In this program, num_pipe is not actually the number of pipes
but the number of commands (very bad name indeed!).
Between two commands you need one pipe, between three commands
you need two pipes ... between N commands you need N-1 pipes.
Each pipe relies on two file descriptors (one for reading, one
for writing) thus 2*(num_pipe-1) file descriptors are needed
for num_pipe commands.
note: the malloc() does not allocate an array of integer pointers
(as stated in the question) but an array of integers.
Following this logic, I would have written
for(i = 0; i < 2*(num_pipe-1); i += 2)
but 2*(num_pipe-1) equals to 2*num_pipe-2 and since the step
is 2, the loop condition is the same with the limit
2*num_pipe-3.
It's just terribly confusing in my opinion.