How to determine the longest increasing subsequence using dynamic programming?

Question

I have a set of integers. I want to find the longest increasing subsequence of that set using dynamic programming.

Answer 1

This can be solved in O(n^2) using Dynamic Programming. Python code for the same would be like:-

def LIS(numlist):
    LS = [1]
    for i in range(1, len(numlist)):
        LS.append(1)
        for j in range(0, i):
            if numlist[i] > numlist[j] and LS[i]<=LS[j]:
                LS[i] = 1 + LS[j]
    print LS
    return max(LS)

numlist = map(int, raw_input().split(' '))
print LIS(numlist)

For input:5 19 5 81 50 28 29 1 83 23

output would be:[1, 2, 1, 3, 3, 3, 4, 1, 5, 3] 5

The list_index of output list is the list_index of input list. The value at a given list_index in output list denotes the Longest increasing subsequence length for that list_index.