Chapter A, Problem 11E

Explanation of Solution

Explanation:

The following diagram describes about the graph of the adjacency matrix

________

$\begin{array}{l}\text{A P S}\\ \text{450}\\ \text{155 135 300}\\ \text{NY 290 130 560 Ch Ch}\\ \text{350}\\ \text{400 350}\\ \text{100 100}\\ \text{B E CI}\end{array}$

The algorithm is represented diagrammatically as above. Here, no values are stored in the nodes and hence, they are represented by infinity value.

The values and nodes are written below the graph.

After applying the Dijkstra’s algorithm, the distances of A and B are updated from NY and it can be described as follows

$\begin{array}{l}\text{A P S}\\ \text{450}\\ \text{155 135 300}\\ \text{NY 290 130 560 Ch Ch}\\ \text{350}\\ \text{400 350}\end{array}$

______

$\begin{array}{l}\text{100}\text{100}\\ \text{B E}\text{CI}\end{array}$

In the above graph representation, the values of A and B are updated to find the shortest distance and the other values and nodes are written below the graph.

A is termed as the shortest distance of 155 from NY and the distances of P and B are updated. It can be described as follows

$\text{A}\text{P}\text{S}$

______

$\begin{array}{l}\text{450}\\ \text{135 300}\\ \text{NY 290 130 560 Ch}\\ \text{400 350}\\ \text{100 350}\\ \text{B E CI}\end{array}$

In the above graph representation, the value of P is updated to find the shortest distance between P and B and the remaining nodes and values are represented below the graph.

B is termed as the shortest distance of 400 from NY and the distance of 500 from E is updated. It can be described as follows

$\text{A}\text{P}\text{S}$

$\begin{array}{l}\text{450}\\ \text{300}\\ \text{135}\\ \text{NY 290 Ch}\\ \text{130 560}\\ \text{350}\\ \text{100 350}\\ \text{B E CI}\end{array}$

In the above graph representation, the value of E is updated to find the shortest distance and the remaining nodes and values are represented below the graph.

E is termed as the shortest distance of 500 from NY and the distances of P and CI are updated from NY