#3311

Hard

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Construct 2D Grid Matching Graph Layout

This problem challenges you to construct a 2D grid from an undirected graph using a given set of edges.

Problem Statement

You are given a graph with n nodes and edges represented as a 2D array. Each edge connects two nodes and is undirected. Your task is to construct a 2D grid such that nodes are placed based on their connectivity in the graph.

Each node should be positioned in the grid in a way that satisfies the structure formed by the given edges. The grid must represent the exact relationship between the nodes, maintaining the graph's adjacency properties.

Examples

Example 1

Input: n = 4, edges = [[0,1],[0,2],[1,3],[2,3]]

Output: [[3,1],[2,0]]

Example 2

Input: n = 5, edges = [[0,1],[1,3],[2,3],[2,4]]

Output: [[4,2,3,1,0]]

Example 3

Input: n = 9, edges = [[0,1],[0,4],[0,5],[1,7],[2,3],[2,4],[2,5],[3,6],[4,6],[4,7],[6,8],[7,8]]

Output: [[8,6,3],[7,4,2],[1,0,5]]

Constraints

2 <= n <= 5 * 104
1 <= edges.length <= 105
edges[i] = [ui, vi]
0 <= ui < vi < n
All the edges are distinct.
The input is generated such that edges can form a 2D grid that satisfies the conditions.

Solution Approach

Array Scanning and Hash Lookup

Start by scanning the graph's edges, using hash tables to track the degree and relationships of each node. This ensures you can quickly group nodes with similar adjacency.

Row and Column Assignment

Using the degree and adjacency data, place nodes into appropriate rows and columns, ensuring that their positions reflect the structure of the graph's edges. The key is ensuring each node has its corresponding neighbors in the correct grid positions.

Handling Grid Constraints

Once nodes are assigned, make sure the grid respects the constraints, such as ensuring there are no duplicate nodes in the same row or column. Carefully manage the grid's size and node placement to avoid conflicts.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time and space complexity depend on the approach used to scan and place nodes. In the worst case, you may have to process each edge and node in linear time. Using hash tables helps efficiently manage adjacency and positioning, ensuring that the solution can scale to large inputs.

What Interviewers Usually Probe

Look for clear understanding of graph traversal and grid placement.
Check if the candidate can efficiently use hash tables to manage node relationships.
Assess the ability to handle large graph sizes while maintaining correct grid structure.

Common Pitfalls or Variants

Common pitfalls

Overcomplicating the row/column assignment without considering adjacency constraints.
Failing to handle edge cases such as disconnected components or varying node degrees.
Incorrectly managing the grid size, leading to inefficient use of space or incorrect node placement.

Follow-up variants

Changing the graph structure to a directed graph.
Increasing the number of nodes significantly.
Requiring more complex relationships between nodes in the grid.

FAQ

What is the main pattern used in the 'Construct 2D Grid Matching Graph Layout' problem?

The main pattern is array scanning combined with hash lookup to manage node adjacency and construct the grid.

How can hash tables help in constructing the 2D grid?

Hash tables allow efficient lookups of node relationships, helping track which nodes need to be placed together in the grid based on their edges.

What should I focus on to avoid pitfalls when solving this problem?

Focus on correctly managing the adjacency relationships and ensuring that nodes are placed in the correct rows and columns without conflicts.

How does GhostInterview help with understanding the grid construction approach?

GhostInterview provides step-by-step guidance on efficiently scanning the graph and placing nodes, emphasizing key strategies like using hash tables for adjacency management.

Can this problem be solved in less than linear time?

No, due to the nature of graph traversal and grid construction, a solution will at least require linear time to process all edges and nodes.

terminal

Solution

Solution 1

#### Python3

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class Solution:
    def constructGridLayout(self, n: int, edges: List[List[int]]) -> List[List[int]]:
        g = [[] for _ in range(n)]
        for u, v in edges:
            g[u].append(v)
            g[v].append(u)
        deg = [-1] * 5
        for x, ys in enumerate(g):
            deg[len(ys)] = x
        if deg[1] != -1:
            row = [deg[1]]
        elif deg[4] == -1:
            x = deg[2]
            for y in g[x]:
                if len(g[y]) == 2:
                    row = [x, y]
                    break
        else:
            x = deg[2]
            row = [x]
            pre = x
            x = g[x][0]
            while len(g[x]) > 2:
                row.append(x)
                for y in g[x]:
                    if y != pre and len(g[y]) < 4:
                        pre = x
                        x = y
                        break
            row.append(x)

        ans = [row]
        vis = [False] * n
        for _ in range(n // len(row) - 1):
            for x in row:
                vis[x] = True
            nxt = []
            for x in row:
                for y in g[x]:
                    if not vis[y]:
                        nxt.append(y)
                        break
            ans.append(nxt)
            row = nxt
        return ans

Continue Practicing

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