search algorithm. #include<iostream.h> #include<conio.h> #define size 10 int i; void linear_search(int array[size],int item) for(i=0;i<size;i++) if(array[i]==item) cout<<"\ndata found, location = "<<i; i=size+1; if(i==size) cout<<"\ndata not found!"; void main() int a[size],x; cout<<"enter elements of array[10]"<<endl; for(i=0;i<size;i++) //reading array cout<<"enter element NO."<<i+1<<": "; cin>>a[i]; cout<<"\nthe array is\n"; for(i=0;i<size;i++) //printing array cout<<a[i]<<"\t"; cout<<"\n\nenter that value you want to search for: "; cin>>x; linear_search(a,x); getch(); Homework 4: Re-write the linear search function using (while) instead of (for). 13

14 Binary Search Kirkuk The binary search is much more efficient than the linear search. It requires the list to be in order. The algorithm starts searching with the middle element. If the item is less than the middle element, it starts over searching the first half of the list. If the item is greater than the middle element, the search starts over starting with the middle element in the second half of the list. It then continues halving the list until the item is found. Example 4: write a C++ program to search an item in a 10-element 1D array using binary search algorithm. #include<iostream.h> #include<conio.h> #define size 10 int i,j,k,temp; void bubble_sort(int array[size]) for(k=0;k<size-1;k++) for(i=0;i<size-1;i++) for(j=i+1;j<size;j++) if(array[i]>array[j]) temp=array[i]; array[i]=array[j]; array[j]=temp; void binary_search(int array[size],int item) int first=0,last=size-1,middle,location=-1; bool found=false; while(!found && first<=last) 14

15 middle=(first+last)/; //calculate middle point if(array[middle]==item) found=true; location=middle; else if(item<array[middle]) last=middle-1; else first=middle+1; if(location==-1) cout<<"\ndata not found!"; else cout<<"data found, location = "<<location; void main() int a[size],x; cout<<"enter elements of array[10]"<<endl; for(i=0;i<size;i++) //reading array cout<<"enter element NO."<<i+1<<": "; cin>>a[i]; cout<<"\nthe array before sorting:\n"; for(i=0;i<size;i++) //printing array cout<<a[i]<<"\t"; bubble_sort(a); cout<<"\n\nthe array after sorting:\n"; for(i=0;i<size;i++) cout<<a[i]<<"\t"; cout<<"\n\nenter that value you want to search for: "; cin>>x; binary_search(a,x); getch(); Kirkuk 15

16 Simulink in MATLAB Kirkuk Used to model, analyze and simulate dynamic systems using block diagrams. Provides a graphical user interface for constructing block diagram of a system, therefore is easy to use. However modeling a system is not necessarily easy! Model simplified representation of a system e.g. using mathematical equation We simulate a model to study the behavior of a system need to verify that our model is correct expect results. Hint: Knowing how to use Simulink or MATLAB does not mean that you know how to model a system Example 5: Build a Simulink model that solves the differential equation Initial condition First, sketch a simulation diagram of this mathematical model (equation). Solution: x ( 0) = 1. Input is the forcing function 3sin(t). Output is the solution of the differential equation x(t). ( ) x = 3sin t 16

17 Now build this model in Simulink Kirkuk 17

18 Kirkuk Example 6: Simulate the resonant circuit and display the current waveform as we change the frequency dynamically. Observe the current. What do you expect? The amplitude of the current waveform will become maximum at resonant frequency, i.e. at ω = 1000 rad/s. How to model our resonant circuit? 18

19 Kirkuk Writing KVL around the loop: Differentiate time and re-arrange: Taking Laplace transform: Simplify the equation: Thus the current can be obtained from the voltage: 19

20 Moving to Simulink to create the simulation circuit. Start Simulink by typing simulink at Matlab prompt Kirkuk Constructing the model using Simulink: Drag and drop block from the Simulink library window to the untitled window Substitution of values: 0

21 Kirkuk We need to vary the frequency and observe the current: The waveform can be displayed using scope similar to the scope in the lab Output waveform: 1