containing dynamic programming and graph programming

1. 1
UNIVERSITY SCHOOL OF INFORMATION COMMUNICATION
AND TECHNOLOGY
LAB FILE-IT354
ALGORITHM DESIGN AND ANALYSIS
SUBMITTED TO SUBMITTED BY
ANURADHA CHUG SURAJ KUMAR
ASSISTANT PROFESSOR 03616403215
B.TECH CSE VI SEM

2. 2
INDEX
PROGRAMS PAGE NO. DATE SIGN
1. PROGRAM FOR SEARCHING. 3 21/1
2. PROGRAM FOR SORTING (ALL) 6 28/1 TO 18/2
3. PROGRAM FOR BREADTH FIRST SEARCH. 14 28/2
4. PROGRAM FOR DEPTH FIRST SEARCH. 15 28/2
5. PROGRAM FOR KRUSKAL ALGORITHM. 16 4/3
6. PROGRAM FOR PRIM’S ALGORITHM. 17 4/3
7. PROGRAM TO IMPLEMENT DIJKSTRA ALGORITHM. 20 11/3
8. PROGRAM TO IMPLEMENT FLOYAD WARSHAL ALGORITHM. 22 11/3
9. PROGRAM TO IMPLEMENT TOPLOGICAL SORT. 23 21/3
10. PROGRAM FOR MEDIAN ORDER STATISTICS. 24 21/3
11. PROGRAM FOR BELLMAN FORD ALGORITHM. 26 21/3
12. PROGRAM FOR MATRIX CHAIN MULTIPLICATION 28 2/4
13. PROGRAM FOR LONGEST COMMOM SUSEQUENCE 30 2/4
14. PROGRAM FOR HUFFMAN CODING. 32 2/4
15. PROGRAM FOR OPTIMAL BST. 35 2/4
16. STRING MATCHING USING NAÏVE ALGO 37 9/4
17. STRING MATCHING USING FINITE AUTOMATA METHOD 39 9/4
18. STRING MATCHING USING RABIN KARP ALGO 42 9/4
19. STRING MATCHING USING KMP ALGO 44 9/4

3. 3
PROGRAM FOR SEARCHING
#include<bits/stdc++.h>
using namespace std;
long int a[1000000];
vector<long int> b[100000];
void linear (long int k,long int n)
{
long int i,j;
for(i=0;i<n;i++)
{
if(a[i]==k)
cout<<"found at "<<i+1<<" position n";
}
}
long int binary(long int k,long int n)
{
long int i,j,hi=n-1,mid,lo=0,found=0;
sort(a,a+n);
mid=(hi+lo)/2;
while(found==0&&lo<=hi)
{
if(a[mid]==k)
{
found=mid+1;
break;
}
else if(k<a[mid])
{
hi=mid-1;
}
else
{
lo=mid+1;
}
mid=(lo+hi)/2;
}
return found;
}
int main()

4. 4
{
long int i,j,k,l,n,x,z=0;
clock_t start, end1;
cout<<"enter the size of arrayn";
cin>>n;
cout<<"enter the arrayn";
for(i=0;i<n;i++)
cin>>a[i];
cout<<"select followingn";
cout<<"select 1 for linear searchn";
cout<<"selcet 2 for binary searchn";
cout<<"selcet 3 for direct searchn";
cin>>l;
if(l==1)
{
cout<<"enter the data to findn";
cin>>k;
start=clock();
linear(k,n);
}
if(l==2)
{
long int m=5;
cout<<"enter the data to findn";
cin>>k;
j=binary(k,n);
if(j==0)
cout<<"not findn";
else
cout<<"found at"<<j<<"n";
}
if(l==3)
{
for(i=0;i<n;i++)
{
x=a[i]%100000;
b[x].push_back(a[i]);

5. 5
}
cout<<"enter the number to findn";
cin>>k;
x=k%100000;
for(j=0;j<b[x].size();j++)
{
if(b[x][j]==k)
{
cout<<"found n";
z=1;
break;
}
}
if(z==0)
cout<<"not foundn";
}
end1=clock();
double time=(end1-start)/CLOCKS_PER_SEC;
cout<<time<<" sec is taken";
}

