That circuit only uses LM317 as a sort of control for the TIP3055 transistor. It's a bit confusing because the pins are not numbered, so it's very easy to connect the LM317 incorrectly in your circuit this way.
Forget about this circuit, because you don't need such complexity for 1A of current.
Open the datasheet for LM317 and build the circuit there, see page 7 and the explanations on the page:
http://www.ti.com/lit/ds/symlink/lm317.pdf Datasheets for the same chip but made by other companies may also give you more details, for example see page 7 on this datasheet :
http://www.onsemi.com/pub_link/Collateral/LM317-D.PDFSo you have the transformer, the bridge rectifier, the capacitor (which can be 2200-3300uF 35-50v, if you use a transformer like the one in the circuit) and then the circuit in the datasheet.
Be sure to put the LM317 on a heatsink... remember, the difference between input voltage and output voltage has to go somewhere, and it goes as heat ... for example 12v input, 5v output at 1A means (12-5)x1 = 7w wasted as heat ... LM317 can only handle about 1-1.5w by itself, without any heatsink.
Even with heatsink, you really shouldn't make the regulator waste more than about 10-15w as heat .. don't put 32v input, 5v output and expect to use more than about 3-400mA before it dies. Be sensible.