Question

How to find the longest continuous number sequence in array of number arrays? Each array of numbers represent one or zero numbers in resulting sequence.

Example ([] – represents array (like in javascript)):

[
    [1, 5, 6],
    [7],
    [22, 34],
    [500, 550],
    [60, 1],
    [90, 100],
    [243],
    [250, 110],
    [150],
    [155],
    [160]
]

Correct output would be: [1, 7, 22, 60, 90, 110, 150, 155, 160]

Detailed output:

1,   -- index  1 all 1, 5 and 6 would match here, pick the smallest
7,   -- index  2
22,  -- index  3
     -- index  4 skipped, the sequence would end here or wouldn't be the longest possible
60,  -- index  5 picked 60, because 1 wouldn't continue in the sequence
90,  -- index  6
     -- index  7 skipped, the sequence would end here or wouldn't be the longest possible
110, -- index  8
150, -- index  9
155, -- index 10
160  -- index 11

Answer 1

A possible approach is to use dynamic programming using as parameters the last value and the index of first sub-array to consider.

This is a solution in Python based on recursion with memoization

data = [[1, 5, 6],
        [7],
        [22, 34],
        [500, 550],
        [60, 1],
        [90, 100],
        [243],
        [250, 110],
        [150],
        [155],
        [160]]

def longest(x0, i, _cache=dict()):
    if i == len(data):
        return []
    try:
        return _cache[x0, i]
    except KeyError:
        best = longest(x0, i+1)
        for x in data[i]:
            if x >= x0:
                L = [x] + longest(x, i+1)
                if len(L) > len(best):
                    best = L
        _cache[x0, i] = best
        return best

print longest(0, 0)