Skip to content

Commit b66bdc5

Browse files
committed
test math rendering
1 parent 9ea5a28 commit b66bdc5

File tree

1 file changed

+6
-2
lines changed

1 file changed

+6
-2
lines changed

docs/Measures-of-disorder.md

Lines changed: 6 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -50,11 +50,15 @@ The *monotonicity* property implies the *prefix monotonicity* one. A measure of
5050

5151
Let $X$ be a sequence of elements, and let $S_X$ be set of all permutations of that sequence:
5252

53-
$$\mathit{below}_M(X) = \{ \pi \vert \pi \in S_X \text{ and } M(\pi) \le M(X) \}$$
53+
```math
54+
\mathit{below}_M(X) = \{ \pi \vert \pi \in S_X \text{ and } M(\pi) \le M(X) \}
55+
```
5456

5557
Let $T_S(X)$ be the number of steps needed for an algorithm $S$ to sort $X$. A sorting algorithm is said to be $M$-optimal if and only if, for some constant $c$, we have for all $X$:
5658

57-
$$T_S(X) \le c \cdot max\{\lvert X \rvert, \log{} |\mathit{below}_M(X)|\}$$
59+
```math
60+
T_S(X) \le c \cdot max\{\lvert X \rvert, \log{} |\mathit{below}_M(X)|\}
61+
```
5862

5963
In other words, a sorting algorithm is considered $M$-optimal if it takes a number of steps that is within a constant factor of the lower bound of $M$ to sort a sequence. For example a $\mathit{Rem}$-optimal algorithm should be able to sort any sequence in $O(\lvert X \rvert \log{} \mathit{Rem}(X))$ steps.
6064

0 commit comments

Comments
 (0)