6. 6
PROGRAM FOR SORTING(ALL)
#include<bits/stdc++.h>
using namespace std;
vector< int> b1[13000];
vector< int> b2[13];
vector< int> b3[13];
int a[100000],b[10004],n=10000;
void select(int);
void bubble(int);
void insertion(int);
void mergesort(int[],int);
void merge1(int[],int[],int[],int,int);
void quick(int,int);
int partion(int,int);
void print(int);
void heapify(int [], int , int );
void heap(int []);
int main()
{
int start=0,last,start1;
char t='y';
int i,j,k,l,x,s=0,end1;
double time;
for (int i=0;i<10000;i++)
{
a[i]=rand()%1000;
}
printf("enter 1 for selection sortn");
printf("enter 2 for bubble sortn");
printf("enter 3 for insertion sortn");
printf("enter 4 for merge sortn");
printf("enter 5 for heap sortn");
printf("enter 6 for quick sortn");
cout<<"enter 7 for bucket sortn";
cout<<"enter 8 for radix sortn";
cout<<"enter 9 for counting sortn";
scanf("%d",&l);
switch(l)
{
case 1:
start1=clock();
select(n);
end1=clock();

7. 7
time=(end1-start)/CLOCKS_PER_SEC;
cout<<time<<" sec is taken";
print(n);
break;
case 2:
bubble(n);
print(n);
break;
case 3:
insertion(n);
print(n);
break;
case 4:
mergesort(a,n);
print(n);
break;
case 5:
heap(a);
print(n);
break;
case 6:
last=n-1;
quick(start,last);
print(n);
break;
}
if(l==7)
{
for(i=0;i<10000;i++)
{
x=a[i]/10;
b1[x].push_back(a[i]);
}
for(i=0;i<1000;i++)
{
sort(b1[i].begin(),b1[i].end());
}
for(i=0;i<1000;i++)
{
for(j=0;j<b1[i].size();j++)
cout<<b1[i][j]<<" ";
}
}

8. 8
if(l==8)
{
int max_digit=3;
for(i=0;i<10000;i++)
{
x=a[i]%10;
b1[x].push_back(a[i]);
}
for(i=0;i<10;i++){
for(j=0;j<b1[i].size();j++){
x=b1[i][j]%100;
x=x/10;
b2[x].push_back(b1[i][j]);
}
}
for(i=0;i<10;i++){
for(j=0;j<b2[i].size();j++){
x=b2[i][j]%1000;
x=x/100;
b3[x].push_back(b2[i][j]);
}
}
for(i=0;i<=9;i++)
{
for(j=0;j<b3[i].size();j++)
cout<<b3[i][j]<<" ",s++;
}
}
if(l==9)
{
k=0;
for(i=0;i<10000;i++)
b[a[i]]++;
for(i=1;i<=1000;i++)
b[i]+=b[i-1];
for(i=0;i<1000;i++)
{
for(j=k+1;j<=b[i];j++)
{
cout<<i<<" ";
}
k=b[i];
}

9. 9
}
}
void select(int n)
{
int i,k,m,l,temp;
for(l=0;l<n-1;l++)
{
k=a[l];
m=l;
for(i=l;i<n;i++)
{
if(k>a[i])
{
m=i;
k=a[i];
}
}
temp=a[l];
a[l]=k;
a[m]=temp;
}
}
void bubble(int n)
{
int i,k,temp;
for(i=0;i<n-1;i++)
{
for(k=0;k<n-i-1;k++)
{
if(a[k]>a[k+1])
{
temp=a[k+1] ;
a[k+1]=a[k];
a[k]=temp;
}
}
}
}
void insertion(int n)
{
int i=0,j,k,temp;
for(i=1;i<n;i++)
{

10. 10
j=i-1;
k=a[i];
while(k<a[j]&&j>=0)
{
a[j+1]=a[j];
j--;
}
a[j+1]=k;
}}
void mergesort(int a[10003],int n)
{
int i,j,k,mid=n/2;
int left[10000],right[10000];
if(n<2)
return;
else
{
for(i=0;i<mid;i++)
{
left[i]=a[i];
}
for(j=mid;j<n;j++)
{
right[j-mid]=a[j];
}
mergesort(left,mid);
mergesort(right,n-mid);
merge1(left,right,a,mid,n-mid);
}
}
void quick(int start,int last)
{
int index;
if(start>=last)
return;
index=partion(start,last);
quick(start,index-1);
quick(index+1,last);
}
void print(int n)
{
int i,s=0;

