Bitmask Encoding - Walkthrough

For a grid with $n$ columns, the profile has $n$ bits. Bit $i$ = $1$ means column $i$ is filled at the current boundary. Example: $n = 4$, mask = $1010_2 = 10$.

Columns $1$ and $3$ are filled, columns $0$ and $2$ are empty. Transition: placing a domino in column $0$-$1$ (horizontal) changes mask from $1010$ to $1011$ (column $0$ now filled). Or placing a vertical domino in column $0$: changes mask from $1010$ to $1011$ and expects column $0$ to be filled in next row.