16 1 19 master method tủ tài liệu training pdf

Design and Analysis
of Algorithms I

Master Method
The Precise
Statement


THE MASTER METHOD
Cool Feature : a “black box” for solving
recurrences.
AssumpFon : all subproblems have
equal size.

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Shangari


RECURRENCE FORMAT

1. Base Case : T(nti <= a constant for all sufficiently small n
2. For all larger n :

where
a = number of recursive calls (>= 1ti
b = input size shrinkage factor ( >
1ti
d = exponent in running Fme of “combine step” (>=0ti
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[a,b,d independent of n ]
Shangari

The Master Method
•

Nextcore AI Gopal Shangari


Master Method

Examples
Design and Analysis
of Algorithms I


The Master Method


EXAMPLE #1
Merge Sort
a=2
b=2
d=1

a

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1, 2, 0 [Case 1]


Example #3
a=4
b=2
d=1

Integer MulKplicaKon Algorithm # 1

Same as gradeNschool
algorithm


BeP er than
the gradeN
school
algorithm!!!


Example #5
Strassen’s Matrix MulKplicaKon Algorithm
a=7
b=2
d=2
=> beats the naïve iteraKve algorithm !


Example #6
FicKKous Recurrence

a=2
b=2
d=2