On a fresh Debian image, cloning https://github.com/python/cpython and running:
sudo apt-get update
sudo apt-get upgrade
sudo apt-get dist-upgrade
sudo apt-get install build-essential python-dev python-setuptools python-pip python-smbus
sudo apt-get install libncursesw5-dev libgdbm-dev libc6-dev
sudo apt-get install zlib1g-dev libsqlite3-dev tk-dev
sudo apt-get install libssl-dev openssl
sudo apt-get install libffi-dev
Now execute the configure file cloned above:
./configure
make # alternatively `make -j 4` will utilize 4 threads
sudo make altinstall
Got 3.7 installed and working for me.
Looks like I said I would update this answer with some more explanation and two years later I don't have much to add.
python-dev might be necessary.altinstall as opposed to install argument in the make command.Aside from that I guess the choice would be to either read through the cpython codebase looking for #include directives that need to be met, but what I usually do is keep trying to install the package and just keep reading through the output installing the required packages until it succeeds.
Reminds me of the story of the Engineer, the Manager and the Programmer whose car rolls down a hill.