You have Sum-of-Subsets with given set S = {3, 9, 14, 15, 20} and sum W = 37; Following backtracking algorithm specify for each node if it is promising or not, and if that node is a solution. Do not list nodes in the pruned part of the tree. You do not need to print and to draw here the actual tree (you may do it for yourself on the piece of paper). Just list all nodes. in the figure 5.14. Count in each row starts from the left most possible position, like (5.1), (5.2). (5.3) and so on. Paragraph B I U A 三、 ►11 о + v Lato (Recom... v 19px... ▼ </> node (0,0) is node (1,1) is node (1,2) is and so on Figure 5.14 The pruned state space tree produced using backtracking in Example 5.6. Stored at each node from top to bottom are the total profit of the items stolen up to the node, their total weight, and the bound on the total profit that Item 1 1[$40] 2 Item 2 [$30] (2, 1) $70 7 $115 (1, 1) $40 2 $115 (0, 0) $0 0 $115 (1,2) $0 0 $82 (2,2) $40 2. $98 could be obtained by expanding beyond the node. The optimal $50 Item 3 10 (3, 1) (3,2) (3, 3) (3,4) $120 $70 $90 $40 17 7 12 2 $80 $98 $50 solution is found at Item 4 the node shaded in 4 [$30] X (4, 1) (4, 2) (4,3) (4, 4) color. Each nonpromising node $80 $70 $100 $90 12 7 17 12 is marked with a cross. $80 $70 $90 ×
You have Sum-of-Subsets with given set S = {3, 9, 14, 15, 20} and sum W = 37; Following backtracking algorithm specify for each node if it is promising or not, and if that node is a solution. Do not list nodes in the pruned part of the tree. You do not need to print and to draw here the actual tree (you may do it for yourself on the piece of paper). Just list all nodes. in the figure 5.14. Count in each row starts from the left most possible position, like (5.1), (5.2). (5.3) and so on. Paragraph B I U A 三、 ►11 о + v Lato (Recom... v 19px... ▼ </> node (0,0) is node (1,1) is node (1,2) is and so on Figure 5.14 The pruned state space tree produced using backtracking in Example 5.6. Stored at each node from top to bottom are the total profit of the items stolen up to the node, their total weight, and the bound on the total profit that Item 1 1[$40] 2 Item 2 [$30] (2, 1) $70 7 $115 (1, 1) $40 2 $115 (0, 0) $0 0 $115 (1,2) $0 0 $82 (2,2) $40 2. $98 could be obtained by expanding beyond the node. The optimal $50 Item 3 10 (3, 1) (3,2) (3, 3) (3,4) $120 $70 $90 $40 17 7 12 2 $80 $98 $50 solution is found at Item 4 the node shaded in 4 [$30] X (4, 1) (4, 2) (4,3) (4, 4) color. Each nonpromising node $80 $70 $100 $90 12 7 17 12 is marked with a cross. $80 $70 $90 ×
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Transcribed Image Text:You have Sum-of-Subsets with given set S = {3, 9, 14, 15, 20} and sum W = 37;
Following backtracking algorithm specify for each node if it is promising or not, and if that node is a
solution. Do not list nodes in the pruned part of the tree. You do not need to print and to draw here the actual
tree (you may do it for yourself on the piece of paper). Just list all nodes.
in the figure 5.14. Count in each row starts
from the left most possible position, like (5.1), (5.2). (5.3) and so on.
Paragraph
B
I U
A
三、
►11
о
+ v
Lato (Recom... v
19px... ▼
</>
node (0,0) is
node (1,1) is
node (1,2) is
and so on
![Figure 5.14
The pruned state
space tree produced
using backtracking
in Example 5.6.
Stored at each node
from top to bottom
are the total profit
of the items stolen
up to the node,
their total weight,
and the bound on
the total profit that
Item 1
1[$40]
2
Item
2 [$30]
(2, 1)
$70
7
$115
(1, 1)
$40
2
$115
(0, 0)
$0
0
$115
(1,2)
$0
0
$82
(2,2)
$40
2.
$98
could be obtained
by expanding
beyond the node.
The optimal
$50
Item 3
10
(3, 1)
(3,2)
(3, 3)
(3,4)
$120
$70
$90
$40
17
7
12
2
$80
$98
$50
solution is found at
Item 4
the node shaded in
4 [$30]
X
(4, 1)
(4, 2) (4,3)
(4, 4)
color. Each
nonpromising node
$80
$70
$100
$90
12
7
17
12
is marked with a
cross.
$80
$70
$90
×](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4fdcb26-bf4f-4942-89d3-0c4d39b5733d%2F3b233c04-2365-419c-bebe-5bfb2cae1c74%2Fqyw2qlo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Figure 5.14
The pruned state
space tree produced
using backtracking
in Example 5.6.
Stored at each node
from top to bottom
are the total profit
of the items stolen
up to the node,
their total weight,
and the bound on
the total profit that
Item 1
1[$40]
2
Item
2 [$30]
(2, 1)
$70
7
$115
(1, 1)
$40
2
$115
(0, 0)
$0
0
$115
(1,2)
$0
0
$82
(2,2)
$40
2.
$98
could be obtained
by expanding
beyond the node.
The optimal
$50
Item 3
10
(3, 1)
(3,2)
(3, 3)
(3,4)
$120
$70
$90
$40
17
7
12
2
$80
$98
$50
solution is found at
Item 4
the node shaded in
4 [$30]
X
(4, 1)
(4, 2) (4,3)
(4, 4)
color. Each
nonpromising node
$80
$70
$100
$90
12
7
17
12
is marked with a
cross.
$80
$70
$90
×
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