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Suppose the seven keys 1, 2, 3, 4, 5, 6, and 7 are inserted in some order into an initially empty binary search tree (BST).

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Suppose the seven keys 1, 2, 3, 4, 5, 6, and 7 are inserted in some order into an initially empty binary search tree (BST). Specify four insertion orders yielding trees of the maximum height and four insertion orders yielding trees of the minimum height. Form an array of each unique digit from your UID (e.g., 1, 2, 3, and 6 for the exemplary UID 6232122). Form another array by taking the complement to 9 (9 minus digit) for each digit (8, 7, 6 and 3 respectively for the same example). Combine these into one array with no duplicates (1, 2, 3,6,7,8 for the same example) and specify two orders of their insertion into an initially empty BST that yield the minimum tree height. Decide how many black nodes can be along every path from the squareroot node to a leaf in a red-black tree built by colouring the 7-node BST below: List or draw all these red-black trees and indicate, which of them are the AA-trees (format for listing each tree: [1(c_1), 2(c_2), 3(c_3), 4(c_2), 2(c_4), 5(c_5), 6(c_6), 7(c_7)] where c_i subset {b,r} indicates black or red colour of the node i subset {1, 2,...,7})

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