Referring to Dijkstra's algorithm as presented in class: (a) Show that at any point in time, we have 8(s,x) 8(s, y) for all R and y E V R. Hint: this can be done with an induction argument very similar to what was done in the proof of correctness of Dijkstra's algorithm. (b) Show that if u is removed from Q, then the next node v removed from Q satisfies d(s, u) d(s, v). Note: this says that nodes are removed from Q in order of increasing distance from s. Hint: this follows very easily from part (a).