Not all homeless are addicts but it is true a proportion are.
I would ban homelessness. I would make it illegal to be homeless.
For those that are homeless, I would bring back the revised workhouse idea, but the key difference would be that they work to clean the streets, pick litter, mow the verges etc and we pay them. The money would not go into their hands, it would go into a bank account to build up until they had enough in it for a deposit on somewhere to rent and they had gone through a mandatory drug/drink rehabilitation programme where they are tested regularly. Failure to attend/complete the programme would get them banged up in an asylum and their earnings revoked. Then they'd get put back onto the programme.