# Dijkstra's algorithm to find the shortest path

Budget ₹1500-12500 INR

Dijkstra's algorithm finds the shortest path from a given node to all other nodes.

1) We observe that we can modify this algorithm to stop as soon as a particular node is reached;

thus producing an algorithm to find the shortest path between a specific pair of points.

However, this algorithm may involve the consideration of a number of points which do not lie

on the final shortest path.

We now consider 2 alternatives:

2) We can modify the algorithm to add nodes to the solution based on an A* criterion derived

from the Euclidean (straight line) distance from each candidate node to the desired end node.

3) We can attempt to improve our efficiency by modifying Dijkstra's algorithm to start at both

the source and destination nodes and to construct two partial solution trees in parallel until

one node is in both partial solution trees.

Your task is to:

1. Code the modified Dijkstra's algorithm to search from the start node out.

2. Code the A* variant.

3. Code the proposed improved algorithm.

Input consists of the following data:

1) The number of nodes in the graph.

2) A set of triples containing the node number, its X-coordinate and its Y coordinate – one triple

for each node in the graph.

3) The number of edges in the graph.

4) A set of triples consisting of two node numbers and a cost – one triple for each edge in the

graph.

5) A pair of node numbers representing the start and end nodes between which a path must be

found.

Output consists of the following data:

The length of the shortest path from solution 1:

The path (ordered list of nodes) from solution 1:

The number of additional nodes in the solution tree for solution 1 (those not in the shortest

path that were added to the selected set):

The length of the shortest path from solution 2:

The path (ordered list of nodes) from solution 2:

The number of additional nodes in the solution tree for solution2 (those not in the shortest

path that were added to the selected set):

The length of the shortest path from solution 3:

The path (ordered list of nodes) from solution 3:

The number of additional nodes in the solution tree for solution 3 (those not in the shortest

path that were added to the selected set).

Notes:

The graph is undirected, so each edge connects the pair of nodes specified in both directions.

Do not use the STL.

The graph will not have more than 100 nodes.

Your program should print an appropriate error message if no path exists between the

specified nodes.

Programs must compile and run under g++ (C++ programs)

You should make a text file containing a brief discussion of your results. You should talk about the relative efficiency of each of the three proposed approaches and note any problems that may arise with each of them

Please refer the attached files for input data and graphs.

## Awarded to:

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