Ada Lab 2009

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Algorithms Lab Manual

printf("\n Element %d is found at position %d",k,pos+1);printf("\n Time taken is %lf CPU1 cycles\n",(end-begin)/CLK_TCK);getch();break;

case 2:printf("\nEnter the number of elements\n");scanf("%d",&n);printf("\nEnter the elements of an array\n");for(i=0;ihigh)return -1;

if(k==a[mid])return(mid);

elseif(k

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return binsearch(n,a,k,low,mid-1);elsereturn binsearch(n,a,k,mid+1,high);

}

int linsearch(int n,int a[],int k){delay(1000);if(n

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Element 12 is found at position 2

Time taken is 1.978022 CPU1 cycles

Case 2

.....MENU.....1.Binary Search

2.Linear Search

3.Exit

Enter your choice

2

Enter the number of elements

4

Enter the elements of an array3

69

12

Enter the elements to be searched9

Element 9 is found at position 3Time taken is 3.021978 CPU cycles

2. Sort a given set of elements using the Heap sort method and determine the time taken to

sort the elements. Repeat the experiment for different values of n, the number of elements in

the list to be sorted and plot a graph of the time taken versus n.

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#include#include#include

void heapcom(int a[],int n){

int i,j,k,item;for(i=1;ia[k]){

a[j]=a[k];j=k;k=j/2;

}a[j]=item;

}}void adjust(int a[],int n){

int item,i,j;j=1;

item=a[j];i=2*j;while(i

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void heapsort(int a[],int n){

int i,temp;delay(1000);heapcom(a,n);

for(i=n;i>=1;i--){temp=a[1];a[1]=a[i];a[i]=temp;adjust(a,i);

}}void main()

{int i,n,a[20],ch=1;clock_t start,end;clrscr();while(ch){printf("\n enter the number of elements to sort\n");scanf("%d",&n);printf("\n enter the elements to sort\n");for(i=1;i

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8

5

63

1

the sorted list of elemnts is

1

35

6

8

3. Sort a given set of elements using Merge sort method and determine the time taken to sort

the elements. Repeat the experiment for different values of n, the number of elements in the

list to be sorted and plot a graph of the time taken versus n.

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#include#include#include#define max 20

void mergesort(int a[],int low,int high);void merge(int a[],int low,int mid,int high);void main(){

int n,i,a[max],ch=1;clock_t start,end;clrscr();while(ch){

printf("\n\t enter the number of elements\n");

scanf("%d",&n);printf("\n\t enter the elements\n");for(i=0;i

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time taken=0.824176

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4. Sort a given set of elements using Selection sort and hence find the time required to sort

elements. Repeat the experiment for different values of n, the number of elements in the list

to be sorted and plot a graph of the time taken versus n.

#include#include#includevoid main(){

int i,n,j,min,k,a[20],ch=1;clock_t begin,end;clrscr();while(ch){

printf("\n enter the number of elements\n");scanf("%d",&n);printf("\n enter the elements to be sorted\n");for(i=0;i

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OUTPUT

enter the number of elements5

enter the elements to be sorted8

3

51

9

the sorted list of elements are:1 3 5 8 9

time taken:0.824176

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5. a. Obtain the Topological ordering of vertices in a given digraph.

#include

#include#define max 20

int a[max][max],n;void topological_sort();void main(){

int i,j;clrscr();printf("\n enter the number of vertices\n");scanf("%d",&n);printf("\n enter the adjacency matrix\n");for(i=1;i

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5 b. Implement All Pair Shortest paths problem using Floyd's

algorithm.

#include#include

#includeint cost[10][10],a[10][10];void all_paths(int [10][10],int [10][10],int);int min1(int,int);

void main(){

int i,j,n;clrscr();printf("\n enter the number of vertices\n");scanf("%d",&n);printf("\n enter the adjacency matrix\n");for(i=1;i

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6. Implement 0/1 Knapsack problem using dynamic programming.

