Objectives

Notes

• We discussed tracing the factorial function

  •          6! = 6 * 5! =                                6 * 120 = 720
                  5! = 5 * 4! =                        5* 24 = 120 ^
                      4! = 4 * 3! =   4 *             6 = 24 ^
                          3! = 3 * 2! = 3 *       2 = 6 ^
                              2! = 2 * 1! = 2*1 = 2 ^  
                                 1! = 1   ^
            

• We discussed tracing the Fibonacci sequence

                    fib(5) = fib(4) + fib(3)  = 5
                               3        2
  
           fib(4) = fib(3) + fib(2)=3      fib(3) = fib(2) + fib(1)=2
                     2        1                     1       1
  fib(3) = fib(2) + fib(1) = 2
             1       1
      

• We discussed an algorithm for binary search

  • Search(a,start, end, key) 
       if (start > end) 
          return NOT_FOUND
       find the middle element
       if  the middle element is equal to the key
          return the position
       else if middle < key
          return Search(a,mid+1, end, key)
       else
          return Search(a,start, mid-1, key) 

  • We wrote the following code binSearch.cpp