Given the recurrence $T(n) = 3T(\frac n3) +2T(\frac n2) + cn, T(1)=\Theta(1)$, I need to find an upper bound for the number of leaves. By generating a recursion tree, I have found that the shorter height is $\log_3n$ and the longer height of the tree is $\lg n$. Is there any way I can intuitively get the number of leaves of the tree from those values? Also, I found a solution to the recurrence: $T(n) = O(n\lg n)$, by getting the sum of the total for each level. How can I prove that using substitution method?
How to get an upper bound for the number of leaves of a recursion tree from a recurrence relation
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algorithms
recurrence-relations
asymptotics
recursion