# 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.
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.
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

Solution
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.

## Java

 `/* Dynamic Programming implementation in Java for longest bitonic``   ``subsequence problem */``import` `java.util.*;``import` `java.lang.*;``import` `java.io.*;`` ` `class` `LBS``{``    ``/* lbs() returns the length of the Longest Bitonic Subsequence in``    ``arr[] of size n. The function mainly creates two temporary arrays``    ``lis[] and lds[] and returns the maximum lis[i] + lds[i] - 1.`` ` `    ``lis[i] ==> Longest Increasing subsequence ending with arr[i]``    ``lds[i] ==> Longest decreasing subsequence starting with arr[i]``    ``*/``    ``static` `int` `lbs( ``int` `arr[], ``int` `n )``    ``{``        ``int` `i, j;`` ` `        ``/* Allocate memory for LIS[] and initialize LIS values as 1 for``            ``all indexes */``        ``int``[] lis = ``new` `int``[n];``        ``for` `(i = ``0``; i < n; i++)``            ``lis[i] = ``1``;`` ` `        ``/* Compute LIS values from left to right */``        ``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``;`` ` `        ``/* Allocate memory for lds and initialize LDS values for``            ``all indexes */``        ``int``[] lds = ``new` `int` `[n];``        ``for` `(i = ``0``; i < n; i++)``            ``lds[i] = ``1``;`` ` `        ``/* Compute LDS values from right to left */``        ``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``;`` ` ` ` `        ``/* Return the maximum value of lis[i] + lds[i] - 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:

` Length of LBS is 7`

Time Complexity: O(n^2)
Auxiliary Space: O(n)

Please refer complete article on Longest Bitonic Subsequence | DP-15 for more details!

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