Web Reference: Jan 11, 2026 · The recursion tree method is used to analyze the time complexity of recursive algorithms by visually representing the recurrence as a tree. Each node of the tree represents the work done in a single recursive call, and each level represents one stage of the recursion. However, if you are very careful when drawing out a recursion tree and summing the costs, you can actually use a recursion tree as a direct proof of a solution to a recurrence. First let's create a recursion tree for the recurrence T (n) = T (α n) + T ((1 α) n) + c n. So we can see not each branch reaches at the bottom at the same time, it might be the left most branch reaches at the bottom first, or the right most branch reaches at the bottom first.
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![L-2.9: Recurrence Relation [T(n)= 2T(n/2) +cn] | Recursive Tree method | Algorithm Content](https://i.ytimg.com/vi/bJg_sv7PV-g/mqdefault.jpg)
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