10. Dijkstra ascending. Referring to Dijkstra's algorithm as presented in class: (a) Show that at any point in time, we have for all x E R and y EVR Hint: this can be done with an induction argument very similar to what was done in the proof of correctncss of Dijkstra's algorithm. (b) Show that if u is removed from Q, then the next node v removed from Q satisfies (s, u) &s,u). Note: this says that nodes are removed from Q in order of increasing distance from s. Hint: this follows very easily from part (a 10. Dijkstra ascending. Referring to Dijkstra's algorithm as presented in class: (a) Show that at any point in time, we have for all x E R and y EVR Hint: this can be done with an induction argument very similar to what was done in the proof of correctncss of Dijkstra's algorithm. (b) Show that if u is removed from Q, then the next node v removed from Q satisfies (s, u) &s,u). Note: this says that nodes are removed from Q in order of increasing distance from s. Hint: this follows very easily from part (a