Discussion on: Algorithms: Common Years Problem

[Nam Hoang Le]

Hi Mohammed Shaikh, I want to contribute to your post to make it clearer and reach more reader.
Firstly, about problem description, there is no reason to return 0 if no two arrays overlap each other, just return all possible years. But, maybe we can return nil if array input is empty.

Next, let me rewrite your solution with some Ruby features I know:

def find_common_year(arr)
    return nil if arr.empty?
    counter = Hash.new(0)
    arr.each do |start_year, end_year|
        while start_year <= end_year do
            counter[start_year] += 1
            start_year += 1
        end
    end
    max_count = counter.values.max
    counter.keys.select { |year| counter[year] == max_count }
end

Finally, if we modify problem statement to find only one year among all possible years then there is another solution which has O(n) complexity with n is length of array input.

Please tell me if I'm wrong somewhere.

[Mohammed Shaikh]

Hi Nam H. Le,
I wanted to return 0 because there are no years overlapping. That was the original question. As for the modification of the problem statement, I am interested. What would be the problem statement. Let me know what you think 😃

[Nam Hoang Le]

First of all, to avoid ambiguation, we assume that if a person born (or die), he will born in the first (last) day of that year.
My solution is to create two 2-tuple for each person: (start_year, 1) and (end_year, -1).
And this one has O(nlogn) complexity. I'm wrong in previous coment.

def find2 arr
  ans, max_count, curr_count = nil, 0, 0
  arr
  .flat_map {|start_year, end_year| [[start_year, 1], [end_year, -1]]}
  .sort {|(s1, e1), (s2, e2)| s1 != s2 ? s1 <=> s2 : e2 <=> e1}
  .each {|year, delta|
    curr_count += delta
    ans, max_count = year, curr_count if curr_count > max_count
  }
  ans
end

find2([[1,5], [5, 9], [2,7]]) #  => 5

# [1      5]
#        [5       9]
#   [2        7]


#           count
# [1, 1]  => 1 
# [2, 1]  => 2
# [5, 1]  => 3 : max
# [5,-1]  => 2
# [7, -1] => 1
# [9,-1]  => 0

[Mohammed Shaikh]

Thanks Nam H. Le. That is an interesting variation of the problem