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First Completely Painted Row or Column

Problem Overview

You are tasked with determining the first index in the array arr where either an entire row or an entire column of the matrix mat becomes fully painted. The painting process follows the order given in arr.

Solution Explanation (Step-by-Step)

C++ Code

  1. Initialize Data Structures:

    • Create a mapping to store the position (row and column) of each value in the matrix. This allows for constant-time lookups.
    • Use two arrays, rowCount and colCount, to track the number of painted cells in each row and column.

  2. Populate the Mapping:

    • Iterate through the matrix and record the row and column of every value in the mapping.

  3. Simulate the Painting Process:

    • Loop through the array arr. For each value:
      • Retrieve its row and column using the mapping.
      • Increment the count for the corresponding row and column.

  4. Check Completion:

    • After updating the counts, check if the row or column has been fully painted. If so, return the current index.

  5. Edge Case:

    • If no row or column becomes fully painted after processing all elements of arr, return -1.

Java Code

  1. Define Position Mapping:

    • Use a HashMap to map each value in the matrix to its row and column. This avoids searching through the matrix repeatedly.

  2. Track Painting Progress:

    • Use two arrays, rowCount and colCount, to count how many cells have been painted for each row and column.

  3. Iterate Through arr:

    • For each number in arr, find its position using the mapping and update the painting counts.

  4. Check Completion:

    • After updating the row and column counts, check if either the row or the column is fully painted. If yes, return the current index.

  5. Handle Edge Cases:

    • If no row or column is fully painted after processing all values in arr, return -1.

JavaScript Code

  1. Setup Position Map:

    • Use a Map to store the position (row and column) of each value in the matrix for fast lookups.

  2. Track Painted Cells:

    • Create two arrays, rowCount and colCount, to track the progress of painting for rows and columns.

  3. Loop Through arr:

    • For each value in arr, get its position using the mapping.
    • Increment the corresponding row and column counts.

  4. Check for Completion:

    • After incrementing, check if the row or column has reached its maximum count. If so, return the current index.

  5. Return Result:

    • If no row or column is completely painted after processing all elements, return -1.

Python Code

  1. Create Position Mapping:

    • Use a dictionary to map each value in the matrix to its row and column. This avoids unnecessary iterations.

  2. Initialize Counters:

    • Use two lists, rowCount and colCount, to track how many cells of each row and column are painted.

  3. Simulate Painting:

    • For every value in arr, look up its position in the mapping and update the corresponding counters.

  4. Completion Check:

    • After updating, check if the row or column has reached its maximum size. If yes, return the current index.

  5. Handle Remaining Cases:

    • If no row or column is painted fully after all iterations, return -1.

Go Code

  1. Build a Position Map:

    • Use a map data structure to store the position of each value in the matrix for efficient lookups.

  2. Initialize Row and Column Counters:

    • Create two slices, rowCount and colCount, to track the progress of painting.

  3. Process the Array:

    • For each value in arr, retrieve its position using the mapping and increment the respective row and column counters.

  4. Check Painting Status:

    • After updating the counters, check if the row or column is fully painted. If so, return the index.

  5. Final Result:

    • If no row or column becomes completely painted, return -1.

Notes for All Implementations

  • Mapping Values:

    • The matrix mapping significantly reduces the computational complexity by avoiding repetitive searches.

  • Optimized Updates:

    • Instead of repeatedly scanning rows or columns, the approach focuses on maintaining a simple count for each row and column.

  • Edge Cases:

    • Handle cases where arr does not result in any fully painted row or column.