Find the Longest Increasing Sub sequence (LIS) in an array. The longest Increasing Sub-sequence (LIS) problem is to find the length of the longest sub-sequence of a given sequence such that all elements of the sub-sequence are sorted in increasing order.
For example, length of LIS for { 10, 22, 9, 33, 21, 50, 41, 60, 80 } is 6 and LIS is {10, 22, 33, 50, 60, 80}.