Use the recursion tree method to determine the asymptoticupper bound of T(n).T(n) satisfies the recurrence T(n)=2T(n-1)+...

Use the recursion tree method to determine the asymptoticupper bound of T(n).T(n) satisfies the recurrence T(n)=2T(n-1)+ c, where c is a positive constant, andT(0)=0.

Expert Solution

T(n) = 2T(n-1) + c

                   T(n) c ^
               / \ |
               T(n-1) T(n-1) 2c
           / \ / \ n times
       T(n-2) T(n-2) T(n-2) T(n-2) 4c
       . |
       .
       . |
       T(0) T(0) ..... T(0) V
       c c ..... c



T(n) = c + 2c + 4c + 8c ..... 2ⁿc
= c( 1 + 2 + 4 +8 ... n times) // sum of geometric progresssion with a = 1 and r = 2
= c * 2ⁿ⁺¹

T(n) = O(2ⁿ)

venereology answered 1 month ago

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Question

Use the recursion tree method to determine the asymptoticupper bound of T(n).T(n) satisfies the recurrence T(n)=2T(n-1)+...

Solutions

Expert Solution

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