Good morning

So:

for (size_t i = 0; i < n * m; ++i) {
		for (size_t k = 0; k < 8; k++) {
			int next_i = x1 + x_move[k];
			int next_j = y1 + y_move[k];
			if (isInside(next_i, next_j, n, m))
				matrix[i][next_i*m + next_j] = 1;
		}
	}

so this should be right

though, is this efficient version you talked about? :

cpp.sh/4iiur

So after the right adjacency matrix

how would we convert the 2d coordinate into 1d?

we should also output the path after determining the number of steps

?

You have the same relation all the time; consider the classic 8x8 chess board:

2D      1D
(0, 0)  0
(0, 1)  1
(0, 2)  2
...
(0, 7)  7
(1, 0)  8
(1, 1)  9
...
(7, 7)  63

To convert one from another:

2D -> 1D: f(x, y) = x*m + y
1D -> 2D: f~(x)   = (x/m, x%m)

very important

as someone who also never played chess too

so now the adjacency matrix, we would have the veritices 0-63

right?

at least for the knight to move in 8 directions

in other words

is this the idea:

each square on the chessboard to be represented as a node in the graph, and each valid move by the knight can be represented as an edge in the graph

Exactly...