a. Design and implement a method height for BinarySearchTree that returns the height of the tree (you have already done this if you completed Exercise 32). b. Define the fullness ratio of a binary tree to be the ratio between its minimum height and its height (given the number of nodes in the tree). For example, the tree in Figure 7.5a has a fullness ratio of 1.00 (its minimum height is 3 and its height is 3) and the tree in Figure 7.6c has a fullness ratio of 0.33 (its minimum height is 3 and its height is 9). Implement a method fRatio to be added to the BinarySearchTree class that returns the fullness ratio of the tree. C. Create an application that generates 10 "random" trees, each with 1,000 nodes (random integers between 1 and 3,000). For each tree output its height, optimal height, and fullness ratio. d. Submit a report that includes your code for the height method, the fRatio method, the application code, sample output, and a short discussion. The discus- sion should include consideration of how the fRatio method might be used by an application to keep its search trees reasonably well balanced.
48. Fullness Experiment:
a. Design and implement a method height for BinarySearchTree that returns the height of the tree (you have already done this if you completed Exercise 32).
b. Define the fullness ratio of a binary tree to be the ratio between its minimum height and its height (given the number of nodes in the tree). For example, the tree in Figure 7.5a has a fullness ratio of 1.00 (its minimum height is 3 and its height is 3) and the tree in Figure 7.6c has a fullness ratio of 0.33 (its minimum height is 3 and its height is 9). Implement a method fRatio to be added to the BinarySearchTree class that returns the fullness ratio of the tree.
C. Create an application that generates 10 "random" trees, each with 1,000 nodes (random integers between 1 and 3,000). For each tree output its height, optimal height, and fullness ratio.
d. Submit a report that includes your code for the height method, the fRatio method, the application code, sample output, and a short discussion. The discus- sion should include consideration of how the fRatio method might be used by an application to keep its search trees reasonably well balanced.
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