Add a visual explanation of the measure of disorder Exc

Author: Morwenn

docs/Measures-of-disorder.md

@@ -246,7 +246,9 @@ $$
 
 Computes the minimum number of exchanges required to sort $X$, which corresponds to $\lvert X \rvert$ minus the number of cycles in the sequence. A cycle corresponds to a number of elements in a sequence that need to be rotated to be in their sorted position; for example, let $\langle 2, 4, 0, 6, 3, 1, 5 \rangle$ be a sequence, the cycles are $\langle 0, 2 \rangle$ and $\langle 1, 3, 4, 5, 6 \rangle$ so $\mathit{Exc}(X) = \lvert X \rvert - 2 = 5$.
 
-**Warning:** `probe::exc` generally returns a result higher than the minimum number of exchanges required to sort $X$ when it contains *equivalent elements*. This is because extending $\mathit{Exc}$ to *equivalent elements* is a NP-hard problem (see *On the Cost of Interchange Rearrangement in Strings* by Amir et al). The function does handle such elements in some simple cases, but not in the general case.
+![Visual representation of the two cycles of exchanges required to sort the aforementioned sequence](images/sorting-exchange-cycles.png)
+
+**Warning:** `probe::exc` generally returns a result greater than the minimum number of exchanges required to sort $X$ when it contains *equivalent elements*. This is because extending $\mathit{Exc}$ to *equivalent elements* is a NP-hard problem (see *On the Cost of Interchange Rearrangement in Strings* by Amir et al). The function does handle such elements in some simple cases, but not in the general case.
 
 | Complexity  | Memory      | Iterators     | Monotonic |
 | ----------- | ----------- | ------------- | --------- |

docs/images/sorting-exchange-cycles.png

@@ -0,0 +1,35 @@
+\documentclass{standalone}
+\usepackage{tikz}
+\usetikzlibrary {arrows.meta}
+\pagestyle{empty}
+
+\begin{document}
+\begin{tikzpicture}
+
+\tikzstyle{every node}=[draw,shape=circle,minimum size=0.5cm,inner sep=0pt,anchor=center];
+
+% Draw the splay tree nodes
+\node (n0) at (2,0) {0};
+\node (n1) at (5,0) {1};
+\node (n2) at (0,0) {2};
+\node (n3) at (4,0) {3};
+\node (n4) at (1,0) {4};
+\node (n5) at (6,0) {5};
+\node (n6) at (3,0) {6};
+
+
+\tikzset{every edge/.append style = {-Stealth,dashed,gray}};
+
+% Visitation: normal edition
+\path[every node/.style={font=\sffamily\small}]
+  (n2) edge[out=290,in=240,orange] (n0)
+  (n0) edge[out=110,in=70,orange] (n2)
+  (n4) edge[out=290,in=240,teal] (n3)
+  (n3) edge[out=110,in=70,teal] (n6)
+  (n6) edge[out=290,in=240,teal] (n5)
+  (n5) edge[out=110,in=70,teal] (n1)
+  (n1) edge[out=110,in=70,teal] (n4);
+
+
+\end{tikzpicture}
+\end{document}