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Course: Numerical Optimization
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Kindly answer questions a, b & c as seen in the picture.
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3. Algorithm analysis and design (Ex. 4.4-7) a. Draw a binary tree with ten nodes labeled 0, 1, 2, ..., 9 in such a way that the inorder and postorder traversals of the tree yield the following lists: 9, 3, 1, 0, 4, 2, 7, 6, 8, 5 (inorder) and 9, 1, 4, 0, 3, 6, 7, 5, 8, 2 (postorder). b. Give an example of two permutations of the same n labels 0, 1, 2,..., n-1 that cannot be inorder and postorder traversal lists of the same binary tree. c. Design an algorithm that constructs a binary tree for which two given lists of n labels 0, 1, 2, ..., n - 1 are generated by the inorder and postorder traversals of the tree. Your algorithm should also identify inputs for which the problem has no solution.