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Consider a list of recursive algorithms and a list of recurrence relations as shown below. Each recurrence relation corresponds to exactly one algorithm and is used to derive the time complexity of the algorithm.
Which of the following is the correct match between the algorithms and their recurrence relations?
  • a)
    P-II, Q-III, R-IV, S-1
  • b)
    P-IV, Q-III, R-I, S-II
  • c)
    P-III, Q-II, R-IV, S-I
  • d)
    R-IV, Q-II, R-I, S-III
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Consider a list of recursive algorithms and a list of recurrence relat...
These are examples of some standard algorithms whose 
Merge Sort:    T(n) = 2T(n/2) + Θ(n). It falls in case 2 as c is 1 and Logba] is also 1 and  the solution is Θ(n Logn) //time complexity can be evaluated using Master Method
Binary Search: T(n) = T(n/2) + Θ(1). It also falls in case 2 as c is 0 and Logba is also 0 and the solution is Θ(Logn) //time complexity can be evaluated using Master Method
Quick Sort : Time taken by QuickSort in general can be written as  T(n) = T(k) + T(n-k-1) + (n)
Tower of Hanoi : T(n) = 2T(n-1) + 1
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Most Upvoted Answer
Consider a list of recursive algorithms and a list of recurrence relat...
These are examples of some standard algorithms whose 
Merge Sort:    T(n) = 2T(n/2) + Θ(n). It falls in case 2 as c is 1 and Logba] is also 1 and  the solution is Θ(n Logn) //time complexity can be evaluated using Master Method
Binary Search: T(n) = T(n/2) + Θ(1). It also falls in case 2 as c is 0 and Logba is also 0 and the solution is Θ(Logn) //time complexity can be evaluated using Master Method
Quick Sort : Time taken by QuickSort in general can be written as  T(n) = T(k) + T(n-k-1) + (n)
Tower of Hanoi : T(n) = 2T(n-1) + 1
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Consider a list of recursive algorithms and a list of recurrence relations as shown below. Each recurrence relation corresponds to exactly one algorithm and is used to derive the time complexity of the algorithm.Which of the following is the correct match between the algorithms and their recurrence relations?a)P-II, Q-III, R-IV, S-1b)P-IV, Q-III, R-I, S-IIc)P-III, Q-II, R-IV, S-Id)R-IV, Q-II, R-I, S-IIICorrect answer is option 'B'. Can you explain this answer?
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