add worst case scenario paragraph

.gitignore

@@ -243,4 +243,5 @@ _Pvt_Extensions
 
 #Solver output file
 output.txt
-multipleSolutions.txt
+multipleSolutions.txt
+costs.txt

PtVzzlexMasCake.Tests/PuzzleSolverTests.cs

@@ -6,12 +6,14 @@ namespace PtVzzlexMasCake.Tests
     [TestClass]
     public class PuzzleSolverTests
     {
-        const int baseTwoExponent = 16;
+        const int baseTwoExponent = 20;
 
         [TestMethod]
         public void PuzzleSolverTest()
         {
             using var sw = new StreamWriter("../../../multipleSolutions.txt");
+            using var sw2 = new StreamWriter("../../../costs.txt");
+
             var result = DijkstraSolver.SolveFull(baseTwoExponent);
 
             foreach (var item in result)
@@ -46,6 +48,11 @@ public void PuzzleSolverTest()
                         sw.WriteLine();
                     }
                 }
+
+                if (true)
+                {
+                    sw2.WriteLine($"{item.Value} {item.Cost}");
+                }
             }
         }
     }

PtVzzlexMasCake.sln

@@ -10,6 +10,7 @@ EndProject
 Project("{2150E333-8FDC-42A3-9474-1A3956D46DE8}") = "Solution Items", "Solution Items", "{6E2BA7B5-4B99-466E-983C-CE6EADEA56EB}"
 	ProjectSection(SolutionItems) = preProject
 		.gitignore = .gitignore
+		costs.png = costs.png
 		dotnet-install.ps1 = dotnet-install.ps1
 		dotnet-install.sh = dotnet-install.sh
 		README.md = README.md

README.md

@@ -50,4 +50,43 @@ dotnet test
 No demonstration that the result is correct is provided, 
 but the algorithm was tested for numbers up to 2 ^ 20 against a completely different mothodology, 
 and the two methodologies provide solutions with the same cost 
-(even if not always the same solutions as multiple optimal exist for a given input).
+(even if not always the same solutions as multiple optimal exist for a given input).
+
+## Worst case scenario
+![alt text](costs.png)
+
+The worst case is for numbers needing one "AddOne" or "SubtractOne" operation every two "Halve" operations, meaning 1.5 Log2(N) operations (the best case scenarion is obviously log2(N) operations).
+
+for example the number 699051 requires the folloqing sequence to reach one:
+
+```
+AddOne
+Halve
+Halve
+AddOne
+Halve
+Halve
+AddOne
+Halve
+Halve
+AddOne
+Halve
+Halve
+AddOne
+Halve
+Halve
+AddOne
+Halve
+Halve
+AddOne
+Halve
+Halve
+AddOne
+Halve
+Halve
+AddOne
+Halve
+Halve
+SubtractOne
+Halve
+```