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6. a) Draw the heap resulting from inserting (into an initially empty heap) the following integers in the order presented: 7,8,9,5,3, 2,1 Show three intermediary stages of building the heap, (i) after inserting 3, (ii) after inserting 2, and iii) the final heap, i.e. after inserting l. b) Draw the AVL binary search tree resulting from inserting (into an initially empty tree) the following integers in the order presented: 5, 4, 3, 2, 1 C) Show two intermediary stages of building the AVL tee, (i after inserting 3, (ii) the final AVL tree after inserting 1. Dijkstra's algorithm determine the shortest path from node vertex to each other node. As you progress through the algorithm, update the following table with both the shortest distance so far from node A (column 2 and the predecessor node (column 30 as we did in lectures, crossing out the distances as smaller ones are found; and (ii list the nodes in the order that they are added to the cloud ofnodes. Node Distance from node A Predecessor node