Leetcode #2513: Minimize the Maximum of Two Arrays
In this guide, we solve Leetcode #2513 Minimize the Maximum of Two Arrays 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
We have two arrays arr1 and arr2 which are initially empty. You need to add positive integers to them such that they satisfy all the following conditions: arr1 contains uniqueCnt1 distinct positive integers, each of which is not divisible by divisor1.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Math, Binary Search, Number Theory
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: divisor1 = 2, divisor2 = 7, uniqueCnt1 = 1, uniqueCnt2 = 3
Output: 4
Explanation:
We can distribute the first 4 natural numbers into arr1 and arr2.
arr1 = [1] and arr2 = [2,3,4].
We can see that both arrays satisfy all the conditions.
Since the maximum value is 4, we return it.
Python Solution
class Solution:
def minimizeSet(
self, divisor1: int, divisor2: int, uniqueCnt1: int, uniqueCnt2: int
) -> int:
def f(x):
cnt1 = x // divisor1 * (divisor1 - 1) + x % divisor1
cnt2 = x // divisor2 * (divisor2 - 1) + x % divisor2
cnt = x // divisor * (divisor - 1) + x % divisor
return (
cnt1 >= uniqueCnt1
and cnt2 >= uniqueCnt2
and cnt >= uniqueCnt1 + uniqueCnt2
)
divisor = lcm(divisor1, divisor2)
return bisect_left(range(10**10), True, key=f)
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.