CEG-7450-01- Packet Routing - Part I. Least Cost Path Routing Java Solution

Are you working on the Packet Routing lab assignment for Wright State University and need help understanding or implementing the solution? You are in the right place.

This lab focuses on Least Cost Path Routing using Java. You are required to determine all the nodes that must appear on every shortest path from the source node to the destination in a directed weighted graph. With large input sizes and a strict time constraint, it tests your grasp on algorithms like Dijkstra’s algorithm, graph traversal, and performance optimization.

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Assignment Requirements:

Packet Routing

Total points: 50 (this lab is optional; completing it will give you extra credits)

Warning: Students are members of a learning community committed to the search for knowledge and truth. Essential to that search is the faithful adherence by all students to the highest standards of honesty and integrity. A grade of “0” or “F” will be assigned to assignments on which cheating, plagiarism, or any other form of academic dishonesty is committed or determined to have occurred. Using source code for your assignments from anywhere is considered plagiarism/cheating and is therefore prohibited. For details, see the Wright State University Student Handbook under “Academic Dishonesty”.

You must not attempt to get help from external sources such as online sites that offer solutions. Any submission for grading must be your own work. You must not copy from others or allow your work to be copied. We will check for similarities in code. Any violation will result in your receiving zero for this assignment. No exceptions.

This project needs to be completed using Java and is an individual project. Naming of your programs must strictly follow the following convention: (1) one file for each part; (2) Lab4 followed by your Uid and I for part I (for example Lab4U00998499I.java). Upload only your source code (one file for each part) and report to the Pilot dropbox.

Your report must adequately describe your solutions, such as algorithm, pseudo code, implementation, time complexity, etc.

The solution's time complexity for this lab is an important consideration in grading. Therefore, you should use proper data structures and implement your solutions carefully. Test cases will exercise your programs thoroughly. Your programs should efficiently handle potentially large problems. Expect that your program produces results for all test cases within 4-5 seconds.

Grading: report (20%) and test cases passed (80%).

Part I: Least Cost Path Routing

Packets in a network need to traverse a minimum-cost route. Design an algorithm to determine which nodes the packets will definitely visit if least cost path(s) are used. Note there may be multiple least cost paths.

Input Format:

Unlike previous labs, this lab reads input from the standard input. DO NOT use the Java keyword package in your program.

The first input line contains two integers n (1 <= n <= 10^5) and m (1 <= m <= 2x10^5): the number of nodes and the number of links. The nodes are numbered 1, 2, …, n. Node 1 is the source, and node n is the destination. After this first line, there are m lines describing the links. Each line has three integers a, b, and c: there is a link from node a to node b with cost c. All links are directional. That is, a, b, c indicates that there is a link from a to b only, with a cost of c. In addition, 1 <= a, b <= n, 1 <= c <= 10^9. You may assume that there is a route from the source to the destination.

Output Format:

Unlike previous labs, the output is to the standard output. First print an integer k: the number of nodes that are certainly in the route. After this, print the k nodes sorted in increasing order.

Sample Input 1:

```

5 6

1 2 3

1 3 4

2 3 1

2 4 5

3 4 1

4 5 8

```

Sample Output 1:

```

4

1 3 4 5

```

Grading

Report (20%): Your report must adequately describe your solutions, such as algorithm, pseudo code, implementation, time complexity, etc.

Test Cases (80%): Your code will be tested using the case given in this handout and 13 test cases (not given to you). Passing a test case is defined as producing the correct output, and the output is produced within a few seconds (<5 seconds). Passing the case given in this handout is worth 7.5 points. Passing each of the 13 test cases is worth 2.5 points.

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