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Problem 6. [For the following two subproblems, give clear pseudo code and English explanat tions, argue their correctness, and analyze its time complexity]. a) Suppose an arithmetic expression is given as a tree. Each leaf is an integer and each internal node is one of the standard arithmetical operations (+,-, *, /). For example, the expression 2 + 3 * 4 + (3 . 4)/5 is represented by the tree in figure below (left). Give an O(n) algorithm for evaluating such an expression, where there are n nodes in the tree. b) Suppose an arithmetic expression is given as a DAG (directed acyclic graph) with common subexpressions removed. Each leaf is an integer and each internal node is one of the standard arithmetical operations (+,-, *, /). For example, the expression 2 + 3 + 4 + (3 * 4)/5 is represented by the DAG in the figure below. Give an O(n + m) algorithm for evaluating such a DAG, where there are n nodes and m edges in the DAG. [ Hint: modify an algorithm for the tree case to achieve the desired efficiency] 2