1. A rooted binary tree is a complete tree if every leaf has exactly the same depth d (i.e. the length of the path from the root to a leaf is d for every leaf) and there are 2d leaves. A subtree is a connected subgraph of the tree. Notice that the subtree is also rooted. Describe and analyze a recursive algorithm to compute the largest complete subtree of a given binary tree. Your algorithm should return the root and the depth of this subtree. See the figure below: Given the binary tree rooted at vertex a, the largest complete subtree is highlighted in bold The algorithm should return b as the root of this subtree and 2 as the depth of the leaves in this subtree. Figure 1: Example output