In python, how does one efficiently find the largest consecutive set of numbers in a list that are not necessarily adjacent?

Question

For instance, if I have a list

[1,4,2,3,5,4,5,6,7,8,1,3,4,5,9,10,11]

This algorithm should return [1,2,3,4,5,6,7,8,9,10,11].

To cl

Answer 1

You need the Maximum contiguous sum(Optimal Substructure):

def msum2(a):
    bounds, s, t, j = (0,0), -float('infinity'), 0, 0

    for i in range(len(a)):
        t = t + a[i]
        if t > s: bounds, s = (j, i+1), t
        if t < 0: t, j = 0, i+1
    return (s, bounds)

This is an example of dynamic programming and is O(N)