16 1 19 master method tủ tài liệu training pdf

Master Method The Precise Statement Design and Analysis of Algorithms I... THE MASTER METHODNextcore AI -Gopal Shangari Cool Feature : a “black box” for solving recurrences.. AssumpFon

Master Method The Precise

Statement

Design and Analysis

of Algorithms I

THE MASTER METHOD

Nextcore AI -Gopal Shangari

Cool Feature : a “black box” for solving

recurrences.

AssumpFon : all subproblems have

equal size.

RECURRENCE FORMAT

Nextcore AI -Gopal Shangari

where

a = number of recursive calls (>= 1ti

b = input size shrinkage factor ( >

1ti

d = exponent in running Fme of “combine step” (>=0ti [a,b,d independent of n ]

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

2 For all larger n :

The Master Method

•

Nextcore AI -Gopal Shangari

Master Method

Examples

Design and Analysis

of Algorithms I

The Master Method

EXAMPLE #1

Nextcore AI -Gopal Shangari

Merge Sort

a = 2

b = 2

d = 1

a

1, 2, 0 [Case 1]

Example #3

Integer MulKplicaKon Algorithm # 1

a = 4

b = 2

d = 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 nạve iteraKve algorithm !

Example #6

FicKKous Recurrence

 a = 2

 b = 2

 d = 2