$6$ Dataflow and Register Allocation $(32$ Points$)$

$1.$ You are given the control$-$flow graph for a function that uses variables $\backslash ($ a $\backslash )$ to $\backslash ($ g $\backslash ),$ with $\backslash ($ a $\backslash )$ and $\backslash ($ b $\backslash )$ being the arguments and $\backslash ($ g $\backslash )$ and $\backslash ($ f $\backslash )$ the return values. Part of the program statements and part of the set of variables that are live right after$/$before the corresponding statement have been removed from this graph, and replaced by empty boxes $/$ brackets. Fill in the missing program statements in the boxes and the missing set of variables that are live right after$/$before the corresponding statements so that the live sets are consistent with the code.

Program statements can take one of the following forms: $\backslash ($ x$=1,$ x$=$y $\backslash )$ or $\backslash ($ x$=$y$+$z $\backslash )($where $\backslash ($ x$,$ y $\backslash )$ and $\backslash ($ z $\backslash )$ can be any one of the variables used by the function$).$ If more than one statement would work in some position, pick the simplest one $($prefer $\backslash ($ x$=1\backslash )$ over $\backslash ($ x$=$y $\backslash ),$ and $\backslash ($ x$=$y $\backslash )$ over $\backslash ($ x$=$y$+$z $\backslash )).$

$2.$ Give the register interference graph for the above code. $[8$ Points$]$