1) BST (5p)
a) Read letters from the keyboard and insert them in a BST. The reading process stops when the user inserts the character 0 (zero) (0.5p)
b) Find the common ancestor of 2 given nodes (0.75p)
c) Write a function to check is a node is a grand-parent of a given node. (0.75p)
d) Design an algorithm which creates a linked list of all the nodes at each depth (i.e., if the tree has depth D, you’ll have D linked lists). (1p)
e) Check if a BST is perfect or not (all leaves are at the same distance from the root and all internal nodes have 2 children) (1p)
f) Perform a right rotation of the BST. (1p)
More info: https://slideplayer.com/slide/14553828/ Ex:
2) Heap (5p)
A tournament tree is a form of max (min) heap which is a complete binary tree. Every external node (leaf) represents a player and an internal node represents a winner. We will thus have N-1 internal nodes in a binary tree with N leaves. Ex:
The above (max) tree contains 4 leaf nodes that represent players (5, 3, 7, and 8). We have 3 levels: 0, 1 and 2. Initially 2 games are played at level 2, one between 5 and 3 and another one between 7 and 8. In the next move (level 1), one more game is conducted between 5 and 8 to conclude the final winner. Overall we need 3 comparisons to find the winner.
a) Check if an input set can form a tournament tree after being inserted in a heap and display an appropriate message. (1p)
Ex: 3, 5, 5, 6, 6, 2, 5 – it can form a tournament tree 3, 5, 5, 6, 2 – it cannot form a tournament tree
Pick a valid set and insert it in your tournament tree.
b) Determinate who is the “second best” player. This is the person who lost in the first round the match against the final winner (here the second best is: 7) (0.5p) c) Display the history of the matches played by the winner at each level. (1p) Ex:
In the first round, the winner defeated 7.
In the second round, the winner defeated 5 etc.
d) Construct a “loser tree” using the previous info from the tournament tree (2p). Ex:
In round 1, between 5 and 3, 3 is the loser; between 7 and 8, 7 is the loser. In round 2, we have the match between the 2 previous winners (5 and 8): the loser is 5. The winner is 8!
e) Determinate the winner and the main loser from the loser tree (0.5p).
