computer operating system:Greedy algorithm

Rita M.Marwada
M.Sc(C.S)
Roll no:17

 Let us consider that you have an array F with size
n.
 F[i] contains the size of ith file
 We want merge that file into one single file.
 What could be the best possible solution for
that….?
 1) A and B are two files with sizes and then time
complexity of merging it is 0(m+n)
 Eg: F={10,5,100,50,20,15}
 N=6

 Select first 2 files and merge them then merge the previous output file with the third file and so on….
 Merge1:F={15,100,50,20,15} cost=15
 Merge2:F={115,50,20,15} cost=115
 Merge3:F={165,20,15} cost=165
 Merge4:F={185,15} cost=185
 Merge5:F={200} cost=200
 Total cost of merging=15+115+165+185+200
 =680
Strategy 2
 Step1:merge the file in group of 2
 Step2:That means after the first step we ll have n/2 intermidiate files.
 Step3:Then merge these intermediate files.
 Step4:Keep merging in that way till all files are merged.
 Step5:This approach is called 2 way merging
 Step6:If we do it in group of elements then it is called k way merging

 We have F={10,5,100,50,20,15}
 Step 1:F{15,150,35} Cost=15+150+35
 Step 2:F{165,35} Cost=165
 Step 3:F{200} Cost=200
 Total cost=15+150+35+165+200=565

 1)sort file in ascending order as F={5,10,15,20,50,100}
 Repeat the process until we have single file
 Take 1st two smallest file then merge them
 Insert the merged file in the sorted list at its correct
position
 F={15,15,20,50,100} cost=15
 f-={20,30,50,100} c0st= 30
 F={50,50,100} cost=50
 F={100,100} cost=100
 F={200} c0st=200
 15+30+50+100+200=395
 Total cost of merging is 395
 This is optimal solution
 Time complexity:0(nlogn)

 An activity selection problem
 Elements of greedy strategy
 Huffman codes

 Greedy algorithm is the concept which observes
subproblems and we need to consider only one
choice.i.e called as greedy choice
 Based on observation greedy choice makes
optimal solution.
 A greedy algorithm always makes the choice that
looks, best at the moment.
 But greedy algorithm do not always read optimal
solution but from many problem they do.
 Greedy algorithm following dynamic
programming approach where recursive calls ,
how been made optimal solution.

 S={a1,a2 ,…………………..an}
 Start time si and finish time fi,
 Where 0 ≤si < fi<∞
 If selected activity ai takes place during the half open time
interval[si,fi),
 Activities a1 and aj are compatible if the intervals [si,fi) and
[si,fj) do not overlap.
 i.e ai and aj are compatible if si≤fj or sj≥fj.
i 1 2 3 4 5 6 7 8 9 10 11
si 1 3 0 5 3 5 6 8 8 2 12
fi 4 5 9 7 9 9 10 11 12 14 16

From the above set of activities we wish to find
maximum set of mutual compatible activities that start
after ak activity finishes and that finished before aj
starts.

S1={a1,a4,a8,a
11}S2={a2,a4,
a9,a11}
S3={a3,a9,,a11}
S4={ a4,a8,a11}
S5={a5,a11}
S6={a6,a11}
S7={a7,a11}
s8={a8,a11}
S9={a9,a11}
S10={a10}
S11={a11}

 m=k+1
 While m≤n and s[m]<f[k]
 M=m+1
 If m≤n
 return{am}URECURSIVE-ACTIVITY-SELECTOR(
s, f, k, n)
 Else return ∅

K sk fk
0 - 0 a0
1 1 4
ao
2 3 5
2 0 6
3 5 7
5 3 9
6 5 9
7 6 10
8 8 11
9 8 12
10 2 14
11 12 16
a1
M=1
Recursive-activity selector(s,f,0,11)
a2
a1
a3
a1
a1 a4
M=4
a1
a4
a5
a1
a1
a1
a4
a4
a4
a6
a7
a8
M=8
a1
a1
a1
a4
a4
a4
a8
a8
a8
a10
a11
M=11
Recursive-activity selector(s,f,11

 n=s.length
 A={a1}
 K=1
 For m=2 to n
 If s[m]≥f[k]
 A=AU{am}
 K=m
 Return A

 Determine the optimal substructure
 Develop the recursive solution
 Prove one of the optimal choice is greedy
choce
 Show that all but one of subproblems are
empty after greedy choice
 Develop a recursive algorithm that
implements the greedy strategy
 Convert the recursive algorithm to an iterative
one.

 Data compression algorithm using greedy
choice.
 Without loss of information.
 Based n assigned codes based on
frequencies.
 Variable length codes are known as prefix
codes.

characte
r
code frequenc
y
A 000 10
E 001 15
I 010 12
S 011 3
T 100 4
P 101 13
Newline 110 1
Total
bits
30
45
36
12
12
39
3
A E I S
T P n
Code tree
0 1
0 1 0
1
0
1
0
1
0 1 0
A 000
E 001
Total :174

 Goal: reduces the code tree.
cha
r
freq
A 10
E 15
I 12
S 3
F 4
P 13
n 1

n
S
4
F
8
A
18
I P
2
5
1 3410
12 13
58
33
E
15

n
S
4
T
8
A
1
8
I P
2
5
1 3410
12 13
58
3
3
E
15
0
1
0 1
0
1
0
1
0
1
0 1
Char Code Freq Total
bits
A 110 10 30
E 10 15 30
I 00 12 24
S 11111 3 15
T 110 4 16
P 01 13 20
n 11110 1 5
Total :146

 n=|C|
 Q=C
 For i=1 to n-1
 Allocate a new node z
 Z.left=x=EXTRACT-MIN(Q)
 Z.left=y=EXTRACT-MIN(Q)
 INSERT(Q,z)
 Return EXTRACT-MIN(Q) //return to the root
of tree

1
0
item3
$60
2
0
30
item1
item2
$120$100
3
0
2
0
50
$120+
$60
$10
0
=$220
$100
+
+
+
+
1
0
20
30
10
$120
$60
=$180=$160
(b)(a) 20
30
20
10
(c)
$100
$60
$80
=$240
An example shows that the greedy
strategy does not work for the 0-1
knapsack problem

a)the thief must select a subset
Of three items shown whose weight
must not exceed 50 pond.
(b)the optimal subset includes items 2
and 3
.any solution with 1 item is suboptimal
even though item 1 has the greatest
value per pound
(c) fractional knapsack problem ,taking
the
Item in order of greatest value per
pound yields an optimal solution

 Introduction to algorithms by THOMAS
H.COREMEN , CHARLES E.LEISERSON, RONALD
L.RIVEST, CLIFFORD STEIN
 WWW.google.com

computer operating system:Greedy algorithm

computer operating system:Greedy algorithm

More Related Content

What's hot

Similar to computer operating system:Greedy algorithm

Recently uploaded

computer operating system:Greedy algorithm