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Questions about the science and art of determining properties of algorithms, often including correctness, runtime and space usage. Use the [runtime-analysis] tag for questions about the runtime of algorithms.
2
votes
How to compare the time-complexity of an optimized algorithm with that of the original?
It appears that, before your optimization, your algorithm had the same worst- and average-case complexity, which is why it was easy to consider.
The change in asymptotic complexity really depends on …
6
votes
Accepted
Is there a more efficient algorithm than backtracking/dynamic programming?
(Throughout this answer I use $\phi = \frac{1+\sqrt{5}}{2}$, which is the Golden Ratio.)
Solution:
If $s\leq n$, the attackers can win in one day.
If $s+dpw<\phi^2n$ and $s<2n$, the attackers can w …