We can represent a path from the root to a given node of a binary tree by means of a binary string,where 0 means go to the left child and 1 means go to the right child. For example, the path from the root to the node storing (8,W) in the heap below is represented by 101. Design an O(log n)-time algorithm (in pseudo-code) for finding the last node of a complete binary tree with n nodes, based on the above representation. Briefly explain how this algorithm can be used in the implementation of a complete binary tree by means of a linked structure that does not keep a reference to the last node

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