Which of the following is a typical application of dynamic programming?

Dynamic programming is a problem-solving approach that is particularly effective for optimization problems and is characterized by breaking down complex problems into simpler subproblems. These subproblems are solved individually and can often be reused multiple times in the computation of larger problems. The key characteristic of dynamic programming is that it uses the principle of overlapping subproblems and optimal substructure.

The knapsack problem is a classic example of dynamic programming. It consists of selecting items with given weights and values, aiming to maximize total value without exceeding a specific weight limit. This problem can be solved efficiently using dynamic programming principles by taking advantage of the smaller solutions to build up to the overall solution. The approach involves creating a table where rows represent items and columns represent possible weights, and then filling this table based on previously computed values.

In contrast, the other choices do not typically rely on dynamic programming techniques. Tree traversal operates using depth-first or breadth-first algorithms, sorting algorithms utilize different techniques such as quicksort or mergesort that do not employ dynamic programming, and stack implementation is based on data structure principles, managing elements in a last-in-first-out manner, which doesn't relate to the optimization approaches of dynamic programming.