Explain further The Manhattan distance from cell C to cell I is 2 (moving 1 unit horizontally and 1 unit vertically).

Certainly! In a grid-based pathfinding problem like the one described, the Manhattan distance is calculated by summing the absolute differences in the x and y coordinates of two points.

Let's take a closer look at the grid and the positions of cell C and cell I:

   A (1, 1)    B (2, 1)    C (3, 1)
   D (1, 2)    E (2, 2)    F (3, 2)
   G (1, 3)    H (2, 3)    I (3, 3)

The x-coordinate represents the horizontal position of a cell, and the y-coordinate represents the vertical position. Each cell in the grid has a unique (x, y) coordinate pair.

In this example:

• Cell C has coordinates (3, 1), because it's in the third column (x-coordinate) and the first row (y-coordinate).

• Cell I has coordinates (3, 3), because it's in the third column (x-coordinate) and the third row (y-coordinate).

To calculate the Manhattan distance between cell C and cell I:

1. Compute the absolute difference between their x-coordinates: |3 - 3| = 0.

2. Compute the absolute difference between their y-coordinates: |1 - 3| = 2.

Finally, sum the absolute differences: Manhattan distance = 0 (horizontal distance) + 2 (vertical distance) = 2.

So, the Manhattan distance from cell C to cell I is 2. This means that it would take two moves to reach cell I from cell C, moving 1 unit horizontally and 1 unit vertically.

Sure! Here's the updated grid with the coordinates added:

Now, each cell in the grid is labeled with its corresponding coordinates in the format (x, y), where:

• x represents the horizontal position (column number).

• y represents the vertical position (row number).

With these coordinates, it's easier to identify the positions of the cells and compute distances between them.