$3.(\backslash (\backslash$mathbf$\{14\backslash \%)\}\backslash )$ Shortest$-$path Algorithm.

Consider the network shown in Figure $1.$ We use the parallel Dijkstra's algorithm based on MapReduce. Based on the steps that we showed in class, show how you can solve for the shortest path distance from node $\backslash ($ n$\_\{0\}\backslash )$ to each of other nodes. You may define $\backslash ($ N$\_\{$i$\}\backslash )($where $\backslash (0\backslash$leq i $\backslash$leq $3\backslash ))$ as the node structure of node $\backslash ($ n$\_\{$i$\}\backslash )$ that contains the adjacency list of node $\backslash ($ n$\_\{$i$\}\backslash )$ and the current shortest path distance from node $\backslash ($ n$\_\{0\}\backslash ).$ Note that all edges are bi$-$directional. In your answers, you need to show the initialized shortest path distances of all node structures before the start of the first MapReduce iteration. For each MapReduce operation, show $($i$)$ the inputs to the map function, $($ii$)$ the outputs emitted by the Map function $($the node structure or distances$),($iii$)$ the inputs to the reduce function $($the node structure or distances$),$ and $($iv$)$ the shortest path distances emitted by the Reduce function. You only need to show the first two MapReduce iterations.

Figure $1$: Network topology for Question $3.$