Algorithm to determine if array contains n…n+m?

Question

I saw this question on Reddit, and there were no positive solutions presented, and I thought it would be a perfect question to ask here. This was in a thread about interview

Answer 1

Any contiguous array [ n, n+1, ..., n+m-1 ] can be mapped on to a 'base' interval [ 0, 1, ..., m ] using the modulo operator. For each i in the interval, there is exactly one i%m in the base interval and vice versa.

Any contiguous array also has a 'span' m (maximum - minimum + 1) equal to it's size.

Using these facts, you can create an "encountered" boolean array of same size containing all falses initially, and while visiting the input array, put their related "encountered" elements to true.

This algorithm is O(n) in space, O(n) in time, and checks for duplicates.

def contiguous( values )
    #initialization
    encountered = Array.new( values.size, false )
    min, max = nil, nil
    visited = 0

    values.each do |v|

        index = v % encountered.size

        if( encountered[ index ] )
            return "duplicates"; 
        end

        encountered[ index ] = true
        min = v if min == nil or v < min
        max = v if max == nil or v > max 
        visited += 1
    end

    if ( max - min + 1 != values.size ) or visited != values.size
        return "hole"
    else
        return "contiguous"
    end

end

tests = [ 
[ false, [ 2,4,5,6 ] ], 
[ false, [ 10,11,13,14 ] ] , 
[ true , [ 20,21,22,23 ] ] , 
[ true , [ 19,20,21,22,23 ] ] ,
[ true , [ 20,21,22,23,24 ] ] ,
[ false, [ 20,21,22,23,24+5 ] ] ,
[ false, [ 2,2,3,4,5 ] ]
]

tests.each do |t|
    result = contiguous( t[1] )
    if( t[0] != ( result == "contiguous" ) )
        puts "Failed Test : " + t[1].to_s + " returned " + result
    end
end