Use Dijkstra's algorithm to find the shortest path from $u$ to $w$ for the following graph.

$($i$)$

The table below is similar to Table $10\mathrm{.}6\mathrm{.}1.$ Fill in the missing entries to show the action of the algorithm.

The table shows the lengths of the shortest paths from $u$ to all the other vertices of the graph. In particular, it shows that the shortest path from $u$ to $w$ has length

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In Step $2,D(x)=u$; in Step $3,D(y)=$

$$ ; and in Step $5,D(w)=yvv.$ Tracing backwards from $w$ gives $D(w)=$ and $D(?vv)=vv.$ So$,$ the shortest path is uvwx.