How do you solve Construct 2D Grid Matching Graph Layout on LeetCode?

Construct 2D Grid Matching Graph Layout (LeetCode #3311) 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: Understanding node degrees helps in constructing the grid efficiently.

What is the time complexity of Construct 2D Grid Matching Graph Layout?

The optimal solution for Construct 2D Grid Matching Graph Layout runs in O(n) time and uses O(n) space. The time complexity is O(n) because we traverse the edges and nodes a limited number of times, making it efficient even for large inputs.

What is the brute force solution for Construct 2D Grid Matching Graph Layout?

The brute force approach for Construct 2D Grid Matching Graph Layout is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible arrangements of the nodes and checking each arrangement to see if it meets the adjacency condition defined by the edges. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Construct 2D Grid Matching Graph Layout?

Construct 2D Grid Matching Graph Layout uses the following concepts: Array, Hash Table, Graph Theory, Matrix. The recommended patterns to study are: Graph Traversal, Degree Counting.

What are the interview tips for Construct 2D Grid Matching Graph Layout?

Clarify the problem requirements before jumping to code. Discuss your thought process and approach clearly. Consider edge cases and constraints during your solution.

What are common mistakes when solving Construct 2D Grid Matching Graph Layout?

Failing to account for all possible node degrees. Not checking adjacency conditions correctly.

#3311

Construct 2D Grid Matching Graph Layout

Hard

ArrayHash TableGraph TheoryMatrixGraph TraversalDegree Counting

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 approach leverages the properties of the graph, particularly the degrees of the nodes. By identifying nodes with degree 1 and 2, we can construct the grid more efficiently without generating permutations.

⚙️

Algorithm

3 steps

1Step 1: Create a degree count for each node based on the edges.
2Step 2: Identify nodes with degree 1 (endpoints) and degree 2 (interior nodes).
3Step 3: Start placing the nodes in the grid from the endpoints, ensuring adjacency based on the edges.

solution.py22 lines

1from collections import defaultdict
2
3def constructGrid(n, edges):
4    degree = defaultdict(int)
5    graph = defaultdict(list)
6    for u, v in edges:
7        degree[u] += 1
8        degree[v] += 1
9        graph[u].append(v)
10        graph[v].append(u)
11    grid = [[-1] * n for _ in range((n + 1) // 2)]
12    idx = 0
13    for node in range(n):
14        if degree[node] == 1:
15            grid[idx // 2][idx % 2] = node
16            idx += 1
17            for neighbor in graph[node]:
18                if degree[neighbor] == 2:
19                    grid[idx // 2][idx % 2] = neighbor
20                    idx += 1
21    return grid
22

ℹ

Complexity note: The time complexity is O(n) because we traverse the edges and nodes a limited number of times, making it efficient even for large inputs.

1Understanding node degrees helps in constructing the grid efficiently.
2Identifying endpoints and interior nodes is crucial for adjacency.

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