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TIME COMPLEXITY PROBLEM

(4 posts)

1. 

   pasinhal
   Member
   Posted 3 months ago #
   
   

   What will be the time complexity T(n) and space complexity S(n) of the following Algorithm?
   How can we build a recursion tree for the same?

   Large(n)
   {
           If(n<=1)
                 Return n;'
            Sum = 0;
            For i= 1 To n-1
                  Sum = Sum + Large(i);
            Return Sum;
   }

2. 

   kartik
   Moderator
   Posted 3 months ago #
   
   

   T(n) = Sum of T(i) for i = 1 to n - 1 + C

   Where C is constant for operations other than recursive calls.

   The recursion tree will look like following:

   Step 1:
                                   C
                      /           |       ...\
               T(n-1)    T(n-2)     T(1)
   

   Step 2:
                                                                      C
                                                 /                    |             \
                                              /                       |               \
                                            C                        C        ...     C
                                       /   | ..  \                  /..\
                            T(n-2)  T(n-1)..T(1)
   

   Recursion tree method doesn't seem very helpful here to find the complexity. You can find the complexity by considering base cases one by one

   T(1) = C
   T(2) = T(1) + C = 2C
   T(3) = T(2) + T(1) + C = 4C
   T(4) = T(3) + T(2) + T(1) + C = 8C
   T(5) = T(4) + T(3) + T(2) + T(1) + C = 16C

   You can see that the complexity increases in powers of 2. So T(n) would be O(2^n)

3. 

   pasinhal
   Member
   Posted 3 months ago #
   
   

   Thanks. But what will be the space complexity?

4. 

   atul007
   Member
   Posted 3 months ago #
   
   

   space complexity is O(n).

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