Question

1. a. Using C++, represent the following graph using adjacency matrix, and implement depth first searching (DFS) by stack (define it with class) to traverse the graph. 6 7 2 4 b. If starting with node 2, when node 7 is printed, what numbers are in the stack (for DFS)? Please draw the stack step by step to show how the numbers are pushed into and popped out of it. 2. a. Given a set of integer numbers as int Al1-(12, 8, 51, 0, 3, 7, 19, 6, 4, 21), please write down the divide and conquer procedure of quick sort (step by step), include all left and right positions adjustment, and overwriting. b. Using C/C++, define two integer arrays; each has 30 integers within [o, 99]. Use loop and rand0 to assign random integers to the arrays; then implement Selection and Insertion and Quick sort algorithms to sort the two arrays in ascending order respectively (i.e. using selection to sort the 1st, and quick to sort the 2nd). For each array, print all array elements after sorting to verifty the results c. based on 2.b and the sorted array, define a function of the Binary Search algorithm, then input a number in main) and call the binary search function to search a number in the sorted array and output the result (Note, search in one of the two sorted arrays will be enough) The following specifications will be expected for each programming proieçt in this lass

Answer 1

1.a

using namespace std; //namespace

#include<iostream> // header files

#include<conio.h>

#include<stdlib.h>

int cost[10][10],i,j,k,ver,stk[10],top,v,visit[10],visited[10];// required variables

int main(){ // main function

int ed;

cout <<"Enter no of vertices:"; // getting number of vertices

cin >> ver;

cout <<"Enter no of edges:"; // getting number of edges

cin >> ed;

cout <<"\nEDGES \n"; // asking the edges

for(k=0; k<ed; k++){

cin >>i>>j;

cost[i][j]=1; // making 1 in the adjacent matrix

cost[j][i]=1;

}

cout <<"Enter initial vertex to traverse from:"; // asking initial vertex

cin >>v;

cout <<"DFS ORDER OF VISITED VERTICES:"; // priting order

cout << v <<" "; // starting for initial vertex

visited[v]=1;

k=0;

while(k<ver) {// for every vertex

for(j=ver-1; j>=0; j--)// checking neighbour for every vertex

if(cost[ver][j]!=0 && visited[j]!=1 && visit[j]!=1) { //if neighbour

visit[j]=1; // make the neighbour as visited

stk[top++]=j; // push into stack

j=0; // break loop

}

ver=stk[--top]; // take vertex from top of stack

cout<<ver << " "; // print it

k++;

visit[ver]=0; // reapeat the same procedure

visited[ver]=1;

}

getch();

return 0;

}

Output;

1.b

2.a

2.b

#include<stdio.h> // header files

#include<conio.h>

void sel(int *a){ // function for sorting (selection sort)

int i,j,loc,temp,min; // declaring required variables

for(i=0;i<30;i++){

min=a[i]; // taking first value of array in min

loc=i; // index number storing in loc

for(j=i+1;j<30;j++){ // from 2nd to last element

if(min>a[j]){ // checking the min of all the ellements comapring with min

min=a[j]; // getting the smallest of all

loc=j; // and index number

}

}

temp=a[i]; // swapping those 2 elements

a[i]=a[loc];

a[loc]=temp;

}

printf("\n\nSorted list after selection sort is as follows\n");

for(i=0;i<30;i++) // printing the sorted list

printf("%d ",a[i]);

}

void qs(int a[],int low,int high){

int pivot;

if(low<high){ / Termination condition! /

pivot=partition(a,low,high); // Divide

qs(a,low,pivot-1);

qs(a,pivot+1,high); // conquer

}

}

int partition(int a[],int low,int high){

int pivot_item,left,right,temp;

pivot_item=a[low];

left=low;

right=high+1;

do {

do

left++; / Move left while item < pivot /

while(a[left]<pivot_item&&left<=high);

do

right--; / Move right while item > pivot /

while(pivot_item<a[right]);

if(left<right) {

temp=a[left];

a[left]=a[right];

a[right]=temp;

