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    • #2100
      shalizy
      Participant

      Detail About Recursion and its Type

      Here I am going to give a detail about Recursion in C++.
      Definition: Recursion is the process where a function is called itself but stack frame will be out of limit because function call will be infinite times. So a termination condition is mandatory to a recursion.
      In C++, Recursion can be divided into two types:

      1. Run- Time Recursion: Normal as in C
      2. Compile- Time Recursion: By using Template

      Each of these can be also divided into following types:

      1. Linear Recursion
      2. Binary Recursion
      3. Tail Recursion
      4. Mutual Recursion
      5. Nested Recursion

      1. Linear Recursion: This recursion is the most commonly used. In this recursion a function call itself in a simple manner and by termination condition it terminates. This process called ‘Winding’ and when it returns to caller that is called ‘Un-Winding’. Termination condition also known as Base condition.

      Example: Factorial calculation by linear recursion
      Run-Time Version


      int Fact(long n)
      {
      if(0>n)
      return -1;
      if(0 == n)
      return 1;
      else
      {
      return ( n* Fact(n-1));
      }
      }

      Winding Process:
      Function
      called
      Function return

      Fact(6) 6*Fact(5)
      Fact(5) 5*Fact(4)
      Fact(4) 4*Fact(3)
      Fact(3) 3* Fact(2)
      Fact(2) 2* Fact(1)
      Fact(1) 1* Fact(0)

      Terminating Point
      Fact(0) 1

      Unwinding Process

      Fact(1) 1*1
      Fact(2) 2*1
      Fact(3) 3*2*1
      Fact(4) 4*3*2*1
      Fact(5) 5*4*3*2*1
      Fact(6) 6*5*4*3*2*1

      Compile-Time Version


      // template for Base Condition
      template <>
      struct Fact<0>
      {
      enum
      {
      factVal = 1
      };
      };

      template
      struct Fact
      {
      // Recursion call by linear method
      enum
      {
      value = n * Fact::factVal
      };
      };

      To test it how it’s working at compile time, just call

            cout << Fact<-1>::factVal ;

      And compile it then compiler error will come, because no template for -1.

      2. Binary Recursion: Binary Recursion is a process where function is called twice at a time inplace of once at a time. Mostly it’s using in data structure like operations for tree as traversal, finding height, merging, etc.

      Example: Fibonacci number

      Run Time Version Code:


      int FibNum(int n)
      {
      // Base conditions
      if (n < 1)
      return -1;
      if (1 == n || 2 == n)
      return 1;

      // Recursive call by Binary Method
      return FibNum(n - 1) + FibNum(n -
      2); // At a time two recursive function called
      so
      // binary
      }

      Compile Time Version Code


      // Base Conditions
      template<>
      struct FibNum<2>
      {
      enum { val = 1 };
      };
      template <>
      struct FibNum<1>
      {
      enum { val = 1 };
      };

      // Recursive call by Binary Method
      template
      struct FibNum
      {
      enum { val= FibNum::val + FibNum::val };
      };

      3. Tail Recursion: In this method, recursive function is called at the last. So it’s more efficient than linear recursion method. Means you can say termination point will come(100%) only you have to put that condition.

      Example: Fibonacci number

      Run Time Version Code:


      int FibNum(int n, int x, int y)
      {
      if (1 == n) // Base Condition
      {
      return y;
      }
      else // Recursive call by Tail method
      {
      return FibNum(n-1, y, x+y);
      }
      }

      Compile Time Version Code


      template
      struct FibNum
      {
      // Recursive call By tail method
      enum
      {
      val = FibNum::val
      };
      };

      // Base Condition or Termination
      template

      struct FibNum<1, x, y>
      {
      enum
      {
      val = y
      };
      };

      4. Mutual Recursion: Functions calling each other. Let’s say FunA calling FunB and FunB calling FunA recursively. This is not actually not recursive but it’s doing same as recursive. So you can say Programming languages which are not supporting recursive calls, mutual recursion can be applied there to fulfill the requirement of recursion. Base condition can be applied to any into one or more than one or all functions.

      Example: To find Even Or Odd number

      Run Time Version Code:


      bool IsOddNumber(int n)
      {
      // Base or Termination Condition
      if (0 == n)
      return 0;
      else
      // Recursive call by Mutual Method
      return IsEvenNumber(n - 1);
      }

      bool IsEvenNumber(int n)
      {
      // Base or Termination Condition
      if (0 == n)
      return 1;
      else
      // Recursive call by Mutual Method
      return IsOddNumber(n - 1);
      }

      Compile Time Version Code


      // Base Or Termination Conditions
      template <>
      struct IsOddNumber<0>
      {
      enum
      {
      val = 0
      };
      };
      template <>
      struct IsEvenNumber<0>
      {
      enum
      {
      val = 1
      };
      };

      // Recursive calls by Mutual Method

      template
      struct IsOddNumber
      {
      enum
      {
      val = n == 0 ? 0 : IsEvenNumber::val
      };
      };


      template
      struct IsEvenNumber
      {
      enum
      {
      val = n == 0 ? 1 : IsOddNumber::val
      };
      };

      3. Nested Recursion: It’s very different than all recursions. All recursion can be converted to iterative (loop) except nested recursion. You can understand this recursion by example of Ackermann function.

      Example: Ackermann function

      Run Time Version Code:


      int Ackermann(int x, int y)
      {
      // Base or Termination Condition
      if (0 == x)
      {
      return y + 1;
      }
      // Error Handling condition
      if (x < 0 || y < 0)
      {
      return -1;
      }
      // Recursive call by Linear method
      else if (x > 0 && 0 == y)
      {
      return Ackermann(x-1, 1);
      }
      // Recursive call by Nested method
      else
      {
      return Ackermann(x-1, Ackermann(x, y-1));
      }
      }

      Compile Time Version Code


      // Base Or Termination condition
      template
      struct Ackermann<0, y>
      {
      enum { val = y + 1 };
      };

      // Recursive Call by Linear Method
      template

      struct Ackermann
      {
      enum
      {
      val = Ackermann::val
      };
      };

      // Recursive Call by Nested Method
      template

      struct Ackermann
      {
      Enum
      {
      val = Ackermann ::val>::val
      };
      };

    • #3388
      Adetutu
      Participant

      Thanks buddy. I have used all the methods but was not aware about these terms.

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