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Commit 221c911

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6 files changed

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6 files changed

+341
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lines changed

‎Dynamic Method/Bellma_input.txt‎

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9
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0 4 0 0 0 0 0 8 0
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4 0 8 0 0 0 0 11 0
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0 8 0 7 0 4 0 0 2
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0 0 7 0 9 14 0 0 0
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0 0 0 9 0 10 0 0 0
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0 0 4 14 10 0 2 0 0
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0 0 0 0 0 2 0 1 6
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8 11 0 0 0 0 1 0 7
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0 0 2 0 0 0 6 7 0
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12+
13+
14+
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6
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0 6 4 5 0 0
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0 0 0 0 -1 0
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0 -2 0 0 3 0
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0 0 -2 0 0 -1
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0 0 0 0 0 3
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0 0 0 0 0 0
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6
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0 1 0 0 5 0
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0 0 4 1 0 0
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0 0 0 0 0 0
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0 0 2 0 0 0
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0 0 0 4 0 1
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1 0 0 0 0 0
30+
31+

‎Dynamic Method/Bellman_Ford.cpp‎

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#include<iostream>
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#include<fstream>
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using namespace std;
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#define INF 9999;
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struct node
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{
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int u , v;
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};
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int pred[100] , dist[100];
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int nv;
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int graph[1000][1000];
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int output[1000][1000]={0};
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node edg[1000];
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bool bellmanford(int n_edg, int s)
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{
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for(int i=0;i<nv;i++)
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{
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pred[i]=-1;
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dist[i]=INF;
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}
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dist[s]=0;
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for(int i=1;i<nv;i++)
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{
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for(int j=0;j<=n_edg;j++)
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{
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node x=edg[j];
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if(dist[x.u]+graph[x.u][x.v]<dist[x.v])
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{
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dist[x.v]=dist[x.u]+graph[x.u][x.v];
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pred[x.v]=x.u;
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}
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}
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}
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for(int i=0 ; i<=n_edg ; ++i)
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{
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node x=edg[i];
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if(dist[x.u]+graph[x.u][x.v]<dist[x.v])
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return false;
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}
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return true;
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}
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int main()
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{
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fstream infile;
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infile.open("Bellma_input.txt" , ios::in);
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if(!infile)
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{
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cout<<"Error on opening file"<<endl;
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return 0;
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}
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infile>>nv;
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for(int i=0;i<nv;i++)
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{
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for(int j=0;j<nv;j++)
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infile>>graph[i][j];
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}
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cout<<"Input graph is"<<endl;
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int n_edg=0;
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for(int i=0;i<nv;i++)
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{
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for(int j=0;j<nv;j++)
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{
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if(graph[i][j])
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{
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edg[n_edg].u=i;
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edg[n_edg].v=j;
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n_edg++;
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}
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cout<<graph[i][j]<<" ";
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}
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cout<<endl;
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}
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cout<<"Number of edges"<<n_edg<<endl;
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cout<<"Edge list is"<<endl;
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for(int i=0;i<n_edg;i++)
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cout<<char(edg[i].u+'A')<<"->"<<char(edg[i].v+'A')<<endl;
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int s;
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cout<<"Enter the source vertext"<<endl;
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cin>>s;
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if(bellmanford(n_edg-1,s))
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{
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for(int i=0;i<nv;i++)
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{
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if(i!=s)
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cout<<char(s+'A')<<"->"<<dist[i]<<"->"<<char(i+'A')<<endl;
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}
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}
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else
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cout<<"Negative cycle is present"<<endl;
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}

‎Dynamic Method/Chain_input.txt‎

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5
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10 20 30 10 40
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4+
5+
6
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2 3 5 2 4 3
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8+
9+
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5
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40 20 30 10 30
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‎Dynamic Method/Floyd_Warshall.cpp‎

