Let's define ~\text{MinDoors}(x, y)~ to be the minimum number of doors which Bob must pass through to get from classroom ~x~ to classroom ~y~. The only options he should consider are to avoid the hallways and pass exclusively through classrooms (which requires ~|y-x|~ doors), or to go through the hallway (which always requires ~2~ doors). Therefore, ~\text{MinDoors}(x, y) = \min(|y-x|, 2)~. The total answer is then the sum of ~\text{MinDoors}(C_i, C_{i+1})~ for each ~i~ from ~1~ to ~M-1~, plus an extra ~2~ (for one door required to get from the hallway to the first class, and another door required to get from the final class to the hallway).