11. 11
for(i=0;i<n;i++)
{
printf("%d ",a[i]);
s++;
}
}
void merge1(int l[10003],int r[10003],int a[10003],int mid,int t)
{
int nl,nr,i=0,j=0,k=0;
nl=mid;
nr=t;
while(i<nl&&j<nr)
{
if(l[i]<r[j])
{
a[k]=l[i];
k++;
i++;
}
else
{
a[k]=r[j];
k++;
j++;
}
}
while(i<nl)
{
a[k]=l[i];
k++;
i++;
}
while(j<nr)
{
a[k]=r[j];
k++;
j++;
}
}
int partion(int start,int last)
{
int j,k,i,temp;
j=start;

12. 12
k=a[last];
for(i=start;i<=last;i++)
{
if(a[i]<k)
{
temp=a[i];
a[i]=a[j];
a[j]=temp;
j++;
}
}
temp=a[j];
a[j]=a[last];
a[last]=temp;
return(j);
}
void heap(int a[ ])
{
int heap_size = n;
for (int i = n / 2 - 1; i >= 0; i--)
heapify(a, heap_size, i);
for(int i = n-1; i >=0 ; i-- )
{
swap(a[ 0 ], a[ i ]);
heap_size = heap_size - 1;
heapify(a,heap_size,0);
}
}
void heapify(int a[], int n, int i)
{
int largest = i;
int l = 2*i + 1;
int r = 2*i + 2;
if (l < n && a[l] > a[largest])
largest = l;
if (r < n && a[r] > a[largest])
largest = r;
if (largest != i)
{
swap(a[i], a[largest]);
heapify(a, n, largest);
}
}

13. 13

14. 14
PROGRAM FOR BREADTH FIRST SEAFRCH.
#include<bits/stdc++.h>
using namespace std;
vector<long int >vect[100000];
long int b[10000];
void dfs(long int k)
{
long int i,l;
stack<long int > s;
s.push(k);
while(!s.empty())
{
l=s.top();
s.pop();
if(b[l]!=1){
for(i=0;i<vect[l].size();i++)
{
s.push(vect[l][i]);
}
b[l]=1;
cout<<l<<" ";}
}
}
int main()
{
long int i,j,k,l,m,n,u,v;
cin>>m>>n;
for(i=0;i<n;i++)
{
cin>>u>>v;
vect[u].push_back(v);
vect[v].push_back(u);
}
for(i=1;i<=n;i++)
{
if(b[i]==0)
dfs(i);
}}

15. 15
PROGRAM FOR DEPTH FIRST SEARCH
#include<bits/stdc++.h>
using namespace std;
vector<long int >vect[100000];
long int b[10000];
void dfs(long int k)
{
long int i,l;
stack<long int > s;
s.push(k);
while(!s.empty())
{
l=s.top();
s.pop();
if(b[l]!=1){
for(i=0;i<vect[l].size();i++)
{
s.push(vect[l][i]);
}
b[l]=1;
cout<<l<<" ";}
}}
int main()
{
long int i,j,k,l,m,n,u,v;
cout<<"enter the number of vertices and edgesn";
cin>>m>>n;
for(i=0;i<n;i++)
{
cin>>u>>v;
vect[u].push_back(v);
vect[v].push_back(u);
}
for(i=1;i<=n;i++)
{
if(b[i]==0)
dfs(i);
}}

16. 16
PROGRAM FOR KRUSKAL ALGORITHM
#include<bits/stdc++.h>
#define MAXN 102
using namespace std;
int P[MAXN], Rank[MAXN];
int Node, edg, Cost;
struct edge { int u, v; int cost; };
edge Edge[MAXN*MAXN]; edge Path[MAXN];
int com(const void *xy, const void *xz) { edge *x = (edge*)xy; edge *y = (edge*)xz; return (x->cost - y-
>cost); }
void In() {
int i; for(i = 1; i<= Node; i++) { P[i] = i; Rank[i] = 1;
} }
int Find(int n) {
if(P[n] != n) P[n] = Find(P[n]); return P[n];
}
void Link(int x, int y)
{
if(Rank[x] > Rank[y])
{
P[y] = x;
}
else
{
P[x] = y; if(Rank[x] == Rank[y]) Rank[y]++;
}
}
void Kruscal()
{
int x, y, total = 0; Cost = 0;
for(int i = 0; i<edg; i++)
{