#include#includeint v[20][20];

int max1(int a,int b){return(a>b)?a:b;

}void main(){

int i,j,p[20],w[20],n,max;clrscr();printf("\n enter the number of items\n");scanf("%d",&n);for(i=1;i

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for(i=n;i>=1;i--)if(v[i][j]!=v[i-1][j]){

printf("\t item %d:",i);j=j-w[i];}printf("}");getch();

}

OUTPUT

enter the number of items

4

enter the weight and profit of the item 1:2 12




enter the capacity of the knapsack5

The table is0 0 0 0 0 0

0 0 12 12 12 12

0 10 12 22 22 220 10 12 22 30 32

0 10 15 25 30 37

The maximum profit is 37

The most valuable subset is:{ item 4: item 2: item 1:}

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7. From a given vertex in a weighted connected graph, find shortest

paths to other vertices using Dijkstra's algorithm.

#include

main (){int n, cost[15][15], i, j, s[15], v, u, w, dist[15],

num, min;clrscr();printf ("Enter the vertices please\n");scanf ("%d", &n);printf ("Enter the cost of the edges please\n");printf ("Enter 999 if the edge is not present or for the

self loop\n");for (i = 1; i

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dist[w] = (dist[u] + cost[u][w]);}

}}

printf ("VERTEX\tDESTINATION\tCOST\n");for (i = 1; i

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8. Sort a given set of elements using Quick sort method and determine the time taken to sort

the elements. Repeat the experiment for different values of n, the number of elements in the

list to be sorted and plot a graph of the time taken versus n.

#include#include#includevoid quicksort(int[],int,int);int partition(int[],int,int);void main(){

int i,n,a[20],ch=1;clock_t begin,end;clrscr();while(ch){

printf("\n enter the number of elements\n");scanf("%d",&n);printf("\n enter the array elements\n");for(i=0;i

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int key,i,j,temp,k;key=a[low];i=low+1;j=high;while(i

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9. Find Minimum Cost Spanning Tree of a given undirected graph

using Kruskal's algorithm-

#include#includeint root[10], flag = 0, count=0, temp, min;int a[20], cost[20][20], n, i, j, k, totalcost = 0, x, y;void find_min (), check_cycle (), update ();main (){clrscr();printf ("Enter the number of vertices please\n");scanf ("%d", &n);printf ("Enter the cost of the matrix please\n");for (i = 1; i

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OUTPUT

Enter the number of vertices please

4Enter the cost of the matrix please999 1 5 2

1 999 999 999

5 999 999 32 999 3 999

1 ---> 2 = 1

1 ---> 4 = 23 ---> 4 = 3

The graph is connected & the min cost is 6

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10. a. Print all the nodes reachable from a given starting node in a digraph using Breadth

First Search method.

#include

#include

void distance(int,int);int a[10][10];

void main()

{int i,j,n;

clrscr();

printf("\n Enter the number of vertices in the diagraph:");

scanf("%d",&n);printf("\n Enter the adjacency matrix\n");

for(i=1;i

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OUTPUT

Enter the number of vertices in the diagraph:4

Enter the adjacency matrix0 1 1 1

0 0 0 1

0 0 0 0

0 0 1 0

the starting vertex is 1

the vertex 1 to 2 is of distance=1



press enter for other source vertex










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10 b. Check whether a given graph is connected or not using DFS method.

#include#includevoid dfs(int n,int cost[10][10],int u,int s[]){

int v;s[u]=1;for(v=0;v

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connected=1;}

if(connected==1)printf("graph is connected\n");elseprintf("graph is not connected\n");getch();

}

OUTPUT

Case 1:

enter the number of nodes

4

enter the adjacency matrix

0 0 0 10 0 0 0

0 0 1 0

0 0 0 1

graph is not connected

Case 2:

enter the number of nodes4

enter the adjacency matrix1 1 1 1

1 1 1 11 1 1 1

1 1 1 1graph is connected

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11. Find a subset of a given set S == {sl,s2,......sn} of n positive

integers whose sum is equal to a given positive integer d. Forexample, if S== (1, 2, 5, 6, 8} and d = 9 there are two solutions

{1,2,6} and {1,8}. A suitable message is to be displayed if the given problem

instance doesn't have a solution.

