What would be the appropriate kind of tree traversal to use?

What would be the appropriate kind of tree traversal to use?

1. You're writing an analysis tool for a hierarchical organization, in which there is one person fundamentally in charge, to whom some number of people report, to each of whom some number of people report, and so on. There is a ranking in the organization, so the person in charge has rank 1, the people who report to that person have the rank 2, the people who report to the rank-2 people have the rank 3, and so on. Your input is this kind of organizational hierarchy. Your desired output is to be able to find the highest-ranking person (i.e., the person with the minimum rank number) who meets some characteristic (such as the highest-ranking person under 30 years old).
2. Your input is a binary tree that is an expression tree, in which each non-leaf node contains a binary mathematical operator (such as +, −, ×, or ÷) and each leaf node contains a numeric value (such as 2 or 9.5). Your desired output is the value of the expression represented by the tree — so, for example, if the tree had a root node + and its two children were the numeric values 3 and 6, the result would be 9.