to ea to ( plus edge be (infgreater than or equal to to (infthe newly calculated route from to via ( plus infinityis still greater than or equal to the current one in the array (infinity)so the column is not changed the shortestpath array now looks like table table step the shortest-path array inf( ( ( (ainf(anow we can see more clearly the role played by the parent vertex shown in parentheses after each distance each column shows the distance from to an ending vertex the parent is the immediate predecessor of the ending vertex along the path from in column cthe parent vertex is bmeaning that the shortest path from to passes through just before it gets to this information is used by the algorithm to place the appropriate edge in the tree (when the distance is infinitythe parent vertex is meaningless and is shown as new minimum distance now that the shortest-path array has been updatedthe algorithm finds the shortest distance in the arrayas you will see with another path key press the message is minimum distance from is to vertex accordinglythe message added vertex to tree appears and the new vertex and edge ac are added to the tree do it againand again now the algorithm goes through the shortest-path array againchecking and updating the distances for destination vertices not in the treeonly and are still in this category column and are both updated the result is shown in table table step the shortest-path array