Test that Mono(Reversed(X)) = Mono(X)

Author: Morwenn

docs/Original-research.md

@@ -236,6 +236,8 @@ The following relations have yet to be analyzed:
 - $Osc \preceq Mono$
 - $Loc \preceq Mono$
 
+Another interesting property of $Mono$ is that it returns the same amount of disorder for a sequence $X$ and for a sequence corresponding to $X$ with the order of all elements reversed, a property that is only shared with $Osc$ in the library.
+
 
   [better-sorting-networks]: https://etd.ohiolink.edu/!etd.send_file?accession=kent1239814529
   [cycle-sort]: https://en.wikipedia.org/wiki/Cycle_sort

tests/probes/mono.cpp

@@ -1,10 +1,13 @@
 /*
- * Copyright (c) 2018-2022 Morwenn
+ * Copyright (c) 2018-2025 Morwenn
  * SPDX-License-Identifier: MIT
  */
+#include <algorithm>
 #include <forward_list>
 #include <vector>
 #include <catch2/catch_test_macros.hpp>
+#include <rapidcheck.h>
+#include <rapidcheck/catch.h>
 #include <cpp-sort/probes/mono.h>
 #include <cpp-sort/utility/size.h>
 #include <testing-tools/internal_compare.h>
@@ -52,4 +55,10 @@ TEST_CASE( "measure of disorder: mono", "[probe][mono]" )
         const std::forward_list<int> li2 = { 1, 1, 2, 8, 3, 3, 2, 1, 1, 5, 6 };
         CHECK( mono(li2) == 2 );
     }
+
+    rc::prop("Mono(Reversed(X)) = Mono(X)", [](std::vector<int> sequence) {
+        auto mono_x = mono(sequence);
+        std::reverse(sequence.begin(), sequence.end());
+        return mono(sequence) == mono_x;
+    });
 }