Long increase subsequences are study in the context of various disciplines associated to mathematics, including algorithmics, random matrix theory, representation theory, and physics. In computer science, the longest increase subsequence problem is to find a subsequence of a given sequence in which the subsequence's components are in sorted order, lowest to highest, and in which the subsequence is as long as possible.

COMING SOON!

```
//Program to calculate length of longest increasing subsequence in an array
#include <bits/stdc++.h>
using namespace std;
int LIS(int a[], int n)
{
int lis[n];
for (int i = 0; i < n; ++i)
{
lis[i] = 1;
}
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < i; ++j)
{
if (a[i] > a[j] && lis[i] < lis[j] + 1)
lis[i] = lis[j] + 1;
}
}
int res = 0;
for (int i = 0; i < n; ++i)
{
res = max(res, lis[i]);
}
return res;
}
int main(int argc, char const *argv[])
{
int n;
cout << "Enter size of array: ";
cin >> n;
int a[n];
cout << "Enter array elements: ";
for (int i = 0; i < n; ++i)
{
cin >> a[i];
}
cout << LIS(a, n) << endl;
return 0;
}
```