For improved efficiency, you should implement the following version of Dijkstra$$s shortest s$-$t path algorithm. Dijkstra$-$ST$($G$,$ w$,$ s$,$ t$)01$: FOR v$=1$ TO n $\{02$: V$[$v$]->$index $=$ v; $03$: V$[$v$]->$key $=$ infinity; $04$: V$[$v$]->$pi $=$ NULL; $05$: V$[$v$]->$color $=$ WHITE; $06$: V$[$v$]->$position $=0$; $407$: $\}08$: Create empty min$-$heap pHeap; $09$: Set the key of s to $0,$ and the color of s to GRAY; $10$: Insert s into pHeap; $11$: WHILE pHeap$->$size $>0\{12$: u $=$ ExtractMin$($pHeap$)$; $13$: IF $($u $==$ t$)$ THEN STOP; $14$: FOR each v on ADJ$[$u$]\{15$: IF v is WHITE $\{16$: Set the color of v to GRAY; $16$: Update v$$s key, pi; $//$ Relax$($u$,$ v$,$ w$)$; $17$: Insert v into pHeap; $18$: $\}$ELSE IF v is GRAY $\{19$: Relax$($u$,$ v$,$ w$)$; $20$: Call DecreaseKey if nexessary; $//$ Using the position field of v $21$: $\}22$: $\}23$: Color u