This segment clearly explains how to derive a recurrence relation for a given function by analyzing the time complexity of its constituent statements, ultimately arriving at the equation t<sub>n</sub> = 2t<sub>n-1</sub> + 1 for n > 0, and t<sub>0</sub> = 1. The presenter meticulously breaks down the algorithm's steps, making the derivation process easy to follow. This segment uses a visual approach (recursion tree) to solve the recurrence relation. The presenter systematically expands the recursive calls, illustrating how the time complexity grows with each level of recursion. This visual representation makes the concept of recursion tree method more intuitive and easier to grasp. The video solves a recurrence relation, T(n) = 2T(n-1) + 1, using two methods: recursion tree and back substitution. Both methods yield a time complexity of O(2<sup>n</sup>). The recursion tree visualizes the algorithm's recursive calls, while back substitution iteratively substitutes the recurrence relation until a closed-form solution is obtained.