- Prepare
- Algorithms
- Dynamic Programming
- The Longest Common Subsequence

# The Longest Common Subsequence

# The Longest Common Subsequence

A subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements. Longest common subsequence (*LCS*) of 2 sequences is a subsequence, with maximal length, which is common to both the sequences.

Given two sequences of integers, and , find the longest common subsequence and print it as a line of space-separated integers. If there are multiple common subsequences with the same maximum length, print any one of them.

In case multiple solutions exist, print any of them. It is guaranteed that at least one non-empty common subsequence will exist.

**Recommended References**

This Youtube video tutorial explains the problem and its solution quite well.

**Function Description**

Complete the *longestCommonSubsequence* function in the editor below. It should return an integer array of a longest common subsequence.

longestCommonSubsequence has the following parameter(s):

*a*: an array of integers*b*: an array of integers

**Input Format**

The first line contains two space separated integers and , the sizes of sequences and .

The next line contains space-separated integers .

The next line contains space-separated integers .

**Constraints**

**Constraints**

**Output Format**

Print the longest common subsequence as a series of space-separated integers on one line. In case of multiple valid answers, print any one of them.

**Sample Input**

```
5 6
1 2 3 4 1
3 4 1 2 1 3
```

**Sample Output**

```
1 2 3
```

**Explanation**

There is no common subsequence with length larger than 3. And "1 2 3", "1 2 1", "3 4 1" are all correct answers.

**Tested by** Khongor