Understanding Matrix Traversal
Matrix traversal, also known as Island problems, often encountered in matrix or grid-based scenarios, typically involves identifying and counting connected components of a specific value (usually represented as '1' for land) in a binary matrix. These problems can be solved using various traversal techniques such as Depth-First Search (DFS) or Breadth-First Search (BFS).
Process
Initialization: Start by initializing variables to keep track of the number of islands or the size of the largest island. Also, a data structure must be initialized to keep track of visited nodes and avoid counting the same island multiple times.
Traversal: Use either DFS or BFS to traverse the matrix. For each cell that contains '1' and has not been visited, initiate a traversal from that cell to explore the entire island.
Marking Visited Nodes: During the traversal, mark each visited cell to ensure it is not revisited. This can be done by setting the cell value to a different value (e.g., '-1' or '2') or using an auxiliary data structure like a boolean matrix.
Exploring Neighbors: For each cell, explore its neighbours (up, down, left, right) and continue the traversal if the neighbour is part of the same island (i.e., has the value '1' and has not been visited).
Counting or Measuring Islands: Each time a new unvisited cell with the value '1' is found, it indicates the start of a new island. Increment the island count or measure the size of the island during the traversal.
Termination: The process terminates when all cells in the matrix have been visited.
When to Use
Counting Islands: To count the number of connected components of '1's in a binary matrix.
Finding the Largest Island: To find the size of the largest connected component of '1's in a binary matrix.
Island Perimeter: To calculate the perimeter of an island or the total perimeter of all islands.
How Does It Reduce Time Complexity?
Linear Time Complexity: The traversal techniques (DFS or BFS) used to solve island problems have a time complexity of O(n * m), where n is the number of rows and m is the number of columns in the matrix. This is because each cell is visited at most once.
Efficient Exploration: The algorithm avoids redundant visits by marking visited nodes, ensuring that each cell is processed only once.
Example problem for better understanding
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