Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Longest Increasing Subsequence
Longest Increasing Subsequence is a subsequence where one item is greater than its previous item. Here we will try to find Longest Increasing Subsequence length, from a set of integers.
Input and Output
Input:
A set of integers. {0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15}
Output:
The length of longest increasing subsequence. Here it is 6.
The subsequence is 0, 2, 6, 9, 13, 15.Algorithm
longestSubSeq(subarray, n)
Input − The sub array and the size of sub array.
Output − Longest increasing sub sequence length.
Begin define array length of size n initially set 0 to all entries of length for i := 1 to n-1, do for j := 0 to i-1, do if subarray[j] < subarray[i] and length[j] > length[i], then length[i] := length[j] done increase length[i] by 1 done lis := 0 for i := 0 to n-1, do lis := maximum of lis and length[i] done return lis End
Example
#include <iostream>
using namespace std;
int longestSubSeq(int subArr[], int n) {
int length[n] = { 0 }; //set all length to 0
length[0] = 1; //subsequence ending with subArr[0] is 1
for (int i = 1; i < n; i++) { //ignore first character, second to all
for (int j = 0; j < i; j++) { //subsequence ends with subArr[j]
if (subArr[j] < subArr[i] && length[j] > length[i])
length[i] = length[j];
}
length[i]++; //add arr[i]
}
int lis = 0;
for (int i = 0; i<n; i++) // find longest increasing subsequence
lis = max(lis, length[i]);
return lis;
}
int main() {
int arr[] = { 0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15};
int n = 16
cout << "Length of Longest Increasing Subsequence is: " << longestSubSeq(arr, n);
return 0;
}Output
Length of Longest Increasing Subsequence is: 6
Updated on: 16-Jun-2020
1K+ Views
Advertisements