1. The document describes an algorithm design and analysis lab file submitted by Suraj Kumar to Anuradha Chug. 2. It contains 19 programs implementing various algorithms including searching, sorting, graph algorithms like BFS, DFS, Kruskal, Prim's, and string matching algorithms. 3. The programs are written in C++ and implement algorithms like linear search, binary search, selection sort, bubble sort, insertion sort, merge sort, quicksort, bucket sort, radix sort, counting sort, breadth first search, depth first search, Kruskal, Prim's, Dijkstra, and string matching algorithms.

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;
}