17. 17
x = Find(Edge[i].u);
y = Find(Edge[i].v);
if(x != y)
{
Path[total++] = Edge[i]; Link(x,y);
Cost += Edge[i].cost; if(total == Node - 1) break;
} } }
void Cal() { qsort(Edge,edg,sizeof(edge),com);
Kruscal();
cout<<"Total Cast :"<<Cost<<endl;
for(int i = 0; i<Node-1; i++)
cout<<Path[i].u<<" "<<Path[i].v<<" "<<Path[i].cost<<endl; }
int main()
{
int i;
cout<<"enter the number of verticesn";
cout<<"enter the number of edgesn";
while(cin>>Node>>edg)
{
In();
for(i = 0; i<edg; i++)
cin>>Edge[i].u>>Edge[i].v>>Edge[i].cost;
Cal();
}
}

18. 18
PROGRAM FOR PRIMS ALGORITHM
#include<bits/stdc++.h>
using namespace std;
long int a[1000][1000],b[1000],near[1000][3];
vector<long int> vect;
#define inf 10000000
int main()
{
long int i,j,k,l,m,n,u,v,c,s=inf,cost=0,co=0,pos;
cin>>n>>m;
for(i=0;i<m;i++)
{
cin>>u>>v>>c;
a[u][v]=c;
a[v][u]=c;
}
for(i=1;i<=n;i++)
{
near[i][2]=inf;
for(j=1;j<=n;j++)
{
if(a[i][j]==0)
a[i][j]=inf;
}
}
pos=1;
for(i=1;i<=n;i++)
{
if(s>a[1][i])
s=a[1][i],pos=i;
}
vect.push_back(1);
vect.push_back(pos);
cost+=s;
co++;
b[1]=-1;
b[pos]=-1;
while(co!=n-1)
{
for(i=1;i<=n;i++)
{
if(b[i]!=-1)
{

19. 19
for(j=1;j<=n;j++)
{
if(b[j]==-1)
{
if(a[i][j]<near[i][2])
near[i][2]=a[i][j],near[i][1]=j;
}
}
}
}
s=inf;
for(i=1;i<=n;i++)
{
if(b[i]!=-1)
{
if(near[i][2]<s)
s=near[i][2],pos=i;
}
}
vect.push_back(near[pos][1]);
vect.push_back(pos);
cost+=s;
b[pos]=-1;
co++;
}
cout<<"cost is "<<cost<<" n";
for(i=0;i<2*co;i+=2)
{
cout<<vect[i]<<" "<<vect[i+1]<<"n";
}
}

20. 20
PROGRAM TO IMPLEMENT DIJKSTRA ALGORITHM
#include<bits/stdc++.h>
using namespace std;
bitset<1000005> b;
#define pi pair<int,int>
#define pb push_back
#define mp make_pair
#define inf 100000000000009
vector<pi> edges[1000002];
long long dis[1000002],node[1000002];
void printpath(long long int n)
{
if(n!=1)
printpath(node[n]);
cout<<n<<" ";
}
void path(long long int k)
{
priority_queue<long long int> q;
q.push(k);
long long int i,l;
while(!q.empty())
{
l=q.top();
q.pop();
for(i=0;i<edges[l].size();i++)
{
if(dis[l]+edges[l][i].second<dis[edges[l][i].first])
{
dis[edges[l][i].first]=dis[l]+edges[l][i].second;
q.push(edges[l][i].first);
node[edges[l][i].first]=l;
}
}
}
}
int main()
{
long long int t,n,i,j,k,l,u,v,w;
// printf("enter the number of vertices");

21. 21
cin>>n;
// printf("enter the number of vertices");
cin>>t;
while(t--)
{
cin>>u>>v>>w;
edges[u].pb(mp(v,w));
edges[v].pb(mp(u,w));
}
for(i=2;i<=n;i++)
dis[i]=inf;
dis[1]=0;
path(1);
if(dis[n]==inf) cout<<"-1"<<endl;
else{
printpath(n);
cout<<endl;
}
}

