Leetcode #1989: Maximum Number of People That Can Be Caught in Tag
In this guide, we solve Leetcode #1989 Maximum Number of People That Can Be Caught in Tag 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 playing a game of tag with your friends. In tag, people are divided into two teams: people who are "it", and people who are not "it".
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Greedy, Array
Intuition
A locally optimal choice leads to a globally optimal result for this structure.
That means we can commit to decisions as we scan without backtracking.
Approach
Sort or preprocess if needed, then repeatedly take the best available local choice.
Maintain the minimal state necessary to validate the greedy decision.
Steps:
- Sort or preprocess as needed.
- Iterate and pick the best local option.
- Track the current solution.
Example
Input: team = [0,1,0,1,0], dist = 3
Output: 2
Explanation:
The person who is "it" at index 1 can catch people in the range [i-dist, i+dist] = [1-3, 1+3] = [-2, 4].
They can catch the person who is not "it" at index 2.
The person who is "it" at index 3 can catch people in the range [i-dist, i+dist] = [3-3, 3+3] = [0, 6].
They can catch the person who is not "it" at index 0.
The person who is not "it" at index 4 will not be caught because the people at indices 1 and 3 are already catching one person.
Python Solution
class Solution:
def catchMaximumAmountofPeople(self, team: List[int], dist: int) -> int:
ans = j = 0
n = len(team)
for i, x in enumerate(team):
if x:
while j < n and (team[j] or i - j > dist):
j += 1
if j < n and abs(i - j) <= dist:
ans += 1
j += 1
return ans
Complexity
The time complexity is , where is the length of the array . 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.