## online solver one pair shortest path problem

Input

Error
in problem solving.

Please enter the input according to the guideline. If you have any question, please email
optimizationcity@gmail.com
.

**Introduction**

**The one pair shortest path problem** is one of the most important issues in the field of operations research. In this problem, we are looking for the shortest path in a weighted graph for a one pair origin-destinaiton (O-D). In Lesson 7 of **Optimization City** website, the shortest path algorithm is teaching with numerous examples.

**Instructions of using online solver one pair shortest path problem **

The GUI of the online solver of the one-pair shortest path problem is as follows:

online solver of the one-pair shortest path problem optimization city

**Input data**

To solver the one-pair shortest path, the required inputs are:

**n:** the number of nodes of the input weighted graph.

**m: **the number of edges of the input weighted graph.

**source:** the source node of the input graph.

**sink:** The destination node is the input graph.

**nodei:** is a vector with m+1 components and the i-th component represents the initial node of the i-th input edges.

**nodej:** is a vector with m+1 components and the i-th component represents the terminal node of the i-th input edges.

**weight:** is a vector with m+1 components and the i-th component shows the weight of the i-th input edges.

**Note:** The weight of the edges must be non-negative.

**Example**

Find the one-pair shortest path for the following network. Node 5 is the source and node 4 is the destination.

**Solution:**

The input data for a given network is as follows.Online Solver One Pair Shortest Path

After entering the data in the online solver, the one-pair shortest path for origin 5 to destination 4 is obtained as follows**.**

After entering the data, we click on the **RUN** button.Online Solver One Pair Shortest Path

The result of running the algorithm is as follows.

In the output part of the algorithm, the shortest route from node 5 to node 4 is that we go from 5 to 1 to 3 to 6 and finally reach destination 4. The length of the shortest path is equal to 9.