22. 22
PROGRAM TO IMPLEMET FLOYAD WARSHAL ALGORITHM
#include<bits/stdc++.h>
using namespace std;
#define inf 100000009;
long int a[1000][1000];
int main()
{
long int i,j,k,l,m,n,u,v,w;
cout<<"enter the number of vertex";
cin>>n;
cout<<"enter the number edges";
cin>>m;
for(i=1;i<=n;i++)
{
for(j=1;j<=n;j++)
a[i][j]=inf;
}
for(i=1;i<=m;i++)
{
cin>>u>>v>>w;
a[u][v]=w;
a[v][u]=w;
a[i][i]=0;
}
for(k=1;k<=n;k++)
{
for(i=1;i<=n;i++)
{
for(j=1;j<=n;j++)
{
a[i][j]=min(a[i][j],a[i][k]+a[k][j]);
}}}
for(i=1;i<=n;i++)
{
for(j=1;j<=n;j++)
cout<<a[i][j]<<" ";
cout<<"n";}}

23. 23
PROGRAM FOR TOPOLOGICAL SORT
#include<bits/stdc++.h>
using namespace std;
vector<long int >vect[100000];
long int b[10000];
stack<long int> s1;
void dfs(long int k)
{
long int i,l;
b[k]=1;
for(i=0;i<vect[k].size();i++)
{
if(b[vect[k][i]]!=1)
dfs(vect[k][i]);}
s1.push(k);}
int main()
{
long int i,j,k,l,m,n,u,v;
cin>>m>>n;
for(i=0;i<n;i++)
{
cin>>u>>v;
vect[u].push_back(v);
//vect[v].push_back(u); }
for(i=1;i<=n;i++)
{
if(b[i]==0)
dfs(i); }
while(!s1.empty()){
k=s1.top();
s1.pop();
cout<<k<<" ";
}

24. 24
PROGRAM FOR MEDIN ORDER STATISTICS
#include<bits/stdc++.h>
using namespace std;
long int a[10000],l,m,n;
long int partion(long int start,long int last)
{
long int j,k,i,temp;
j=start;
k=a[last];
for(i=start;i<=last;i++)
{
if(a[i]<=k&&i!=last)
{
temp=a[i];
a[i]=a[j];
a[j]=temp;
j++;
}
}
temp=a[j];
a[j]=a[last];
a[last]=temp;
l=j;
if(l==m-1){
return l; }
else if(m-1>l)
partion(l+1,n-1);
else
partion(0,l-1);
}
int main()
{
long int i,j=0,s,z=5;
cout<<"enter the size of arrayn";
cin>>n;
cout<<"enter the array elementsn";
for(i=0;i<n;i++)
cin>>a[i];
while(z--)
{
cout<<"enter the position to findn";
cin>>m;

25. 25
s=partion(0,n-1);
cout<<"the value is "<<a[s]<<"n";
}
}

26. 26
PROGRAM FOR BELLMAN FORD ALGORITHM
#include<bits/stdc++.h>
using namespace std;
# define inf 100000009
long int a[100000][5],dis[100005],dis1[100005];
int main()
{
long int i,j,k,l,m,n,u,v,w,z=0;
cout<<"enter the number of verticesn";
cin>>n;
cout<<"enter the number of edgesn";
cin>>m;
for(i=0;i<=n;i++)
dis[i]=inf;
dis[1]=0;
for(i=0;i<m;i++)
{
cin>>u>>v>>w;
a[i][0]=u;
a[i][1]=v;
a[i][2]=w;
}
for(i=1;i<=n-1;i++)
{
for(j=0;j<m;j++)
{
u=a[j][0];
v=a[j][1];
w=a[j][2];
if(dis[u]+w<dis[v])
dis[v]=dis[u]+w;
if(dis[v]+w<dis[u])
dis[u]=dis[v]+w;
}
}
for(i=1;i<=n;i++)
dis1[i]=dis[i];
for(j=0;j<m;j++)
{
u=a[j][0];
v=a[j][1];
w=a[j][2];
if(dis[u]+w<dis[v])
dis[v]=dis[u]+w;

27. 27
if(dis[v]+w<dis[u])
dis[u]=dis[v]+w;
}
for(i=1;i<=n;i++)
{
if(dis[i]!=dis1[i])
z=1;
}
if(z==1)
cout<<"negative cycle";
else
{
for(i=1;i<=m;i++)
cout<<dis[i]<<" ";
}
}

