Here's a solution that takes O(P + R) time, where P is the number of people and R is the total range of birth years. First, notice that you don't really care w

Here's a solution that takes O(P + R) time, where P is the number of people and R is the total range of birth years. First, notice that you don't really care who died when. All that matters is someone died. People's birth and death years are fungible, in a sense. Each birth increases the population by one and each death increases the population by one. Basically, you'll create an array where the value at each index represents how much the population changed in that year (steps 1 to 3). Then you can use that array to find the highest population (step 4). 1. Get the min birth year and the max birth year. 2. Create an array where the size is the above range. Set to all zeros. Each index will map to / represent a year in the range. 3. Loop through all the people. For each person, increment the index of their birth year and decrement their death year (or the following year, depending on whether or not they're counted as alive the entire year of their death) 4. Just loop through the array, tracking the running sum at each index. The biggest running sum will indicate the highest population. There are some other good solutions depending on what assumptions you make about P and R's relative size.