{"id":26243,"date":"2017-10-26T20:41:28","date_gmt":"2017-10-26T15:11:28","guid":{"rendered":"https:\/\/www.wikitechy.com\/technology\/?p=26243"},"modified":"2017-10-26T20:41:28","modified_gmt":"2017-10-26T15:11:28","slug":"java-programming-longest-bitonic-subsequence","status":"publish","type":"post","link":"https:\/\/www.wikitechy.com\/technology\/java-programming-longest-bitonic-subsequence\/","title":{"rendered":"Java Programming – Longest Bitonic Subsequence"},"content":{"rendered":"

Given an array arr[0 \u2026 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.<\/span>
\nA 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.<\/p>\n

Examples:<\/strong><\/p>\n

Input arr[] = {1, 11, 2, 10, 4, 5, 2, 1};\r\nOutput: 6 (A Longest Bitonic Subsequence of length 6 is 1, 2, 10, 4, 2, 1)\r\n\r\nInput arr[] = {12, 11, 40, 5, 3, 1}\r\nOutput: 5 (A Longest Bitonic Subsequence of length 5 is 12, 11, 5, 3, 1)\r\n\r\nInput arr[] = {80, 60, 30, 40, 20, 10}\r\nOutput: 5 (A Longest Bitonic Subsequence of length 5 is 80, 60, 30, 20, 10)<\/pre>\n
Solution<\/strong>
\nThis 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] \u2013 1 where i is from 0 to n-1.<\/p>\n[ad type=”banner”]\n
Following is Java\u00a0implementation of the above Dynamic Programming solution.<\/p>\n
 
 Java<\/span> <\/div> 
\/* 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 ));    }}<\/code><\/pre> <\/div>\n
Output :<\/strong><\/p>\n
 Length of LBS is 7\r\n<\/pre>\n
Time Complexity: O(n^2)
\nAuxiliary Space: O(n)<\/p>\n[ad type=”banner”]\n","protected":false},"excerpt":{"rendered":"
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