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🚀 Step-by-Step Explanation of the Solution

This README provides a detailed, step-by-step explanation of how the solution for the "Highest Peak" problem works across multiple languages: C++, Java, JavaScript, Python, and Go. Each explanation dives into the logic while keeping the explanation language-agnostic.

🛠 Key Steps in Solving the Problem

  1. Input Grid Initialization

    • We are given a grid where cells are either 1 (water) or 0 (land).
    • The goal is to determine the height of each cell such that:
      • Water cells have a height of 0.
      • Land cells have heights calculated based on their distance from the nearest water cell.

  2. Mark Water Cells

    • Traverse the grid and identify all cells marked as water (1).
    • These cells are immediately set to a height of 0.
    • Land cells are marked as "unvisited" or assigned a default value (e.g., -1 or Infinity).

  3. Breadth-First Search (BFS) Initialization

    • Use a queue (or similar data structure) to perform a level-wise traversal (BFS).
    • Initially, add all water cells into the queue as the starting points.

  4. BFS Traversal to Calculate Heights

    • Process each cell in the queue:
      • For each cell, check all its neighbors (up, down, left, right).
      • If the neighbor is unvisited (land), calculate its height as current_cell_height + 1.
      • Add the neighbor to the queue for further exploration.

  5. Continue Until All Cells Are Processed

    • BFS ensures that heights are calculated layer by layer, starting from the water cells.
    • This guarantees that each cell's height is the shortest distance from the nearest water cell.

  6. Return the Resulting Grid

    • Once BFS completes, the updated grid contains the required heights for all cells.

📌 Explanation for Each Language

C++ Code

  1. Define the Input and Output Grid

    • Use a 2D vector to represent the grid.

  2. Initialize the Queue

    • Use a queue to store coordinates of all water cells ({x, y}).

  3. BFS Traversal

    • Iterate over all four possible directions (up, down, left, right) using a directions array.
    • For each unvisited neighbor, update its height and push it into the queue.

  4. Complete the Grid Update

    • Continue the BFS until the queue is empty.
    • The final grid contains heights for all cells.

Java Code

  1. Prepare the Input Grid

    • Use a 2D array for the grid and a Queue to store coordinates of water cells.

  2. Add Water Cells to the Queue

    • Iterate through the grid, marking water cells as 0 and land cells as -1.

  3. Perform BFS Traversal

    • Use a directions array to move in all four cardinal directions.
    • For each neighbor, calculate the height (current_height + 1) and enqueue it.

  4. Return the Updated Grid

    • BFS ensures that all cells are visited in the shortest possible distance order.

JavaScript Code

  1. Grid Initialization

    • Represent the grid as a 2D array and use a queue to track BFS levels.

  2. Identify Water Cells

    • Mark all water cells (1) with height 0 and add them to the queue.
    • Land cells are initially marked as unvisited (-1).

  3. BFS Traversal

    • For each cell, explore its neighbors using predefined directions.
    • Update the neighbor's height if it is unvisited, then add it to the queue.

  4. Update the Grid

    • Continue processing until all cells are visited and their heights are calculated.

Python Code

  1. Input Grid and Initialization

    • Use a 2D list to represent the grid.
    • Initialize a deque with all water cells and mark land cells as unvisited (-1).

  2. BFS Setup

    • Store all water cells in the deque with height 0.
    • Use directions to move up, down, left, and right during traversal.

  3. Calculate Heights Using BFS

    • For each cell, check all its neighbors.
    • If the neighbor is unvisited, assign its height (current_height + 1) and add it to the deque.

  4. Return the Result

    • The final grid contains calculated heights for all cells.

Go Code

  1. Input Grid Representation

    • Use a 2D slice to represent the grid.

  2. Initialize the Queue

    • Create a queue and add all water cells as starting points.

  3. BFS Traversal

    • Use a directions array to explore all neighbors of each cell.
    • Update the height of each unvisited neighbor and push it to the queue.

  4. Update and Return the Grid

    • Continue BFS until all cells are processed.
    • The resulting grid contains the required heights.

🌟 Complexity Analysis

  • Time Complexity:
    $$O(n \times m)$$, where (n) and (m) are the dimensions of the grid. Each cell is processed once.

  • Space Complexity:
    $$O(n \times m)$$ for the BFS queue and auxiliary storage.

🔗 Additional Notes

This problem emphasizes the importance of BFS for multi-source shortest path problems. The key takeaway is that BFS ensures layer-wise traversal, making it ideal for calculating distances in grid-based problems.