# CSCI203 ASSIGNMENT 3

CSCI203 ASSIGNMENT 3
.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.
1. Code the modified Diskstra'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.
A pair of node numbers representing the start- and end -nodes between which paths must be found.
Output consists of the following data for each :
x The length of the shortest path from solution 1:
x The Path (list of nodes) from solution 1:
x The number of additional nodes in the solution tree for solution 1(those not in the shortest
path)
x The length of the shortest path from solution 2:
x The Path (list of nodes) from solution 2:
x The number of additional nodes in the solution tree for solution2(those not in the shortest
path)
x The length of the shortest path from solution 3:
x The Path (list of nodes) from solution 3:
x The number of additional nodes in the solution tree for solution 3(those not in the shortest
path)
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