28. 28
PROGRAM FOR MATRIX CHAIN MULTIPLICATION
#include<bits/stdc++.h>
using namespace std;
long int a[100000],b[100][100];
int main()
{
long int i,j,k,l,m,n,p,z=9999999;
cout<<"enter the NUMBER of matricen";
cin>>n;
cout<<"enter the matrices ordern";
cin>>a[0]>>a[1];
for(i=2;i<=n;i++)
{
cin>>k>>m;
a[i]=m;
}
//cin>>a[n];
for(l=2;l<=n;l++)
{
for(i=1;i<=n-l+1;i++)
{
j=i+l-1;
b[i][j]=z;
for(k=i;k<=j-1;k++)
{
p=b[i][k]+b[k+1][j]+a[i-1]*a[k]*a[j];

29. 29
if(p<b[i][j])
{
b[i][j]=p;
}}
}}
cout<<b[1][n];
}

30. 30
PROGRAM FOR LONGEST COMMOM SUSEQUENCE
#include<bits/stdc++.h>
using namespace std;
long int i,j,k,l,m,n,l1,c[1000][1000];
int main()
{
char a[1000],b[1000];
cout<<"enter the first stringn";
cin>>a;
cout<<"enter the second stringn";
cin>>b;
l=strlen(a);
l1=strlen(b);
for(i=l-1;i>=0;i--)
a[i+1]=a[i];
for(i=l1-1;i>=0;i--)
b[i+1]=b[i];
for(i=1;i<=l;i++)
{
for(j=1;j<=l1;j++)
{
if(a[i]==b[j])
{
c[i][j]=c[i-1][j-1]+1;

31. 31
}
else
{
c[i][j]=max(c[i-1][j],c[i][j-1]);
}
}
}
cout<<c[l][l1];
}

32. 32
PROGRAM FOR HUFFMAN CODING.
#include <bits/stdc++.h>
using namespace std;
long int i,j,k,n,f[1000];
char d[1000];
struct minheap {
char data;
int freq;
minheap *left, *right;
minheap(char data, int freq)
{
left = right = NULL;
this->data = data;
this->freq = freq;
}
};
struct compare {
bool operator()(minheap* l, minheap* r)
{
return (l->freq > r->freq);
}
};
void print(struct minheap* root, string str)
{
if (!root)
return;
if (root->data != '#')

33. 33
cout << root->data << ": " << str << "n";
print(root->left, str + "0");
print(root->right, str + "1");
}
void Huffman()
{
struct minheap *left, *right, *top;
priority_queue<minheap*, vector<minheap*>, compare> minheaps;
for (int i = 0; i < n; ++i)
minheaps.push(new minheap(d[i], f[i]));
while (minheaps.size() != 1) {
left = minheaps.top();
minheaps.pop();
right = minheaps.top();
minheaps.pop();
top = new minheap('#', left->freq + right->freq);
top->left = left;
top->right = right;
minheaps.push(top);
}
print(minheaps.top(), "");
}
int main()
{
cout<<"enter the number of charractersn";
cin>>n;
cout<<"enter the charraectersn";

34. 34
for(i=0;i<n;i++)
cin>>d[i];
cout<<"enter the frequencyn";
for(i=0;i<n;i++)
cin>>f[i];
Huffman();
return 0;
}

35. 35
PROGRAM FOR OPTIMAL BST.
#include<bits/stdc++.h>
using namespace std;
long int c[1000][1000],f[1000],a[1000],p;
int sum(int i, int j)
{
int s = 0;
for (int k = i; k <=j; k++)
s += f[k];
return s;
}
int main()
{
long int i,j,k,l,m,n,z=999999;
cout<<"enter the size of bstn";
cin>>n;
cout<<"enter the bst elementn";
for(i=0;i<n;i++)
cin>>a[i];
cout<<"enter the frequency of elementsn";
for(i=0;i<n;i++)
cin>>f[i];
for(i=0;i<n;i++)
c[i][i]=f[i];
for(l=2;l<=n;l++)
{
for(i=0;i<n-l+1;i++) {

36. 36
j=i+l-1;
c[i][j]=z;
for(k=i;k<=j;k++)
{
p=0;
if(k>i)
p+= c[i][k-1];
if(k<j)
p+=c[k+1][j];
p+=sum( i, j);
if(p<c[i][j])
{
c[i][j]=p;
}}}}
cout<<c[0][n-1];
}

37. 37
STRING MATCHING USING NAÏVE ALGO
#include<bits/stdc++.h>
using namespace std;
int main()
{
char a[1000],b[1000];
long int i,j,k,l,l1,m,n,s=0;
cout<<"enter the stringn";
cin>>a;
cout<<"enter the string to matchn";
cin>>b;
l=strlen(a);
l1=strlen(b);
for(i=0;i<l;i++)
{
k=i;
s=0;
for(j=0;j<l1;j++)
{
if((a[k]!=b[j])||((k==l-1)&&(j!=l1-1)))
{
s=1;
break;
}
else
{

