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Find the Maximum Fish in a Grid

Step-by-Step Explanation

This problem involves finding the maximum number of fish that can be collected in a grid by exploring connected components. Below is a detailed breakdown of the approach and logic used in the implementation across C++, Java, JavaScript, Python, and Go. Each step explains the logic for all the solutions without directly revealing the code.

General Approach

  1. Identify Connected Components

    • The problem can be visualized as identifying connected groups of grid cells containing fish (non-zero values).
    • Use Depth First Search (DFS) or Breadth First Search (BFS) to traverse connected cells starting from any cell with a positive value.

  2. Collect Fish from Connected Cells

    • As you traverse each connected component, sum up the values (number of fish) in that component.

  3. Track the Maximum Fish Count

    • Compare the total fish collected from each connected component to keep track of the maximum.

C++ Code: Step-by-Step

  1. Grid Traversal

    • Loop through each cell in the grid. If the cell contains fish (non-zero value) and hasn't been visited yet, initiate a DFS traversal.

  2. DFS Implementation

    • Use a recursive function to traverse all connected cells, summing up the fish values.
    • Mark visited cells to avoid processing them again.

  3. Track Maximum Fish

    • After completing the DFS for each component, compare the total fish count with the current maximum and update accordingly.

Java Code: Step-by-Step

  1. Grid Traversal

    • Use nested loops to go through all the grid cells. Start DFS whenever a fish-filled cell is found.

  2. DFS as a Helper Function

    • Implement DFS recursively or with a stack. For each connected cell, add the fish value to a running total and mark it as visited.

  3. Compare and Update Maximum

    • At the end of the traversal for each component, compare its total fish count with the global maximum.

JavaScript Code: Step-by-Step

  1. Iterate Through the Grid

    • Use nested for loops to inspect each cell in the grid. When a cell with fish is found, initiate a DFS.

  2. Handle Connected Components

    • Implement a DFS function using recursion or an iterative approach (using a stack) to explore all connected cells. Add fish values and mark cells as visited.

  3. Update Maximum Fish Count

    • After completing the DFS for one component, compare its total fish count with the global maximum and store the higher value.

Python Code: Step-by-Step

  1. Loop Over the Grid

    • Iterate through every cell using nested loops. When a cell with fish is encountered, start a DFS.

  2. Recursive DFS Implementation

    • Use a recursive function to traverse all connected cells. Add the value of each cell to the total count and mark it as visited.

  3. Global Maximum Update

    • At the end of each DFS, compare the total fish collected in that component with the maximum recorded so far and update as needed.

Go Code: Step-by-Step

  1. Traverse Each Cell

    • Loop over all the cells in the grid. When a cell containing fish is found, trigger a DFS.

  2. DFS with a Helper Function

    • Implement DFS to explore connected cells. Maintain a running total of fish and ensure cells are marked as visited.

  3. Update Maximum Fish Count

    • After completing the DFS for a component, compare its total fish count with the global maximum and update.

Complexity Analysis

  • Time Complexity:
    $$O(n \times m)$$ for all solutions, where (n) and (m) are the grid dimensions. This is because each cell is processed once during the traversal.

  • Space Complexity:

    • For DFS: (O(\text{stack depth})), which is proportional to the size of the grid in the worst case.
    • For BFS: (O(n \times m)) for the queue used to store cells during traversal.