Broken Profile Dynamic Programming: Grid Tiling & Contour Line State Transitions

When tiling an $N imes M$ grid with dominoes, standard row-by-row bitmask DP requires evaluating all valid row transitions in $O(M 2^{2N})$. Broken Profile DP advances cell-by-cell along a contour boundary, reducing transition branching to $O(1)$ per cell and overall complexity to $O(N M 2^N)$.