Find the time period with the maximum number of overlapping intervals - algorithm

Question

There is one very famous problem. I am asking the same here.
There is number of elephants time span given, here time span means, year of birth to year of death.
You have to calculate the period where maximum number of elephants are alive.
Example:
1990 - 2013
1995 - 2000
2010 - 2020
1992 - 1999
Answer is 1995 - 1999
I tried hard to solve this, but I am unable to do so.
How can I solve this problem?
I got approach for when a user asks to find the number of elephants in any year. I solved that by using segment tree, whenever any elephants time span given, increase every year of that time span by 1. We can solve that in this way. Can this be used to solve the above problem?
For above question, I only need the high-level approach, I will code it myself.

Answer 1

Split each date range into start date and end date.
Sort the dates. If a start date and an end date are the same, put the end date first (otherwise you could get an empty date range as the best).
Start with a count of 0.
Iterate through the dates using a sweep-line algorithm:
If you get a start date:
Increment the count.
If the current count is higher than the last best count, set the count, store this start date and set a flag.
If you get an end date:
If the flag is set, store the stored start date and this end date with the count as the best interval so far.
Reset the flag.
Decrement the count.
Example:
For input:
1990 - 2013
1995 - 2000
2010 - 2020
1992 - 1999
Split and sorted: (S = start, E = end)
1990 S, 1992 S, 1995 S, 1999 E, 2000 E, 2010 S, 2013 E, 2020 E
Iterating through them:
count = 0
lastStart = N/A
1990: count = 1
count = 1 > 0, so set flag
and lastStart = 1990
1992: count = 2
count = 2 > 0, so set flag
and lastStart = 1992
1995: count = 3
count = 3 > 0, so set flag
and lastStart = 1995
1999: flag is set, so
record [lastStart (= 1995), 1999] with a count of 3
reset flag
count = 2
2000: flag is not set
reset flag
count = 1
2010: count = 2
since count = 2 < 3, don't set flag
2013: flag is not set
reset flag
count = 1
2020: flag is not set
reset flag
count = 0

Answer 2

How about this?
Say I have all the above data stored in a file. Read it into two arrays separated by the " - ".
Hence, now I have birthYear[] which contains all the birth years and deathYear[] containing all the death years.
so birthYear[] = [1990, 1995, 2010, 1992]
deathYear[] = [2013, 2000, 2020, 1999]
Get the min birth year and the max death year. Create a Hashtable with the Key as a year, and the Value as the count.
Hence,
HashTable<String, Integer> numOfElephantsAlive = new HashTable<String, Integer>();
Now, from the min(BirthYear) to the max(BirthYear), do the following :
Iterate through the Birth Year Array and do an add to the HashTable all the years in between the BirthYear and Corresponding DeathYear with the count being 1. If the key already exists, add 1 to it. Hence, for the last case :
1992 - 1999
HashTable.put(1992, 1)
HashTable.put(1993, 1)
and so on for every year.
Say, for example, you have a Hashtable that looks like this at the end of it:
Key Value
1995 3
1996 3
1992 2
1993 1
1994 3
1998 1
1997 2
1999 2
Now, you need the range of the Years when the number of elephants were maximum. Hence, let's iterate and find the year with the max value. This is pretty easy. Iterate over the keySet() and get the year.
Now, you need a contiguous range of years. You can either do this in two ways:
Do Collections.sort() over the keySet() and when you hit the max value, save all contiguous locations.
Hence, on hitting 3 for our example at 1994, we would check for all the following years with a 3. This will return you your range which is the min-year, max-year combo.

Answer 3

One approach maybe:
Iterate through the periods. Keep track of a list of periods up to now. Note: At each step, the number of periods increases by 2 (or 1 if there is no overlap with the existing list of periods).
For example
1990 - 2013
Period List contains 1 period { (1990,2013) }
Count List contains 1 entry { 1 }
1995 - 2000
Period List contains 3 periods { (1990,1995), (1995,2000), (2000,2013) }
Count List contains 3 entries { 1, 2, 1 }
2010 - 2020
Period List contains 5 periods { (1990,1995), (1995,2000), (2000,2010), (2010, 2013), (2013, 2020) }
Count List contains 5 entries { 1, 2, 1, 2, 1 }
1992 - 1999
Period List contains 7 periods { (1990,1992), (1992,1995), (1995,1999), (1999,2000), (2000,2010), (2010, 2013), (2013, 2020) }
Count List contains 7 entries { 1, 2, 3, 2, 1, 2, 1 }

Answer 4

1) arrange in assending order year wise starting from the largest series.
2) count the years for largest series for whole data set
3) then identify the largest count.
4) the largest count is your answer for years... this can be done in Algo.