1854. Maximum Population Year
Description
You are given a 2D integer array logs
where each logs[i] = [birthi, deathi]
indicates the birth and death years of the ith
person.
The population of some year x
is the number of people alive during that year. The ith
person is counted in year x
's population if x
is in the inclusive range [birthi, deathi - 1]
. Note that the person is not counted in the year that they die.
Return the earliest year with the maximum population.
Example 1:
Input: logs = [[1993,1999],[2000,2010]] Output: 1993 Explanation: The maximum population is 1, and 1993 is the earliest year with this population.
Example 2:
Input: logs = [[1950,1961],[1960,1971],[1970,1981]] Output: 1960 Explanation: The maximum population is 2, and it had happened in years 1960 and 1970. The earlier year between them is 1960.
Constraints:
1 <= logs.length <= 100
1950 <= birthi < deathi <= 2050
Solutions
Solution 1: Difference Array
We notice that the range of years is $[1950,..2050]$. Therefore, we can map these years to an array $d$ of length $101$, where the index of the array represents the value of the year minus $1950$.
Next, we traverse $logs$. For each person, we increment $d[birth_i - 1950]$ by $1$ and decrement $d[death_i - 1950]$ by $1$. Finally, we traverse the array $d$, find the maximum value of the prefix sum, which is the year with the most population, and add $1950$ to get the answer.
The time complexity is $O(n)$, and the space complexity is $O(C)$. Where $n$ is the length of the array $logs$, and $C$ is the range size of the years, i.e., $2050 - 1950 + 1 = 101$.
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