# C++ Program to Find the Longest Increasing Subsequence of a Given Sequence

Longest Increasing Subsequence is a subsequence where one item is greater than its previous item.

Here we will try to find Longest Increasing Subsequence length, from a set of integers.

Input: A set of integers. {0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15}
Output: The length of longest increasing subsequence. Here it is 6.
The subsequence is 0, 2, 6, 9, 13, 15.

## Algorithm

### longestSubSeq(subarray, n)

Input: The sub array and the size of sub array.

Output: Longest increasing sub sequence length.

Begin
define array length of size n
initially set 0 to all entries of length
for i := 1 to n-1, do
for j := 0 to i-1, do
if subarray[j] < subarray[i] and length[j] > length[i], then
length[i] := length[j]
done
increase length[i] by 1
done
lis := 0
for i := 0 to n-1, do
lis := maximum of lis and length[i]
done
return lis
End

## Example Code

#include <iostream>
using namespace std;
int longestSubSeq(int subArr[], int n) {
int length[n] = { 0 }; //set all length to 0
length[0] = 1;    //subsequence ending with subArr[0] is 1
for (int i = 1; i < n; i++) {    //ignore first character, second to all
for (int j = 0; j < i; j++) {    //subsequence ends with subArr[j]
if (subArr[j] < subArr[i] && length[j] > length[i])
length[i] = length[j];
}
}
int lis = 0;
for (int i = 0; i<n; i++) // find longest increasing subsequence
lis = max(lis, length[i]);
return lis;
}
int main() {
int arr[] = { 0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15 };
int n = 16;
cout << "Length of Longest Increasing Subsequence is: " << longestSubSeq(arr, n);
return 0;
}

## Output

Length of Longest Increasing Subsequence is: 6

Updated on: 30-Jul-2019

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