Question 5: The Longest Increasing Subsequence (LIS) problem is to find the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order. For example, the length of LIS for {10, 22, 9, 33, 21, 50, 41, 60, and 80} is 6 and LIS is {10, 22, 33, 50, 60, and 80}. arr[] 10 22 9 33 21 50 41 60 80 LIS 1 3 4 5 More Examples: Input : arr[] - (3, 10, 2, 1, 20)} Output : Length of LIS - 3 The longest increasing subsequence is 3, 10, 20 Input : arr[] - (3, 2} Output : Length of LIS - 1 The longest increasing subsequences are {3} and {2} Input : arr[] - (50, 3, 10, 7, 40, 80} Output : Length of LIS = 4 The longest increasing subsequence is (3, 7, 40, 80}

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
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Question 5:
The Longest Increasing Subsequence (LIS) problem is to find the length of the longest
subsequence of a given sequence such that all elements of the subsequence are sorted in
increasing order. For example, the length of LIS for {10, 22, 9, 33, 21, 30, 41, 60, and 80} is 6
and LIS is {10, 22, 33, 50, 60, and 80}.
arr[]
10
22
33
21
50
41
60
80
LIS
2
3
4
More Examples:
Input : arr[] = (3, 10, 2, 1, 20}
Output : Length of LIS = 3
The longest increasing subsequence is 3, 10, 20
Input : arr[] - (3, 2}
Output : Length of LIS - 1
The longest increasing subsequences are {3} and {2}
Input : arr[] - {50, 3, 10, 7, 40, 80}
Output : Length of LIS = 4
The longest increasing subsequence is (3, 7, 40, 80}
9
Transcribed Image Text:Question 5: The Longest Increasing Subsequence (LIS) problem is to find the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order. For example, the length of LIS for {10, 22, 9, 33, 21, 30, 41, 60, and 80} is 6 and LIS is {10, 22, 33, 50, 60, and 80}. arr[] 10 22 33 21 50 41 60 80 LIS 2 3 4 More Examples: Input : arr[] = (3, 10, 2, 1, 20} Output : Length of LIS = 3 The longest increasing subsequence is 3, 10, 20 Input : arr[] - (3, 2} Output : Length of LIS - 1 The longest increasing subsequences are {3} and {2} Input : arr[] - {50, 3, 10, 7, 40, 80} Output : Length of LIS = 4 The longest increasing subsequence is (3, 7, 40, 80} 9
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