Python Coding Practice

Solve Bipartite Graph using Python Language

Solve Bipartite Graph using Python to enhance your skills with python coding practice , master coding concepts, and prepare for interviews with practical exercises and detailed solutions.

Bipartite Graph

Difficulty : Medium

Categories :

  • Graphs

Given an undirected graph represented as an adjacency list adj, determine if it is bipartite. A graph is bipartite if its vertices can be divided into two independent sets such that every edge connects vertices from different sets.

Key Properties:

  • A graph is bipartite if it can be colored using exactly two colors such that no adjacent vertices have the same color
  • All edges must connect vertices from one set to vertices in the other set
  • No edges can exist between vertices within the same set

Constraints:

  • 1 ≤ adj.size() ≤ 104
  • 1 ≤ adj[i][j] ≤ 104
  • Graph is undirected, meaning if there's an edge from u to v, there's also an edge from v to u

Examples:

Input: adj = [[1], [0,2], [1]]
Output: true
Explanation: Can color vertices {0,2} and {1} with different colors
Input: adj = [[2], [2], [0,1]]
Output: false
Explanation: Cannot color adjacent vertices with different colors

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Choose from the following categories

Arrays A collection of elements stored in contiguous memory locations, allowing efficient random access and manipulation.

Linked Lists A linear data structure where each element (node) points to the next, offering dynamic memory allocation and efficient insertions/deletions.

Trees A hierarchical data structure with nodes connected by edges, used in applications like databases, file systems, and parsing.

Graphs A collection of nodes (vertices) connected by edges, representing relationships, widely used in networking, routing, and social networks.

Dynamic Programming An optimization technique that solves problems by breaking them into overlapping subproblems and storing their results.

Backtracking A problem-solving method that explores all possibilities recursively, backtracking when a solution is not feasible.

Sorting Algorithms Techniques for arranging elements in a specific order, such as quicksort, mergesort, and bubble sort, essential for data organization.

Searching Algorithms Methods for finding elements in a dataset, such as binary search, linear search, and graph traversal techniques.

Mathematics A field of study involving numbers, calculations, and logical reasoning, forming the foundation for algorithms and problem-solving.

Recursion A programming technique where a function calls itself to solve smaller instances of the same problem, often used in divide-and-conquer approaches.

Bit Manipulation Operations performed directly on binary representations of data, used for efficient computations and optimization tasks.