the provided code for minimum gas station problem. Q$1$: provide a solution with greedy method. Q$2$: provide a solution with dynamic proggramming. note: please provide formal proof for both instead of trying to proof with explaning the algorithm or with giving example. public int minstops$($int target, int sfuel, int$[]$ stations, int index$)\{$

$//$ Base case: if the target can be reached with the current fuel

if $($target $$ sfuel $+$ stations$[$index$])\{$

return ${}_{\text{;}}$

$\}$

$//$ Base case: if there are no more gas stations to visit

if $($index $$ stations.length$)\{$

return Integer.MAX$\_$VALUE;

$\}$

$//$ Check if we can reach the current gas station

int weCanReach $=$ sfuel $+$ stations$[$index$]$;

if $($weCanReach $$ stations $[$index$])\{$

$//$ Try picking the current gas station

int pick $=1+$ minStops$($target$,$ sfuel: sfuel $-$ stations$[$index$],$ stations, index: index $+1$