How do you solve Valid Arrangement of Pairs on LeetCode?

Valid Arrangement of Pairs (LeetCode #2097) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Pairs can be treated as directed edges in a graph.

What is the brute force solution for Valid Arrangement of Pairs?

The brute force approach for Valid Arrangement of Pairs is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible permutations of the pairs and checking each permutation to see if it forms a valid arrangement. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Valid Arrangement of Pairs?

Valid Arrangement of Pairs uses the following concepts: Array, Depth-First Search, Graph Theory, Eulerian Circuit. The recommended patterns to study are: Graph Traversal, Depth-First Search.

What are the interview tips for Valid Arrangement of Pairs?

Understand the underlying graph structure of the problem. Practice DFS and graph traversal techniques. Be prepared to explain your thought process clearly during the interview.

What are common mistakes when solving Valid Arrangement of Pairs?

Not recognizing the graph nature of the problem. Failing to implement DFS correctly.

#2097

Valid Arrangement of Pairs

Hard

ArrayDepth-First SearchGraph TheoryEulerian CircuitGraph TraversalDepth-First Search

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution treats the pairs as a directed graph where each pair represents an edge. We can use a depth-first search (DFS) to find an Eulerian path, which guarantees a valid arrangement of pairs.

⚙️

Algorithm

3 steps

1Step 1: Build a graph using a hashmap where each key is a start node and its value is a stack of end nodes.
2Step 2: Perform a depth-first search (DFS) starting from any node to traverse the graph and collect the pairs in the correct order.
3Step 3: Reverse the collected pairs to get the valid arrangement.

solution.py13 lines

1from collections import defaultdict
2
3def valid_arrangement(pairs):
4    graph = defaultdict(list)
5    for start, end in pairs:
6        graph[start].append(end)
7    result = []
8    def dfs(node):
9        while graph[node]:
10            dfs(graph[node].pop())
11        result.append(node)
12    dfs(pairs[0][0])
13    return [[result[i], result[i+1]] for i in range(len(result)-1)][::-1]

ℹ

Complexity note: The time complexity is O(n) because we traverse each pair once to build the graph and again during the DFS. The space complexity is O(n) due to the storage of the graph and the result list.

1Pairs can be treated as directed edges in a graph.
2A valid arrangement corresponds to finding an Eulerian path.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.