Program – 7
From a given vertex in a weighted connected
graph, find shortest paths to other vertices using
Dijkstra's algorithm. Write the program in Java.
import java.util.Scanner;
public class DijkstrasClass
{
final static int MAX = 20;
final static int infinity = 999;
static int n;
// No. of vertices of G
static int a[ ][ ]; // Cost matrix
static Scanner scan = new Scanner(System.in);
public static void main(String[ ] args)
{
ReadMatrix( );
int s = 0;
// starting vertex
System.out.println("Enter starting vertex: ");
s = scan.nextInt( ); //starting vertex s=1
Dijkstras(s);
}
// find shortest path
4
2
static void ReadMatrix( )
3
2
1
{
3
4
7
6
5
5
4
a = new int[MAX][MAX];
System.out.println("Enter the number of vertices:");
n = scan.nextInt( );
//n=5
System.out.println("Enter the cost adjacency matrix:");
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++)
1
2
3
1
0
3
999 7
999
2
3
0
4
2
999
999 4
0
5
6
4
7
5
0
4
5
999 999 6
4
0
a[i][j] = scan.nextInt( ); 3
}
2
4
5
static void Dijkstras(int s)
{
int S[ ] = new int[MAX]; // to store visited vertex
int d[ ] = new int[MAX]; //to store distance from source
vertex
int u, v;
S[i]
1
2
3
4
5
int i;
0
0
0
0
0
for (i = 1; i <= n; i++)
{
d[i]
1
2
3
4
5
S[i] = 0;
0
3
999 7
999
d[i] = a[s][i];
S[i]
1
2
3
4
5
}
1
0
0
0
0
S[s] = 1;
d[s] = 1;
d[i]
1
2
3
4
5
1
3
999
7
999
S[i]
i = 2;
while (i <= n)
1
2
3
4
5
1
1
0
0
0
{
u = Extract_Min(S, d);
// u=2
S[u] = 1;
//S[2]=1
i++;
//i=3
for (v = 1; v <= n; v++)
{
if (((d[u] + a[u][v] < d[v]) && (S[v] == 0)))
d[v] = d[u] + a[u][v];
}
}
if (i != s)
System.out.println(i + ":" + d[i]);
}
//end of Dijkstras(s);
d[i] 1 2
3
4
1 3 999 7 7 5
5
999
V=1 if (((d[2] + a[2][1] < d[1])
&& (S[1] == 0)))
if (((3 + 3 < 1) && (1 == 0))) F
V=2 if (((d[2] + a[2][2] < d[2])
&& (S[2] == 0)))
if (((3 + 0 < 3) && (1 == 0))) F
V=3 if (((d[2] + a[2][3] < d[3])
&& (S[3] == 0)))
if (((3 + 4 < 999) && (0 == 0)))T
d[v] = d[u] + a[u][v];
d[3] = d[2] + a[2][3];=3+4=7
V=4 if (((d[2] + a[2][4] < d[4])
&& (S[4] == 0)))
if (((3 + 2 < 7) && (0 == 0)))T
d[v] = d[u] + a[u][v];
d[4] = d[2] + a[2][4];=3+2=5
V=5 if (((d[2] + a[2][5] < d[5])
&& (S[5] == 0)))
if (((3 + 999 < 999) &&
(0 == 0))) F
static int Extract_Min(int S[ ], int d[ ])
{
int i, j = 1, min;
min = infinity; //min=999;
for (i = 1; i <= n; i++)
{
if ((d[i] < min) && (S[i] == 0))
{
min = d[i];
j = i;
}
}
return (j);
//return(2)
}
} //class
i=1 If(1<999) && S[1]==0) F
i=2 if(3<999) && S[2]==0) T
min=3
j=i (ie., j=2)
i=3 if(999<3) && S[3]==0) F
i=4 if(7<3) && S[4]==0) F
i=5 if(999<3) && S[5]==0) F
S[i] 1
2
3
4
5
1
0
0
0
0
d[i]
1
2
3
4
1
3
999 7
5
999
4
b
3
a
Tree vertices
a(-,0)
7
2
c
5
d
d
6
4
e
Remaining vertices
b(a,3) c(-,∞) d(a,7) e(-,∞)
3
a
b(a,3)
2
c(b,3+4) d(b,3+2) e(-,∞)
c(b,7) e(d,5+4)
3
a
c(b,7)
e(d,9)
1
e(d,9)
2
7
6
5
e
4
4
2
e
c
d
7
6
4
4
2
3
c
d
b
e
4
5
2
7
6
5
4
b
3
c
d
7
a
d(b,5)
4
b
3
6
5
4
5
4
8