38. 38
k++;
}
}
if(s==0)
{
break;
}
}
if(s==0)
cout<<"pattern is present in string";
else
cout<<"no match";
}

39. 39
STRING MATCHING USING FINITE AUTOMATA METHOD
#include<bits/stdc++.h>
using namespace std;
long int c[1000][256];
char a[1000],b[1000];
set<char > d;
set<char>::iterator iter;
long int nextstate(long int st,long int m,char x)
{
long int nextst,i,j,l;
if (st < m && x ==b[st])
return st+1;
for (nextst = st; nextst > 0; nextst--)
{
if (b[nextst-1] == x)
{
for (i = 0; i < nextst-1; i++)
if (b[i] != b[st-nextst+1+i])
break;
if (i == nextst-1)
return nextst;
}}}
void form()
{
long int i,j,k,l,m,p,q;
m=strlen(b);

40. 40
for(i=0;i<=m;i++)
{
for(iter=d.begin(); iter!=d.end();++iter)
{
p=(*iter);
l=nextstate(i,m,p);
c[i][p]=l;
}}}
void match()
{
long int i,j,k=0,m,z=0,l;
m=strlen(a);
l=strlen(b);
for(j=0;j<m;j++)
{
k=c[k][a[j]];
if(k==l)
{
z=1;
break;
}}if(z==1)
{
cout<<"found at pos"<<j-l+2;
}
else

41. 41
cout<<"not found";
}
int main()
{
long int i,j,k,l,m,n;
cout<<"enter the stringn";
cin>>a;
cout<<"enter the patternn";
cin>>b;
l=strlen(b);
for(i=0;i<l;i++)
{
d.insert(b[i]);
}
form();
match();
}

42. 42
STRING MATCHING USING RABIN KARP ALGO
#include<bits/stdc++.h>
using namespace std;
int main()
{
long int i,j,k,l,l1,p=199,d=256,m=1,n,x=0,y=0,flag=0;
char a[1000],b[1000];
cout<<"enter the stringn";
cin>>a;
cout<<"enter the patternn";
cin>>b;
l=strlen(a);
l1=strlen(b);
for(i=0;i<l1-1;i++)
m=(m*d)%p;
for(i=0;i<l1;i++)
{
x=(x*d+b[i])%p;
y=(y*d+a[i])%p;
}
for(i=0;i<=l-l1;i++)
{
// cout<<x<<" "<<y<<"n";
if(x==y)
{
for(j=0;j<l1;j++)

43. 43
{
if(a[i+j]!=b[j])
break;
} }
if(j==l1){
cout<<"found at index "<<i+1<<"n";
flag=1;
break;
}
if ( i <l-l1 )
{
y = (d*(y - a[i]*m) + a[i+l1])%p;
if (y < 0)
y = (y + p);
}}
if(flag==0)
cout<<"not found";
}

44. 44
STRING MATCHING USING KMP ALGO
#include<bits/stdc++.h>
using namespace std;
void computeLPSArray(char *pat, int M, int *lps);
void KMPSearch(char *pat, char *txt)
{
int M = strlen(pat);
int N = strlen(txt);
int lps[M];
computeLPSArray(pat, M, lps);
int i = 0;
int j = 0;
while (i < N)
{
if (pat[j] == txt[i])
{
j++;
i++;
}

45. 45
if (j == M)
{
printf("Found pattern at index %d n", i-j);
j = lps[j-1];
}
else if (i < N && pat[j] != txt[i])
{
if (j != 0)
j = lps[j-1];
else
i = i+1;
}
}
}
void computeLPSArray(char *pat, int M, int *lps)
{
int len = 0;
lps[0] = 0;
int i = 1;
while (i < M)

46. 46
{
if (pat[i] == pat[len])
{
len++;
lps[i] = len;
i++;
}
else
{
if (len != 0) {
len = lps[len-1];
}
else
{
lps[i] = 0;
i++;
}
}
}
}
int main()
{
char txt[1000],pat[1000];

47. 47
cout<<"enter the string ";
cin>>txt;
cout<<"enter the patternn";
cin>>pat;
KMPSearch(pat, txt);
return 0;
}