Leetcode #1956: Minimum Time For K Virus Variants to Spread
In this guide, we solve Leetcode #1956 Minimum Time For K Virus Variants to Spread 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
There are n unique virus variants in an infinite 2D grid. You are given a 2D array points, where points[i] = [xi, yi] represents a virus originating at (xi, yi) on day 0.
Quick Facts
- Difficulty: Hard
- Premium: Yes
- Tags: Geometry, Array, Math, Binary Search, Enumeration
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: points = [[1,1],[6,1]], k = 2
Output: 3
Explanation: On day 3, points (3,1) and (4,1) will contain both virus variants. Note that these are not the only points that will contain both virus variants.
Python Solution
Complexity
The time complexity is O(log n) or O(n log n). The space complexity is O(1).
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.