}

}while(left<right);

a[low]=a[right]; / right is final position for the pivot /

a[right]=pivot_item;

return(right);

}

main(){

int a1[30],i,a2[30]; // decalring 2 arrays

for (i=0;i<30;i++){ // for size of array

a1[i]=rand()%99; // fill the arrays with random elemenst in range 1 to 100

a2[i]=rand()%99;

}

printf("\nArray 1\n");

for(i=0;i<30;i++) // printing the sorted list

printf("%d ",a1[i]);

printf("\nArray 2\n");

for(i=0;i<30;i++) // printing the sorted list

printf("%d ",a2[i]);

sel(a1);

qs(a2, 0, 29);

printf("\n\nSorted list after quick sort is as follows\n");

for(i=0;i<30;i++) // printing the sorted list

printf("%d ",a2[i]);

getch();

}

Output:

2.c

#include<stdio.h> // header files

#include<conio.h>

void binary(int a[],int s) { // function to search an element in an array

int l = 0, h = 30,mid; // initial variables

while (l <= h) { // termination condition

mid = (l+h)/2; // calculating middle value of the array

if (a[mid] == s) { // if the searched element is the middle value

printf("\nSearch Element : %d : Found at Position : %d.\n", s, mid+1); // print it

break;

}

else if (a[mid] < s) // elese in 1st half of the array

l = mid + 1;

else

h = mid - 1; // or 2nd part of the array

}

if (l > h)

printf("\nSearch Element : %d, Not Found \n", s);

}

void sel(int *a){ // function for sorting (selection sort)

int i,j,loc,temp,min; // declaring required variables

for(i=0;i<30;i++){

min=a[i]; // taking first value of array in min

loc=i; // index number storing in loc

for(j=i+1;j<30;j++){ // from 2nd to last element

if(min>a[j]){ // checking the min of all the ellements comapring with min

min=a[j]; // getting the smallest of all

loc=j; // and index number

}

}

temp=a[i]; // swapping those 2 elements

a[i]=a[loc];

a[loc]=temp;

}

printf("\n\nSorted list after selection sort is as follows\n");

for(i=0;i<30;i++) // printing the sorted list

printf("%d ",a[i]);

}

void qs(int a[],int low,int high){

int pivot;

if(low<high){ / Termination condition! /

pivot=partition(a,low,high); // Divide

qs(a,low,pivot-1);

qs(a,pivot+1,high); // conquer

}

}

int partition(int a[],int low,int high){

int pivot_item,left,right,temp;

pivot_item=a[low];

left=low;

right=high+1;

do {

do

left++; / Move left while item < pivot /

while(a[left]<pivot_item&&left<=high);

do

right--; / Move right while item > pivot /

while(pivot_item<a[right]);

if(left<right) {

temp=a[left];

a[left]=a[right];

a[right]=temp;

}

}while(left<right);

a[low]=a[right]; / right is final position for the pivot /

a[right]=pivot_item;

return(right);

}

main(){

int a1[30],i,a2[30],s; // decalring 2 arrays

for (i=0;i<30;i++){ // for size of array

a1[i]=rand()%99; // fill the arrays with random elemenst in range 1 to 100

a2[i]=rand()%99;

}

printf("\nArray 1\n");

for(i=0;i<30;i++) // printing the sorted list

printf("%d ",a1[i]);

printf("\nArray 2\n");

for(i=0;i<30;i++) // printing the sorted list

printf("%d ",a2[i]);

sel(a1);

qs(a2, 0, 29);

printf("\n\nSorted list after quick sort is as follows\n");

for(i=0;i<30;i++) // printing the sorted list

printf("%d ",a2[i]);

printf("\nEnter the number to be search: ");

scanf("%d",&s);// getting number to search

binary(a2,s);

getch();

}

Output: