computer science - An example of Dijkstra's algorithm to fail with one negative edge -

i'm trying think of graph edges have positive weights, except of 1 edge such dijkstra's algorithm fails produce correct output.

i'd glad idea.

edit:
i've seen graph counter-example don't understand why. vertex a last pop-out queue , relax() edge a->e. path s->a->e chosen, correct path (and not s->b->e claimed)

thanks

dijkstra terminates upon expanding goal node. use priority queue in dijkstra (not queue) expand node has least cost. in example never expanded.

  open list = [ s cost:0 ] // priortiy queue pop s out of open list   closed list = [ s cost:0 ]   open list = [ b cost:1 ; cost:5 ] pop b out of open list   closed list = [ s cost:0 ; b cost:1 ]   open list = [ e cost:2 ; cost:5 ] pop e out of open list // it's better terminate when reach goal if don't // doesn't make difference going find shortest path // other nodes    closed list = [ s cost:0 ; b cost:1 ; e cost:2 ]    open list = [ cost:5 ] pop out of open list    // there isn't nodes can push open list    closed list = [ s cost:0 ; b cost:1 ; e cost:2 ; cost:5 ]    open_list = [] 

dijkstra push node closed list upon expanding because assumes has find shortest path it. if don't terminate upon reaching goal never expand because in our closed list.