Discussion
Breadth first search has time complexity \( O(b^{d}) \). How many nodes for b = 10 and d = 6?
Answer: D
Raising the branching factor to the depth gives:
\[ 10^{6} = 1000000 \]
so about one million nodes. At a million nodes a second that is a second of computation but around a gigabyte of memory, which is why space rather than time is usually the binding constraint. Working the numbers for a realistic branching factor is the quickest way to see why exhaustive search fails on anything but small problems.
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