this is for holding javascript data
Xavier Holt edited begin_claim_The_algorithm_runs__.tex
about 8 years ago
Commit id: f7022575938c010877338a94be3698d64fab270d
deletions | additions
diff --git a/begin_claim_The_algorithm_runs__.tex b/begin_claim_The_algorithm_runs__.tex
index 7097822..c268f11 100644
--- a/begin_claim_The_algorithm_runs__.tex
+++ b/begin_claim_The_algorithm_runs__.tex
...
&= O(n\log n) + n^{\log 2}O(1) + \sum_{j=0}^{\log n-1} 2^j (\log n - \log{2^j}) \\
&= O(n\log n) + O(n) + \left(\log n\sum_{j=0}^{\log n-1} 2^j - \sum_{j=0}^{\log n-1} 2^j\log{2^j} \right)\\
&= O(n\log n) + \left(\log n \times 2^{\log n} - C \right) &\text{with $C\geq0$}\\
&= O(n\log n) + \left(n\log n - C \right)
&\text{the term inside the &\text{inner bracket
must be $>0$ as it was a sum of $\log$ values} $\geq 0$} \\
\end{align*}
\end{proof}