Branches and Recursive Functions

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• Questions?
• Recursive Functions
  • Example: Fibonacci numbers
    • For natural numbers n:
      • F(n) = 0 if n = 0
      • F(n) = 1 if n = 1
      • F(n) = F(n-1) + F(n-2) otherwise
    • e.g., F(1) = 1, F(3) = 2
    • This can be translated fairly directly into a Matlab function
      

      function [ F ] = fib( n )
      %FIB Compute nth Fibonacci number
      if ( n == 0 )
          F = 0;
      elseif ( n == 1 )
          F = 1;
      else                % n > 1
          F = fib( n-1 ) + fib( n-2 );
      end
      end

    • Calling the function produces the expected results
      

      >> fib(1)
      ans =
           1
      >> fib(3)
      ans =
           2
      >> fib(6)
      ans =
           8

  • This idea of defining something in terms of simpler instances of itself is recursion
  • It’s a natural way to define many things in math, and those definitions translate well into programming functions based on branching
  • (It’s also very powerful tactic in designing and programming algorithms, aspects we won’t go into in this course)
• Branching Lab
  • Beware that testing to see if a value lies in a range requires 2 comparisons and an “and” in Matlab
    

    >> x = 10
    x =
        10
    >> % 0 <= x <= 1?
    >> 0 <= x <= 1
    ans =
         1
    >> % Something is wrong: 10 is clearly not between 0 and 1
    >> 0 <= x & x <= 1
    ans =
         0
    >> % This expression produced the correct result

• Next
  • Matlab’s debugger—a way to watch functions execute
  • Watch “Matlab Debugging Tutorial” at https://www.youtube.com/watch?v=PdNY9n8lV1Y

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