This document describes finding the longest path between two nodes in a graph using a modified Dijkstra's algorithm. It provides an example graph and walks through the steps of the algorithm to calculate the longest path from node A to B. Pseudocode is provided for the longest path Dijkstra's algorithm. Programming code in C is shown to implement the algorithm on the example graph. The output of running the program on the input graph is the longest path A B C F E D.

1. Data Structure & Algorithm
ICT-5102
Homework Assignment 2
To Honorable:
Dr. Hussain Asiful Mustafa
Assistant Professor
IICT-BUET.
Submitted By:
Md.Dedarul Hasan
Reg.Id: 0417311011
PGD in IT, IICT-BUET.
4/9/2019
IICT, BUET

2. TO FIND THE LONGEST PATH FOR THAT GRAPH BY DIJKSTRA ALGORITHM
Distance (A)=0
Source=’A’
Fig : 1 .given graph for longest path find
Dijkstra’s algorithm to find the Longest path between A and B. It picks the unvisited vertex with the
lowest distance, calculates the distance through it to each unvisited neighbor and updates the neighbors
distance if smaller. Mark visited when done with neighbors.
But for that requirement of Dijkstra’s algorithm to find out the longest path we will find pick the
unvisited vertex with the highest distance & calculate the distance through it to each unvisited neighbor &
updates the neighbors distance if greater. Mark visited when done with the neighbors.
Modification of that graph by Dijkstra Algorithm- step by step for longest path:
 First Source ‘A’ is ‘0’ & others vertex is ∞
 We have picked highest distance for unvisited vertex & calculated through it to each unvisited neighbor
and updated the neighbor distance for greater.
A
F
CB
DE
56
2
3
2
5
3
3 1
4
0
∞∞
∞
∞
∞

3. ALGORITHM FOR THAT GRAPH TO FIND LONGEST PATH
STEP1:
Distance(B)=6
Distance(C)=5
Fig: 2Pick vertex in List with maximum distance, i.e., B
A
F
CB
DE
56
2
3
2
5
3
3 1
4
0
56
∞
∞
∞

4. STEP2:
Distance(C)=6+5=11
Fig: 3
A
F
CB
DE
56
2
3
2
5
3
3 1
4
0
116
3
∞
2

5. STEP3:
Distance(F)=11+3=14
Distance(D)=11+2=13
Fig: 4
A
F
CB
DE
56
2
3
2
5
3
3 1
4
0
116
3
13
14

6. STEP4:
Distance(E)=14+3=17
Distance(D)=14+1=15
Fig :5
A
F
CB
DE
56
2
3
2
5
3
3 1
4
0
116
17
15
14

7. STEP5:
Distance(D)=17+4=21
Fig: 6
A
F
CB
DE
56
2
3
2
5
3
3 1
4
0
116
17
21
14

8. STEP6:
Longest Path Cost is= 6+11+14+17+21=69
Fig: 7
A
F
CB
DE
56
2
3
2
5
3
3 1
4
0
116
17
21
14

9. STEP7:
The Final Graph for longest path
Fig: 7 –Longest Path Final for the graph G(V,E)
A
B
F
E D
C
0
116
14
21
17

10. PSEUDOCODES FOR THAT LONGEST PATH USING DIJKSTRA’S ALGORITHM
Dijkstra():
for each vertex v:
v's distance:=infinity.
v's previous:=none.
v1's distance:=0.
List:={all vertics}
while List is not empty:
v:=remove List vertex with MAXIMUM distance.
Mark v as known.
for each unknown neighbor n of v:
dist:=v's distance+edge(v,n)'s weight.
if dist is GREATER than n's distance:
n's distance:=dist.
n's previous:=v.
Reconstruct path from v2 back to v1, following previous pointers.

11. IMPLEMENTATIONS CODE
We have assigned that graph which has to be converted as a tree node structure: [input array]
From Step 1-7:
A B C D E F
A 0 6 5 0 0 0
B 0 0 5 0 3 2
C 0 5 0 2 0 3
D 0 0 0 0 0 1
E 0 0 0 4 0 0
F 0 0 0 0 3 0
Programming Code Using c :

12. EXECUTION OF PROGRAM IMPLEMENTATION & OUTPUT GRAPH WHERE SOURCE IS ‘A’
Output:

13. RESULT as Graph
METARIALS
CodeBlocks
Sublime Text Editor
Ms Word To Draw Graph
CONCLUSION
Total Longest Path Graph is: A B C F E D
REFERENCE
Class Lectures
Stack Overflow
Dynamic Programming For Longest Path Solution Sequence
A
B
F
E D
C