#includeint s[10],d,n,set[10],count=0;void display(int);int flag = 0;

void main(){

int subset(int,int);int i;clrscr();printf("Enter the Number of elements in the set\n");scanf("%d",&n);printf("enter the set values\n");for(i=0;id || i>=n) return;else{

set[count]=s[i];count++;subset(sum+s[i],i+1);count--;

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subset(sum,i+1);}

}

void display(int count){

int i;printf("{ ");for(i=0;i

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12. a. Implement Horspool algorithm for String Matching,

#include#includevoid main(){

int table[126];char t[100],p[25];int n,i,k,j,m,flag=0;clrscr();printf("Enter the Text\n");gets(t);n=strlen(t);printf("Enter the Pattern\n");gets(p);

m=strlen(p);for(i=0;i

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OUTPUT

Case 1:

Enter the Text

acharya_computer_science_engineering

Enter the Patternscience

The position of the pattern is 18

Case 2:

Enter the Textacharya_computer_sceince_engineering

Enter the Pattern

cjPattern is not found in the given text

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12. b. Find the Binomial Co-efficient using Dynamic Programming.

#include#includevoid main()

{ int i,j,k,n,c[50][50];clrscr();printf("\n enter the value of n & k\n");scanf("%d%d",&n,&k);for(i=0;i

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OUTPUT

enter the value of n & k

6 3

the table for valuation is

11 1

1 2 1

1 3 3 1

1 4 6 41 5 10 10

1 6 15 20

the binomial coefficient of C(6,3) is 20

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13. Find Minimum Cost Spanning Tree of a given undirected graph

using Prims algorithm.

#include

#includevoid main(){

int cost[20][20],t[20][20],near1[20],a[20];int i,j,n,min,minimum,k,l,mincost,c,b;clrscr();printf("\n enter the number of nodes\n");scanf("%d",&n);printf("\n enter the adjacency matrix\n");for(i=1;i

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a[j]=cost[j][near1[j]];if(min>a[j]){

min=a[j];

c=near1[j];b=j;printf("\n");

}}

}mincost=mincost+cost[b][c];near1[b]=0;for(k=1;kcost[k][b]))

near1[k]=b;}printf("\n\ the cost of minimum spanning tree is=

%d",mincost);getch();

}

OUTPUT

enter the number of nodes

4

enter the adjacency matrix

999 1 5 21 999 999 999

5 999 999 3

2 999 3 999

the cost of minimum spanning tree is=6

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14. Compute the transitive closure of a given directed graph

using Warshall's algorithm.

#include

#include

int a[10][10];void main(){

int i,j,k,n;clrscr();printf("\n enter the number of vertices\n");scanf("%d",&n);printf("\n enter the adjacency matrix\n");for(i=1;i

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OUTPUT

enter the number of vertices4

enter the adjacency matrix0 1 0 0

0 0 0 1

1 0 1 00 0 0 0

the tranitive closure is

0 1 0 10 0 0 1

1 1 1 1

0 0 0 0

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15. Implement N Queen's problem using Back Tracking

#include#include#include

int x[20],count=1;void queens(int,int);int place(int,int);

void main(){

int n,k=1;clrscr();printf("\n enter the number of queens to be placed\n");scanf("%d",&n);queens(k,n);

}void queens(int k,int n){

int i,j;for(j=1;j

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OUTPUT

enter the number of queens to be placed4

1 solution1 row 2 column

2 row 4 column

3 row 1 column4 row 3 column

2 solution

1 row 3 column

2 row 1 column3 row 4 column

4 row 2 column

Ada Lab 2009

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