(Solved): (a) In terms of the Binary Search Tree (BST) data structure, we know that the values of all the e ...

(a) In terms of the Binary Search Tree (BST) data structure, we know that the values of all the elements of the left sub-tree will be less than the value of the root and values of all the elements residing on the right sub-tree will be greater than the value of the root. In that sense, we can easily buildup/construct the specific BST if only the PREORDER TRAVERSAL or only the POSTORDER TRAVERSAL is given! Now think of the Binary Tree (BT) data structure! In terms of BT, there are no rules that the values of all the elements of the left sub-tree will be less than the value of the root and values of all the elements residing on the right sub-tree will be greater than the value of the root. The only rule is that, in BT, every node would have maximum of two child nodes. Nothing to worry about the value of the elements. So in that sense, so many BT structures can be constructed if only the PREORDER TRAVERSAL or only the POSTORDER TRAVERSAL is given! If we want to get one or two specific Binary Tree solution, we need to know any two of the PREORDER, POSTORDER and INORDER TRAVERSALs of the same Binary Tree (BT) all-together. Construct the exact Binary Tree (BT) structure from the following Traversals of the same Tree: Postorder Traversal: $F$ D $H$ H $CJ$ J $G$ E I B Inorder Traversal: $DFCHBEGI$ (b) Discuss with proper examples the two properties that must be present for a problem if you want to solve it using Dynamic Programming paradigm. (c) Given a set of resources, $\mathbf{W}=\{1,2,3,4,7\}$ and $\mathbf{V}\mathbf{M}=9$. Using the Dynamic Programming paradigm determine in how many ways it is possible to form the value of $\mathbf{V}\mathbf{M}$ using different resource(s) from $W$ where the usage frequency for each resource is more than one.