Leetcode #2449: Minimum Number of Operations to Make Arrays Similar
In this guide, we solve Leetcode #2449 Minimum Number of Operations to Make Arrays Similar 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 two positive integer arrays nums and target, of the same length. In one operation, you can choose any two distinct indices i and j where 0 <= i, j < nums.length and: set nums[i] = nums[i] + 2 and set nums[j] = nums[j] - 2.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Greedy, Array, Sorting
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: nums = [8,12,6], target = [2,14,10]
Output: 2
Explanation: It is possible to make nums similar to target in two operations:
- Choose i = 0 and j = 2, nums = [10,12,4].
- Choose i = 1 and j = 2, nums = [10,14,2].
It can be shown that 2 is the minimum number of operations needed.
Python Solution
class Solution:
def makeSimilar(self, nums: List[int], target: List[int]) -> int:
nums.sort(key=lambda x: (x & 1, x))
target.sort(key=lambda x: (x & 1, x))
return sum(abs(a - b) for a, b in zip(nums, target)) // 4
Complexity
The time complexity is , where is the length of the array . The space complexity is O(1) to O(n).
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.