Leetcode #1854: Maximum Population Year
In this guide, we solve Leetcode #1854 Maximum Population Year in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Array, Counting, Prefix Sum
Intuition
Range queries become simple once we precompute cumulative sums.
We can transform subarray conditions into prefix comparisons.
Approach
Compute prefix sums and use a map to find matching prefixes.
This avoids nested loops while keeping the logic clear.
Steps:
- Compute prefix sums.
- Use a map to find valid ranges.
- Update the answer.
Example
Input: logs = [[1993,1999],[2000,2010]]
Output: 1993
Explanation: The maximum population is 1, and 1993 is the earliest year with this population.
Python Solution
class Solution:
def maximumPopulation(self, logs: List[List[int]]) -> int:
d = [0] * 101
offset = 1950
for a, b in logs:
a, b = a - offset, b - offset
d[a] += 1
d[b] -= 1
s = mx = j = 0
for i, x in enumerate(d):
s += x
if mx < s:
mx, j = s, i
return j + offset
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.