Question $2$: Bad sizes $2($C$)$ Recover the solution in terms of the growth from each drop of fertilizer. $[16]$: ## Test Code: Do not edit

print$($minGoodDrops$\_$Solution$(9))$ # should be $2,[4,4]$

print$($minGoodDrops$\_$Solution$(13))$ # should be $2,[11,1]$

print$($minGoodDrops$\_$Solution$(19))$ # should be $4,[4,5,4,5]$

print$($minGoodDrops$\_$Solution$(34))$ # should be $5,[5,1,11,11,5]$

print$($minGoodDrops$\_$Solution$(43))$ # should be $5,[4,5,11,11,11]$

print$($minGoodDrops$\_$Solution$(55))$ # should be $6,[5,11,11,11,11,5]$

print$($minGoodDrops$\_$Solution$(69))$ # should be $8,[11,1,11,11,11,11,11,1]$

inf

$1$

Mr E has noticed something quite strange: Any bean stalk whose length leaves a remainder of $2$ when divided by $7$ dies over night.

He demands you change your algorithm to avoid these 'dead lengths.$\text{'}$ You think it might just be his cat digging around in the pots late at night, but you don't wish to argue.

$2($A$)$ Write a recurrence.

Write a recurrence minGoodDrops $(j,n)$ that represents the minimum number of drops of fertilizer necessary to grow a bean stalk from $j$ inches to $n$ inches, avoiding any intermediate stage of length $k$ when $k$ mod $7=2.$

$*[1]$: def minGoodDrops$($j$,$ n$)$:print$($minGoodDrops$(1,9))$ # should be $2$

print$($minGoodDrops$(1,13))$ # should be $2$

print$($minGoodDrops$(1,19))$ # should be $4$

print$($minGoodDrops$(1,34))$ # should be $5$

print$($minGoodDrops$(1,43))$ # should be $5$

print$($minGoodDrops$(1,55))$ # should be $6$

inf

$1$

$1$

$12($B$)$ Memoize the recurrence in $2($A$)$

$[10]$: def minGoodDrops$\_$Memoize$($n$)$: # j is assumed to be $1$

return $100$print$($minGoodDrops$\_$Memoize$(9))$ # should be $2$

print$($minGoodDrops$\_$Memoize$(13))$ # should be $2$

print$($minGoodDrops$\_$Memoize$(19))$ # should be $4$

print$($minGoodDrops$\_$Memoize$(34))$ # should be $5$

print$($minGoodDrops$\_$Memoize$(43))$ # should be $5$

print$($minGoodDrops$\_$Memoize$(55))$ # should be $6$

print$($minGoodDrops$\_$Memoize$(69))$ # should be $8$

print$($minGoodDrops$\_$Memoize$(812))$ # should be $83$

$100$

$100$

$100$