How do you solve Possible Bipartition on LeetCode?

Possible Bipartition (LeetCode #886) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n + m) time complexity and O(n) space complexity. Key insight: Understanding how to represent relationships as a graph is crucial for solving bipartition problems.

What is the time complexity of Possible Bipartition?

The optimal solution for Possible Bipartition runs in O(n + m) time and uses O(n) space. This complexity is due to traversing the graph with n nodes and m edges, which is efficient for this problem size.

What is the brute force solution for Possible Bipartition?

The brute force approach for Possible Bipartition is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach tries every possible combination of groups to see if a valid split can be made. This is straightforward but inefficient, as it checks all possible groupings. The optimal Optimal Solution approach improves this to O(n + m).

What algorithm or data structure is used to solve Possible Bipartition?

Possible Bipartition uses the following concepts: Depth-First Search, Breadth-First Search, Union-Find, Graph Theory. The recommended patterns to study are: Graph Theory, Bipartite Graphs, Breadth-First Search (BFS), Depth-First Search (DFS).

What are the interview tips for Possible Bipartition?

Always clarify the problem constraints and edge cases before diving into coding. Explain your thought process and the reasoning behind your chosen approach. Practice graph traversal techniques like BFS and DFS, as they are commonly used in similar problems.

What are common mistakes when solving Possible Bipartition?

Failing to check all nodes in the graph, especially in disconnected graphs. Not correctly implementing the coloring logic, leading to false positives.

#886

Possible Bipartition

Medium

Depth-First SearchBreadth-First SearchUnion-FindGraph TheoryGraph TheoryBipartite GraphsBreadth-First Search (BFS)Depth-First Search (DFS)

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n + m)Space O(n)

The optimal solution uses graph theory to represent the problem as a bipartite graph. We can check if the graph can be colored with two colors, where adjacent nodes (people who dislike each other) have different colors.

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Algorithm

4 steps

1Step 1: Create an adjacency list from the dislikes array to represent the graph.
2Step 2: Initialize a color array to keep track of the color assigned to each person.
3Step 3: For each person, if not colored, perform a BFS or DFS to color the graph. Assign one color to the person and the opposite color to their neighbors.
4Step 4: If a conflict arises (two adjacent nodes have the same color), return false. If all nodes are colored successfully, return true.

solution.py22 lines

1# Full working Python code
2from collections import defaultdict, deque
3
4def possible_bipartition(n, dislikes):
5    graph = defaultdict(list)
6    for a, b in dislikes:
7        graph[a].append(b)
8        graph[b].append(a)
9    color = [0] * (n + 1)
10    for person in range(1, n + 1):
11        if color[person] == 0:
12            queue = deque([person])
13            color[person] = 1
14            while queue:
15                current = queue.popleft()
16                for neighbor in graph[current]:
17                    if color[neighbor] == 0:
18                        color[neighbor] = -color[current]
19                        queue.append(neighbor)
20                    elif color[neighbor] == color[current]:
21                        return False
22    return True

ℹ

Complexity note: This complexity is due to traversing the graph with n nodes and m edges, which is efficient for this problem size.

1Understanding how to represent relationships as a graph is crucial for solving bipartition problems.
2Using BFS or DFS to color the graph helps identify conflicts quickly.

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