javascript - Dijkstra's algorithm on three dimensional array -

i cannot figure out how implement in psuedo-code. user enters in this:

[   [      [0,1]   ],   [     [5,6],[7,8]   ],   [     [91,17],[18,42]   ],   [     [20,54]   ] ] 

basically path [0,1] maps ([5,6] , [7,8]) each of maps ([91,17] , [18,42]) , on, cost distance between points. starting point [0, 1] , ending point [20,54]. there 1 starting point , 1 ending point, , points in previous index map points in next index.

how implement dijkstra's algorithm kind of data structure?

this image may (not scale):

green start , red end.

notice given array 2 dimensional if considered entry in array pair (x, y).

the basic idea build graph, assign cost of edges, , apply standard dijkstra's algorithm.

building graph:

make 2 hash tables h , q h([x,y]) maps vertex (x,y) number between 0 , n - 1, , q maps integer between 0 , n - 1 vertex (x, y). n number of vertices in graph. can find n looping on vertices in given 2d array. let's call given array a

pseudo-code of hashing:

n = 0 for(i = 0; < length of ; i++)     for(int j = 0; j < length of a[i]; j++)             h[a[i][j]] = n             q[n] = a[i][j]             n++ 

notice a[i][j] pair of integers, key of h should pair of integers.

now can build graph considering vertices numbers between 0 , n - 1. can represent graph adjacency list

psudo-code of constructing graph:

array g[n][]                              //-- adjacency list of graph for(int = 0; < length of - 1; i++)  //-- notice "-1"     for(int j = 0; j < length of a[i]; j++)         for(int k = 0; k < length of a[i + 1]; k++)             g[ h[a[i][j]] ].insert (h[ a[i + 1][k] ])             g[ h[ a[i + 1][k] ].insert( h[a[i][j]] )     //-- assuming graph undirected 

by doing this, have built graph. can apply standard dijkstra's algorithm on graph g. find cost of edge between 2 vertices u , v can use hash table q in order coordinates of u , v. cost of edge euclidean distance between points q[u] , q[v].

pseudo-code cost of edge between 2 vertices u , v

cost(int u, int v)     return euclidean_distance(q[u], q[v])