C# : Collections
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["trlwrjtekdtrkrrt. 3cCaBCCST~~}T~~YF565656FFsCC.C#CCEcBCP5G5FXCCP565G5F*3BC,CBZBBCeBXS}T~~}T~~","Recursion."," This is a concept. A recursive method calls itself. Recursive methods are used extensively in programming and in compilers.","Recursion, notes."," These algorithms help with complex problems. They solve problems and puzzles with brute force. They exhaust all possibilities. ","Tip: ","Recursive algorithms are often used for complex searching and simulation. They add needless complication in other programs.","Example."," Here is a recursive method. The method has 2 parameters, including a ref parameter. It checks a condition near the top of its method body, as many recursive algorithms do. ","Ref ","ref","And: ","It calls itself again based on an incremented value of the parameter it receives. The program also has a commented-out exception.","Tip: ","This demonstrates the appearance of the method call stack frames in a recursive algorithm.","ins","class","adsbygoogle","data-ad-client","ca-pub-4712093147740724","data-ad-slot","6227126509","data-ad-format","auto","ins","class","adsbygoogle","data-ad-client","ca-pub-4712093147740724","data-ad-slot","6227126509","data-ad-format","auto","Based on:"," .NET 4.6\n\n","C# program that uses recursive method","\n\nusing System;\n\nclass Program\n{\n static int ","Recursive","(int value, ref int count)\n {\n count++;\n if (value >= 10)\n {","\n // throw new Exception(\"End\");\n ","return value;\n }\n return ","Recursive","(value + 1, ref count);\n }\n\n static void Main()\n {","\n //\n // Call recursive method with two parameters.\n //\n ","int count = 0;\n int total = ","Recursive","(5, ref count);","\n //\n // Write the result from the method calls and also the call count.\n //\n ","Console.WriteLine(total);\n Console.WriteLine(count);\n }\n}\n\n","Output","\n\n10 Total value of 10 was added up.\n6 Six method calls.\n\n","Exception thrown when throw uncommented:","\n\nUnhandled Exception: System.Exception: End\n at Program.Recursive(Int32 value, Int32& count) ...Program.cs:line 10\n at Program.Recursive(Int32 value, Int32& count) ...Program.cs:line 13\n at Program.Recursive(Int32 value, Int32& count) ...Program.cs:line 13\n at Program.Recursive(Int32 value, Int32& count) ...Program.cs:line 13\n at Program.Recursive(Int32 value, Int32& count) ...Program.cs:line 13\n at Program.Recursive(Int32 value, Int32& count) ...Program.cs:line 13\n at Program.Main() in ...Program.cs:line 22","Notes, an end."," Every recursive method sequence must be terminated. Often the first part of the recursive method will have a branch that tests for a condition being met. ","And: ","In this way, the recursive methods continue until the result is attained (or the algorithm fails).","Note: ","The primitive example here continues until it sums up a value of 10 by incrementing an integer.","Notes, ref."," The ref keyword is useful when dealing with recursive methods. We have the recursive method return more than one value without using any allocations on the managed heap. ","Tip: ","You may want to use the count parameter to make sure you don't enter an infinite recursion series.","Notes, call stack."," The call stack has six method stack frames with the Recursive method signature in them. The top frame is the exact line where the exception was thrown. ","Then: ","The next five show the intermediate method calls\u2014these exited at a later point.","So: ","If you see the same method signature repeated many times in the call stack, you have a recursive method.","Activation Record ","activation-record","StackOverflowException."," This may be the shortest valid C# program that will crash. The Main method calls Main. The stack will overflow, leading to a memory error. ","StackOverflowException ","stackoverflowexception","Tip: ","The exception here is a good thing, as it stops a process that would otherwise continue infinitely, wasting time and resources.","C# program that causes StackOverflowException","\n\nclass Program\n{\n static void ","Main","()\n {","\n // Do not run this program.\n ","Main","();\n }\n}\n\n","Output","\n\nProcess is terminated due to StackOverflowException.","Tail recursion."," Does the C# compiler optimize tail recursion? Here we show a method called Recurse that could be optimized to iteration using tail recursion. ","Result: ","The compiler does not optimize the tail calls in this program. So it causes a stack overflow.","Thus: ","The programmer will need to write tail-recursive methods with iteration to achieve optimal performance in C# programs.","C# program that tests for tail recursion","\n\nclass Program\n{\n static void ","Recurse","(int remaining)\n {","\n // This method could be optimized with tail recursion.\n ","if (remaining <= 0)\n {\n return;\n }\n ","Recurse","(remaining - 1);\n }\n\n static void Main()\n {","\n // Attempt to call this method.\n ","Recurse","(1000000);\n }\n}\n\n","Output","\n\nProcess is terminated due to StackOverflowException.","Compilers."," The concept of recursion is used in compilers. Every compiler uses some form of recursion. The C# compiler logically uses recursion to parse and compile every program.","Compilers, continued."," In compilers, consider the type inference algorithm. This is recursive. This algorithm determines the best fit for method overloading based on method signatures. ","Overload ","overload","Also: ","These algorithms can be represented using an iterative algorithm that is recursive only in a logical sense.","Stacks."," Recursion can be changed to use a stack-type structure instead of true recursion. This exchanges method call frames for object instances on the managed heap. ","And: ","This is a good reason to prefer a Stack-based collection over a true recursive method.","Stack ","stack","Uses."," Algorithms that solve puzzles use recursion. We can implement a brute-force search of all possibilities and all possibilities after that. ","Constraint Puzzle ","constraint","Maze ","maze","Tip: ","Recursion can be used to implement certain forms of artificial intelligence.","Some research."," In The Art of Computer Programming, Donald Knuth discusses recursion at depth and uses examples of combinatorics. Anagrams can be implemented with recursive algorithms. ","Anagram ","anagram","A summary."," There are tricks to using recursive methods. Reference parameters (with the ref and out keywords) are often useful. We examined the call stack for a recursive algorithm. 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)","url(data:image/jpeg;base64,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)","url(data:image/png;base64,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)"]