. Given a sequence of integers, a longest increasing sequence corresponds to a longest directed path in DAG (Directed Acyclic Graph), such as 1 → 23 →6 →7, in the DAG below for the sequence 1, 18, 5, 3, 6, 9, 7 2 3 4 5 6 6 7 8
. Given a sequence of integers, a longest increasing sequence corresponds to a longest directed path in DAG (Directed Acyclic Graph), such as 1 → 23 →6 →7, in the DAG below for the sequence 1, 18, 5, 3, 6, 9, 7 2 3 4 5 6 6 7 8
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please explain why the missing entires are 2,3,5
![Given a sequence of integers, a longest increasing sequence corresponds to a longest directed path in a
DAG (Directed Acyclic Graph), such as 1 → 2 → 3 → 6 → 7, in the DAG below for the sequence 1, 2,
18, 5, 3, 6, 9, 7
1
2
2
8
3
1
5
4
3
5
Figure 2: DAG for the sequence 1, 2, 8, 5, 3, 6, 9, 7
The length, L[j], of a longest strictly increasing sequence ending at node indexed, j (index label of a
node is outside the circle), is found using the formula:
L[j] = 1 + max{L[i]: (i, j) € E},
(1)
where (i, j) is a directed edge (arrow) going from index i to index j and E is set of all such directed
edges. The array L[1..8] below, has some entries missing. Fill them up using the formula above:
6
3 4
Ans: From left to right, the missing entries are 2, 3 and 5.
8
5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40a93fbf-cd84-46cf-939a-402485a39dd9%2Fccfd8d7d-efcb-488a-87af-c3b99d4fbbf5%2Fky7yiys_processed.png&w=3840&q=75)
Transcribed Image Text:Given a sequence of integers, a longest increasing sequence corresponds to a longest directed path in a
DAG (Directed Acyclic Graph), such as 1 → 2 → 3 → 6 → 7, in the DAG below for the sequence 1, 2,
18, 5, 3, 6, 9, 7
1
2
2
8
3
1
5
4
3
5
Figure 2: DAG for the sequence 1, 2, 8, 5, 3, 6, 9, 7
The length, L[j], of a longest strictly increasing sequence ending at node indexed, j (index label of a
node is outside the circle), is found using the formula:
L[j] = 1 + max{L[i]: (i, j) € E},
(1)
where (i, j) is a directed edge (arrow) going from index i to index j and E is set of all such directed
edges. The array L[1..8] below, has some entries missing. Fill them up using the formula above:
6
3 4
Ans: From left to right, the missing entries are 2, 3 and 5.
8
5
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