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Mazdak Farrokhzad edited d) Quicksort average complexity.tex
about 10 years ago
Commit id: 3b80cce40efdc9b9f61a92f1afae55b9a6d24619
deletions | additions
diff --git a/d) Quicksort average complexity.tex b/d) Quicksort average complexity.tex
index e37f5b0..f35c763 100644
--- a/d) Quicksort average complexity.tex
+++ b/d) Quicksort average complexity.tex
...
C(n) = \left(\prod_{k=0}^{n-1}\left[1+\frac{1}{k+1}\right]\right)\left(\frac{C(0)}{\prod_{k=0}^{-1}\left[1+\frac{1}{k+1}\right]} + \sum_{m=0}^{n-1}\left[\frac{2 - \frac{1}{m+1}}{\prod_{k=0}^{m}\left[1+\frac{1}{k+1}\right]}\right]\right)\\
\Updownarrow\\
C(n) = \left(n+1\right)\left(C(0) + \sum_{m=0}^{n-1}\left[\frac{2 - \frac{1}{m+1}}{m+2}\right]\right)\\
\Updownarrow\\
(n+1)\left(C(0) + \sum_{m=0}^{n-1}\left[\frac{2}{m+2}\right] + \sum_{m=0}^{n-1}\left[\frac{1}{(m+1)(m+2)}\right]\right)
\]