Recursion tree as a visualization technique

The recursion tree method is a powerful technique for solving and visualizing recurrence functions, particularly those that arise in the analysis of divide-and-conquer algorithms. It involves visualizing the recursive process as a tree, where each node represents a subproblem, and the edges represent the recursive calls. By summing the costs at each level of the tree, we can determine the overall complexity of the algorithm.

Here’s the step-by-step explanation of the recursion tree method:

1. Construct the recursion tree:
   • Begin by writing down the original recurrence function
   • Each node in the tree represents a call to the recurrence
   • The root of the tree corresponds to the original problem
   • The children of a node represent the subproblems generated by the recursive calls
2. Identify the costs:
   • Determine the cost at each node. This cost typically corresponds to the non-recursive work done at that step, often denoted as .
   • Write down...