Java Program to Find the Longest Bitonic Subsequence
Last Updated :
21 Dec, 2021
Given an array arr[0 … n-1] containing n positive integers, a subsequence of arr[] is called Bitonic if it is first increasing, then decreasing. Write a function that takes an array as argument and returns the length of the longest bitonic subsequence.Â
A sequence, sorted in increasing order is considered Bitonic with the decreasing part as empty. Similarly, decreasing order sequence is considered Bitonic with the increasing part as empty.Â
Examples:
Input arr[] = {1, 11, 2, 10, 4, 5, 2, 1};
Output: 6 (A Longest Bitonic Subsequence of length 6 is 1, 2, 10, 4, 2, 1)
Input arr[] = {12, 11, 40, 5, 3, 1}
Output: 5 (A Longest Bitonic Subsequence of length 5 is 12, 11, 5, 3, 1)
Input arr[] = {80, 60, 30, 40, 20, 10}
Output: 5 (A Longest Bitonic Subsequence of length 5 is 80, 60, 30, 20, 10)
Source: Microsoft Interview Question
Â
SolutionÂ
This problem is a variation of standard Longest Increasing Subsequence (LIS) problem. Let the input array be arr[] of length n. We need to construct two arrays lis[] and lds[] using Dynamic Programming solution of LIS problem. lis[i] stores the length of the Longest Increasing subsequence ending with arr[i]. lds[i] stores the length of the longest Decreasing subsequence starting from arr[i]. Finally, we need to return the max value of lis[i] + lds[i] – 1 where i is from 0 to n-1.
Following is the implementation of the above Dynamic Programming solution.Â
Â
Java
import java.util.*;
import java.lang.*;
import java.io.*;
class LBS
{
static int lbs( int arr[], int n )
{
int i, j;
int [] lis = new int [n];
for (i = 0 ; i < n; i++)
lis[i] = 1 ;
for (i = 1 ; i < n; i++)
for (j = 0 ; j < i; j++)
if (arr[i] > arr[j] && lis[i] < lis[j] + 1 )
lis[i] = lis[j] + 1 ;
int [] lds = new int [n];
for (i = 0 ; i < n; i++)
lds[i] = 1 ;
for (i = n- 2 ; i >= 0 ; i--)
for (j = n- 1 ; j > i; j--)
if (arr[i] > arr[j] && lds[i] < lds[j] + 1 )
lds[i] = lds[j] + 1 ;
int max = lis[ 0 ] + lds[ 0 ] - 1 ;
for (i = 1 ; i < n; i++)
if (lis[i] + lds[i] - 1 > max)
max = lis[i] + lds[i] - 1 ;
return max;
}
public static void main (String[] args)
{
int arr[] = { 0 , 8 , 4 , 12 , 2 , 10 , 6 , 14 , 1 , 9 , 5 ,
13 , 3 , 11 , 7 , 15 };
int n = arr.length;
System.out.println( "Length of LBS is " + lbs( arr, n ));
}
}
|
Output:Â
Length of LBS is 7
Time Complexity: O(n^2)Â
Auxiliary Space: O(n)
Â
Please refer complete article on Longest Bitonic Subsequence | DP-15 for more details!
Like Article
Suggest improvement
Share your thoughts in the comments
Please Login to comment...