Fix osc.max_for_size for size=1 and for even sizes

Author: Morwenn

docs/Measures-of-presortedness.md

@@ -235,7 +235,7 @@ Computes the *Oscillation* measure described by C. Levcopoulos and O. Petersson
 
 When there isn't enough extra memory available, `probe::osc` falls back to an in-place O(n²) algorithm.
 
-`max_for_size`: (|*X*| * (|*X*| - 2) - 1) / 2 when the values in *X* are strongly oscillating.
+`max_for_size`: it is reached when the values in $X$ are strongly oscillating, and equals $\frac{|X|(|X| - 2)}{2}$ when $|X|$ is even, and $\frac{|X|(|X| - 2) - 1}{2}$ when $|X|$ is odd.
 
 **Note:** *Osc* does not respect Mannila's criterion 5: $Osc(\langle 2, 4, 1, 3, 1, 3 \rangle) \not \le |\langle 4, 1, 3, 1, 3 \rangle| + Osc(\langle 4, 1, 3, 1, 3 \rangle)$, though it is possible that it only happens when equivalent elements are involved.
 

include/cpp-sort/probes/osc.h

@@ -1,5 +1,5 @@
 /*
- * Copyright (c) 2016-2022 Morwenn
+ * Copyright (c) 2016-2025 Morwenn
  * SPDX-License-Identifier: MIT
  */
 #ifndef CPPSORT_PROBES_OSC_H_
@@ -210,7 +210,12 @@ namespace probe
             static constexpr auto max_for_size(Integer n)
                 -> Integer
             {
-                return n == 0 ? 0 : (n * (n - 2) - 1) / 2;
+                if (n < 2) return 0;
+                if (n % 2 == 0) {
+                    return (n * (n - 2)) / 2;
+                } else {
+                    return (n * (n - 2) - 1) / 2;
+                }
             }
         };
     }

tests/probes/osc.cpp

@@ -1,5 +1,5 @@
 /*
- * Copyright (c) 2016-2022 Morwenn
+ * Copyright (c) 2016-2025 Morwenn
  * SPDX-License-Identifier: MIT
  */
 #include <forward_list>
@@ -31,13 +31,27 @@ TEST_CASE( "presortedness measure: osc", "[probe][osc]" )
     {
         // Example from the paper Adaptive Heapsort
         // by Levcopoulos and Petersson, the upper bound
-        // should be (size * (size - 2) - 1) / 2
+        // should be:
+        // - When size is even: (size * (size - 2)) / 2
+        // - When size is odd: (size * (size - 2) - 1) / 2
 
-        std::forward_list<int> li = { 8, 5, 10, 3, 12, 1, 13, 2, 11, 4, 9, 6, 7 };
-        auto max_n = osc.max_for_size(cppsort::utility::size(li));
-        CHECK( max_n == 71 );
-        CHECK( osc(li) == max_n );
-        CHECK( osc(li.begin(), li.end()) == max_n );
+        // Even number of elements
+        {
+            const std::forward_list<int> li = { 8, 5, 10, 3, 12, 1, 13, 2, 11, 4, 9, 6 };
+            auto max_n = osc.max_for_size(cppsort::utility::size(li));
+            CHECK( max_n == 60 );
+            CHECK( osc(li) == max_n );
+            CHECK( osc(li.begin(), li.end()) == max_n );
+        }
+
+        // Odd number of elements
+        {
+            const std::forward_list<int> li = { 8, 5, 10, 3, 12, 1, 13, 2, 11, 4, 9, 6, 7 };
+            auto max_n = osc.max_for_size(cppsort::utility::size(li));
+            CHECK( max_n == 71 );
+            CHECK( osc(li) == max_n );
+            CHECK( osc(li.begin(), li.end()) == max_n );
+        }
     }
 
     SECTION( "regressions" )