Problem Description

You are given an m x n 2D array grid of positive integers. Your task is to traverse grid in a zigzag pattern while skipping every alternate cell. The zigzag pattern is defined with the following steps:

• Start at the top-left cell (0, 0).
• Move right within a row until you reach the end of the row.
• Drop down to the next row, then traverse left until you reach the beginning of that row.
• Continue alternating between right and left traversal until each row has been traversed.

Important to note that every alternate cell is skipped during the traversal. Return an array of integers result containing, in order, the value of the cells visited during this zigzag traversal with skips.

Intuition

The key to solving this problem lies in understanding the zigzag traversal pattern across the grid. We can break down the solution using the following intuitive approach:

1. Alternating Row Traversal: Recognize that for a zigzag traversal, we need to alternate row-by-row. Going right on even-indexed rows and left on odd-indexed rows creates the zigzag pattern. This can be achieved by reversing the elements of the odd-indexed rows.

2. Alternate Cell Skipping: It is also necessary to skip every alternate cell during the traversal. This is achieved by maintaining a toggle or a boolean switch. Start with a boolean set to True, and toggle its value (i.e., switch it to False after visiting every cell and back to True again). Only append the value to the results list when the boolean is True.

3. Implementation: Traverse through the grid row by row. Reverse rows as needed (specifically those with an odd index) to implement the zigzag pattern dynamically. Use the boolean toggle to selectively append the appropriate values to the output list.

These steps combine to provide a clean and direct traversal approach that aligns with the problem constraints and requirements.

Solution Approach

The implementation of the zigzag traversal solution uses a straightforward simulation approach. Here’s a detailed walkthrough of the solution algorithm:

1. Initial Setup:

   • Create a boolean variable ok initialized to True. This will help in determining whether to visit (append) a cell or skip it, adhering to the requirement of skipping every alternate cell.
   • An empty list ans is initialized to collect the values of the visited cells.

2. Iterate Over Each Row:

   • Use a loop to iterate over each row in the grid, indexed by i.
   • If i is odd, reverse the elements of the current row using row.reverse(). This reversal ensures that the traversal is in the opposite direction (left-to-right for odd-indexed rows).

3. Process Each Cell in the Row:

   • For each element x in the row, check the value of ok.
   • If ok is True, append the element to the ans list, indicating this cell is part of the zigzag path.
   • Toggle the boolean ok to switch its state after each cell is processed, allowing alternate cells to be skipped.

4. Return the Result:

   • Once all rows have been processed, the list ans which contains the values of cells visited in zigzag order with skips is returned as the final result.

The core pattern here is iterating over the entire 2D grid, alternating directions via row reversal and strategically appending elements based on the toggling boolean to establish skipping. This solution approach efficiently handles the problem requirements by combining these logical operations with basic data structure manipulations.

Example Walkthrough

Let's consider a small example grid to illustrate the solution approach. Suppose the grid is given by:

grid = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9]
]

We aim to traverse this grid in a zigzag manner while skipping every alternate cell.

1. Initial Setup:

   • Initialize a boolean variable ok to True.
   • Create an empty list ans to store visited cells' values.

2. Process Each Row:

   • First Row (i = 0):

     • The top-left starting point is (0, 0), i.e., 1.

     • Traverse to the right: [1, 2, 3].

     • Traversing:

       • Cell 1: ok = True, add 1 to ans, toggle ok.
       • Cell 2: ok = False, skip 2, toggle ok.
       • Cell 3: ok = True, add 3 to ans, toggle ok.

     • The result from the first row is [1, 3].

   • Second Row (i = 1):

     • Reverse direction (traverse left): [6, 5, 4].

     • Traversing:

       • Cell 6: ok = False, skip 6, toggle ok.
       • Cell 5: ok = True, add 5 to ans, toggle ok.
       • Cell 4: ok = False, skip 4, toggle ok.

     • The result from the second row is [5].

   • Third Row (i = 2):

     • Traverse right: [7, 8, 9].

     • Traversing:

       • Cell 7: ok = True, add 7 to ans, toggle ok.
       • Cell 8: ok = False, skip 8, toggle ok.
       • Cell 9: ok = True, add 9 to ans, toggle ok.

     • The result from the third row is [7, 9].

3. Combine the Results:

   • Resulting traversal path: [1, 3, 5, 7, 9].

Thus, the final result array produced by visiting the zigzag pattern with skips is [1, 3, 5, 7, 9].

Solution Implementation

Time and Space Complexity

The time complexity of the given code is O(m \times n), where m is the number of rows and n is the number of columns in the 2D array grid. This is because the code iterates over each element of the grid exactly once, either to append it to the ans list or to toggle the ok flag after checking the condition.

The space complexity, disregarding the space used for the output list ans, is O(1). This is because the code uses a constant amount of additional space for variables such as ok, i, row, and x, regardless of the size of the grid.

Learn more about how to find time and space complexity quickly.