Introduction to Algorithms : Recurrence
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  •  Consider another recurrence:
T(n)

= O(1)                        if n = 1

= 2T(n/2) + O(n)        if n > 1
  • In the above recurrence relation O(1) means a constant. So we can replace with some constant c1.
  • Similarly,O(n) means a function of order n. So we can replace with C2n.Hence, the recurrence can be rewritten as
<= C1 if n=1
T(n)
            <= 2T(n/2) + C2n if n > 1
  • Solution by Iterative method:
<= 2T(n/2) + C2n
T(n)

<= 2( 2T(n/4) + C2n/2) + C2n

<= T() + C2n + C2n

<= (2 T() + C2) + C2n + C2n

<= T() + C2n + C2n + C2n
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<= T() + C2 n i

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