# dijkstra

## PURPOSE

Runs Dijkstra's shortest path algorithm on a distance matrix.

## SYNOPSIS

function [D,P] = dijkstra( G, varargin )

## DESCRIPTION

     Runs Dijkstra's shortest path algorithm on a distance matrix.

     Runs Dijkstra's on the given SPARSE nxn distance matrix G, where missing
     values mean no edge (infinite distance). Uses a Finonacci heap resulting
     in fast computation. Finds the shortest path distance from every point
     S(i) in the 1xp source vector S to every other point j, resulting in a
     pxn distance matrix D. P(i,j) contains the second to last node on the
     path from S(i) to j. If point j is not reachable from point S(i) then
     D(i,j)=inf and P(i,j)=-1.

     USAGE
       [D P] = dijkstra( G, [S] )

     INPUT
       G   - sparse nxn distance matrix
       S   - 1xp array of source indices i

     OUPUT
       D   - pxn - shortest path lengths from S(i) to j
       P   - pxn - indicies of second to last node on path from S(i) to j

     EXAMPLE
      n=11; G=sparse(n,n); for i=1:n-1, G(i,i+1)=1; end; G=G+G';
      [D,P] = dijkstra(G,5), % D=[4:-1:0 1:6]; P=[2:5 -1 5:10];

     See also

     Piotr's Image&Video Toolbox      Version 3.20
     Copyright 2013 Piotr Dollar.  [pdollar-at-caltech.edu]
     Please email me if you find bugs, or have suggestions or questions!
     Licensed under the Simplified BSD License [see external/bsd.txt]