This is a Java Program to implement Longest Increasing Subsequence Algorithm. This program finds the longest increasing sequence of numbers from an array of numbers.

Here is the source code of the Java Program to implement Longest Increasing Subsequence Algorithm. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

`/**`

`** Java Program to implement Longest Increasing Subsequence Algorithm`

`**/`

import java.util.Scanner;

`/** Class LongestIncreasingSubsequence **/`

public class LongestIncreasingSubsequence

`{`

`/** function lis **/`

public int[] lis(int[] X)

`{`

int n = X.length - 1;

int[] M = new int[n + 1];

int[] P = new int[n + 1];

int L = 0;

for (int i = 1; i < n + 1; i++)

`{`

int j = 0;

`/** Linear search applied here. Binary Search can be applied too.`

`binary search for the largest positive j <= L such that`

`X[M[j]] < X[i] (or set j = 0 if no such value exists) **/`

for (int pos = L ; pos >= 1; pos--)

`{`

if (X[M[pos]] < X[i])

`{`

j = pos;

break;

`}`

`}`

P[i] = M[j];

if (j == L || X[i] < X[M[j + 1]])

`{`

M[j + 1] = i;

L = Math.max(L,j + 1);

`}`

`}`

`/** backtrack **/`

int[] result = new int[L];

int pos = M[L];

for (int i = L - 1; i >= 0; i--)

`{`

result[i] = X[pos];

pos = P[pos];

`}`

return result;

`}`

`/** Main Function **/`

public static void main(String[] args)

`{`

Scanner scan = new Scanner(System.in);

System.out.println("Longest Increasing Subsequence Algorithm Test\n");

System.out.println("Enter number of elements");

int n = scan.nextInt();

int[] arr = new int[n + 1];

System.out.println("\nEnter "+ n +" elements");

for (int i = 1; i <= n; i++)

arr[i] = scan.nextInt();

LongestIncreasingSubsequence obj = new LongestIncreasingSubsequence();

int[] result = obj.lis(arr);

`/** print result **/`

System.out.print("\nLongest Increasing Subsequence : ");

for (int i = 0; i < result.length; i++)

System.out.print(result[i] +" ");

System.out.println();

`}`

`}`

Longest Increasing Subsequence Algorithm Test Enter number of elements 16 Enter 16 elements 0 8 4 12 2 10 6 14 1 9 5 13 3 11 7 15 Longest Increasing Subsequence : 0 2 6 9 11 15

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