Concept explainers
(a)
To determine the asymptotic bounds for the recurrence relation using master method.
(a)
Explanation of Solution
Given Information: The recurrence relation is
Explanation:
For a divide and conquer recurrence of the form
Case 1: If
Case 2: If
Case 3: If
The values of
Therefore,
So, case 3 of the master method applies.
Hence,
(b)
To determine the asymptotic bounds for the recurrence relation using master method.
(b)
Explanation of Solution
Given Information: The recurrence relation is
Explanation:
The values of
Therefore,
So, case 3 of the master method applies.
Hence,
(c)
To determine the asymptotic bounds for the recurrence relation using master method.
(c)
Explanation of Solution
Given Information: The recurrence relation is
Explanation:
The values of
Therefore,
So, case 2 of the master method applies.
Hence,
(d)
To determine the asymptotic bounds for the recurrence relation using master method.
(d)
Explanation of Solution
Given Information: The recurrence relation is
Explanation:
The values of
Therefore,
So, case 3 of the master method applies.
Hence,
(e)
To determine the asymptotic bounds for the recurrence relation using master method.
(e)
Explanation of Solution
Given Information: The recurrence relation is
Explanation:
The values of
Therefore,
So, case 1 of the master method applies.
Hence,
(f)
To determine the asymptotic bounds for the recurrence relation using master method.
(f)
Explanation of Solution
Given Information: The recurrence relation is
Explanation:
The values of
Therefore,
So, case 2 of the master method applies.
Hence,
(g)
To determine the asymptotic bounds for the recurrence relation using master method.
(g)
Explanation of Solution
Given Information: The recurrence relation is
Explanation:
The recurrence relation is not in the form of master theorem. Therefore, it cannot be solve by master theorem.
Solve the recurrence relation
as follows:
Therefore, the asymptotic notation of the recurrence
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Chapter 4 Solutions
Introduction to Algorithms
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