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#include<iostream>
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#include<fstream>
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using namespace std;
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#define INF 99
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int pred[100][100] , dist[100][100];
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int nv;
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int graph[1000][1000];
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int output[1000][1000]={0};
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void Floyd_Warshall()
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{
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for(int i=0;i<nv;i++)
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{
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for(int j=0;j<nv;j++)
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{
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pred[i][j] = -1;
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dist[i][j] = INF;
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}
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}
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for(int i=0;i<nv;i++)
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{
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for(int j=0;j<nv;j++)
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{
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dist[i][j]=graph[i][j];
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if(graph[i][j]==0 || graph[i][j]==INF)
28+
pred[i][j]=-1;
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else
30+
pred[i][j]=i;
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}
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}
33+
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for(int k=0;k<nv;k++)
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{
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for(int i=0;i<nv;i++)
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{
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for(int j=0;j<nv;j++)
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{
40+
if(dist[i][k]+dist[k][j] < dist[i][j])
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{
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dist[i][j]=dist[i][k]+dist[k][j];
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pred[i][j]=pred[k][j];
44+
}
45+
}
46+
}
47+
48+
}
49+
}
50+
51+
void shortest_path(int i, int j)
52+
{
53+
if(i==j)
54+
{
55+
cout<<char(i+'A')<<"->";
56+
return;
57+
}
58+
59+
if(pred[i][j]==-1)
60+
{
61+
cout<<"No shortest path is found"<<endl;
62+
return;
63+
}
64+
65+
else
66+
{
67+
shortest_path(i,pred[i][j]);
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cout<<char(j+'A')<<"->";
69+
}
70+
}
71+
72+
int main()
73+
{
74+
fstream infile;
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infile.open("Floyd_input.txt" , ios::in);
76+
if(!infile)
77+
{
78+
cout<<"Error!"<<endl;
79+
return 0;
80+
}
81+
infile>>nv;
82+
for(int i=0 ; i<nv ; ++i)
83+
{
84+
for(int j=0 ; j<nv ; ++j)
85+
infile>>graph[i][j];
86+
}
87+
88+
cout<<"Input graph is"<<endl;
89+
int n_edg=0;
90+
for(int i=0;i<nv;i++)
91+
{
92+
for(int j=0;j<nv;j++)
93+
cout<<graph[i][j]<<" ";
94+
cout<<endl;
95+
}
96+
97+
Floyd_Warshall();
98+
99+
for(int i=0;i<nv;i++)
100+
{
101+
for(int j=0;j<nv;j++)
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{
103+
if(dist[i][j]==INF)
104+
cout<<"INF"<<"\t";
105+
else
106+
cout<<dist[i][j]<<"\t";
107+
}
108+
cout<<endl;
109+
}
110+
int i , j;
111+
cout<<"Enter two vertices"<<endl;
112+
cin>>i>>j;
113+
cout<<"shortest path between "<<char(i+'A')<<"and "<<char(j+'A')<<" is"<<endl;
114+
shortest_path(i,j);
115+
return 0;
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}
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‎Dynamic Method/Floyd_input.txt‎

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4
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0 10 5 3
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1 0 99 99
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99 2 0 99
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99 99 2 0
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7+
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#include <iostream>
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#include <fstream>
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using namespace std;
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int m[100][100];
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int s[100][100];
7+
8+
int Chain_Mul (int arr[],int i,int j)
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{
10+
if(i>=j)
11+
return 0;
12+
13+
if(m[i][j]!=0)
14+
return m[i][j];
15+
16+
int part,temp,mini = INT_MAX;
17+
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for(int k=i;k<j;k++)
19+
{
20+
temp = Chain_Mul(arr,i,k) + Chain_Mul(arr,k+1,j) + (arr[i-1]*arr[k]*arr[j]);
21+
if(temp < mini)
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{
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mini = temp;
24+
part = k;
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}
26+
}
27+
m[i][j] = mini;
28+
s[i][j] = part;
29+
30+
return m[i][j];
31+
}
32+
33+
void parenthesisation(int i,int j)
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{
35+
if(i==j)
36+
cout<<"A"<<i<<" ";
37+
else
38+
{
39+
cout<<"(";
40+
parenthesisation(i,s[i][j]);
41+
parenthesisation(s[i][j]+1,j);
42+
cout<<")";
43+
}
44+
}
45+
46+
int main()
47+
{
48+
int n;
49+
fstream infile;
50+
infile.open("Chain_input.txt" , ios::in);
51+
if(!infile)
52+
{
53+
cout<<"Error on opening file"<<endl;
54+
return 0;
55+
}
56+
infile>>n;
57+
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int arr[n];
59+
for(int i=0;i<n;i++)
60+
infile>>arr[i];
61+
62+
for (int i=1;i<=n;i++)
63+
{
64+
for (int j=1;j<=n;j++)
65+
m[i][j]=0;
66+
}
67+
68+
cout<<"Minimum No of Multiplications: "<<Chain_Mul(arr,1,n-1)<<endl;
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parenthesisation(1,n-1);
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cout<<endl;
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}
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