Cracking the Coding Interview, 4 Edition - 150 Programming Interview Questions and Solutions

Solutions to Chapter 4 | Trees and Graphs
average of lg n amount of work on each step), or we can be super mathematical:
There are 2^r nodes at level r.
1*2^1 + 2*2^2 + 3*2^3 + 4*2^4 + ... d * 2^d
= sum(r * 2^r, r from 0 to depth)
= 2 (d-1) * 2^d + 2
n = 2^d ==> d = lg n
NOTE: 2^lg(x) = x
O(2 (lg n - 1) * 2^(lg n) + 2) = O(2 (lg n - 1) * n ) = O(n lg n)
Following similar logic, our space complexity is O(n lg n).
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