Input matrix with reed switches

I’m about to buy components for my first Arduino project: Reed contacts for my model railroad (H0 scale) to detect track usage. I don’t want to use special shields, but use as few components as possible to directly connect the reed switches to the Arduino.

To make good use of the Arduino Nano, I’d like to use an input matrix. Let me summarize, how I understand the matrix (here it’s 4 by 4, but with 14 digital IO pins, I could have a 7 by 7 matrix, right?):

To see the closed contacts, I switch on the one of the inputs at a time (I, R1, S1, T1) and read all of the outputs (N, O, P, Q). If R1 is active and I receive a high on O and P, then both of the middle contacts would be closed.

Since I’m a real newbie here, I’m unsure about the specs I should look for in the reed switches and the diodes. Also, do I miss any components (resistors?) or are switches and diodes enough?

Thank you!