What is the primary algorithmic approach for solving the Valid Arrangement of Pairs problem?

The problem can be solved using graph traversal with depth-first search (DFS), where pairs are treated as directed edges in a graph.

How does the Eulerian path relate to the Valid Arrangement of Pairs?

The problem can be viewed as finding an Eulerian path in a directed graph, where nodes represent numbers and edges represent the pairs. The conditions for an Eulerian path help ensure a valid arrangement.

What is the time complexity of solving the Valid Arrangement of Pairs?

The time complexity is O(V + E), where V is the number of nodes and E is the number of edges. This is due to the graph traversal via DFS.

Can there be multiple valid arrangements for the same input in the Valid Arrangement of Pairs?

Yes, there can be multiple valid arrangements. The problem only requires one valid arrangement, but multiple solutions may exist depending on the traversal order.

What happens if the input size is too large for a brute-force solution?

A brute-force solution would fail to meet the time constraints. A more efficient approach using DFS and graph traversal ensures scalability for larger inputs.

#2097

Hard

auto_awesome图·DFS·traversal

LeetCode 题解工作台

合法重新排列数对

给你一个下标从 0 开始的二维整数数组 pairs ，其中 pairs[i] = [start i , end i ] 。如果 pairs 的一个重新排列，满足对每一个下标 i （ 1 ）都有 end i-1 == start i ，那么我们就认为这个重新排列是 pairs 的一个合法重新排列。…

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题目描述

给你一个下标从 0 开始的二维整数数组 pairs ，其中 pairs[i] = [start_i, end_i] 。如果 pairs 的一个重新排列，满足对每一个下标 i （ 1 <= i < pairs.length ）都有 end_i-1 == start_i，那么我们就认为这个重新排列是 pairs 的一个 合法重新排列 。

请你返回 任意一个 pairs 的合法重新排列。

注意：数据保证至少存在一个 pairs 的合法重新排列。

示例 1：

输入：pairs = [[5,1],[4,5],[11,9],[9,4]]
输出：[[11,9],[9,4],[4,5],[5,1]]
解释：
输出的是一个合法重新排列，因为每一个 end_i-1 都等于 start_i 。
end₀ = 9 == 9 = start₁ 
end₁ = 4 == 4 = start₂
end₂ = 5 == 5 = start₃

示例 2：

输入：pairs = [[1,3],[3,2],[2,1]]
输出：[[1,3],[3,2],[2,1]]
解释：
输出的是一个合法重新排列，因为每一个 end_i-1 都等于 start_i 。
end₀ = 3 == 3 = start₁
end₁ = 2 == 2 = start₂
重新排列后的数组 [[2,1],[1,3],[3,2]] 和 [[3,2],[2,1],[1,3]] 都是合法的。

示例 3：

输入：pairs = [[1,2],[1,3],[2,1]]
输出：[[1,2],[2,1],[1,3]]
解释：
输出的是一个合法重新排列，因为每一个 end_i-1 都等于 start_i 。
end₀ = 2 == 2 = start₁
end₁ = 1 == 1 = start₂

提示：

1 <= pairs.length <= 10⁵
pairs[i].length == 2
0 <= start_i, end_i <= 10⁹
start_i != end_i
pairs 中不存在一模一样的数对。
至少存在一个合法的 pairs 重新排列。

lightbulb

解题思路

方法一

1

2

speed

复杂度分析

指标	值
时间	O(V + E)
空间	O(V + E)

psychology

面试官常问的追问

外企场景

question_mark
Check if the candidate understands the problem as a graph traversal challenge.
question_mark
Look for familiarity with Eulerian path conditions and how to apply them in DFS.
question_mark
Evaluate the candidate's ability to handle large inputs efficiently, ensuring time complexity constraints are respected.

warning

常见陷阱

外企场景

error
Forgetting to handle nodes with no outgoing edges or incoming edges can lead to an incomplete traversal.
error
Not considering the graph construction properly might make the DFS traversal invalid.
error
Failing to efficiently handle large inputs within the time constraints can lead to performance issues.

swap_horiz

进阶变体

外企场景

arrow_right_alt
If the input allows for multiple valid arrangements, ensure that the algorithm can return any valid solution.
arrow_right_alt
Variants may ask for optimizations based on specific graph properties or constraints, such as disallowing certain types of pair connections.
arrow_right_alt
In some variations, the problem might involve finding an arrangement that minimizes or maximizes certain properties, such as the number of hops between nodes.

help

常见问题

外企场景

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