CSULB$-$CECS $325$ Section $1\backslash$& $2$ System Programming Program $\backslash$#$5-$ goldRabbits: using maps

I got a pair of rabbits for my birthday. I did some research and found out that apparently rabbits multiply like... well, Rabbits! So I have a great idea that will help me retire. I$\text{'}$m going to start a rabbit ranch. I need to plan for the future and determine how much land and rabbit food I will need for my rabbits.

Here are the Rabbit Rules:

$-$ New$-$born rabbits take one month to mature.

$-$ One pair of mature rabbits will have a pair of baby rabbits after one month.

$-$ Mature rabbits will continue to produce a new pair of baby rabbits every month.

$-$ Rabbits never die

I plan to retire in $10$ years. How many rabbits will I have by then?

I did some hand calculations and I came up with this:

At the start of month $\backslash (0,$ I $\backslash )$ receive the baby rabbits so I have $\backslash (\backslash$mathbf$\{1\}\backslash )$ pair of rabbits.

At the start of month $1,$ the baby rabbits are grown and the female becomes pregnant. But I still have only $1$ pair of rabbits.

At the start of month $2,$ the first pair give birth to $1$ pair of rabbits, so now I have $\backslash (\backslash$underline$\{2\}\backslash )$ pairs of rabbits. The first pair $($the adults$)$ immediately become pregnant again.

At the start of month $3,$ the second pair is now mature and the first pair give birth again to $1$ pair of rabbits. This gives me $\backslash (\backslash$mathbf$\{3\}\backslash )$ pairs of rabbits.

At the start of month $4,$ the first pair gives birth to a new pair, the second pair gives birth to a new pair, and the third pair are all grown up and ready to start family life. So now I have $\backslash (\backslash$underline$\{\backslash$mathbf$\{5\}\}\backslash )$ pairs of rabbits.

By now I was getting confused with counting rabbits, but I noticed a pattern. It seemed like each new month the total number of pairs of rabbits was equal to the total number from the month before plus the total number from $2$ months before. That's really cool that I can predict the number of rabbit pairs with an equation.

I$\text{'}$m gonna call it MGRCFRRPG or "Master Gold's Really Cool Formula for Rapid Rabbit Population Growth", or just GoldRabbits for short. $($Apparently some Italian dude from the year $1202$ named Fibonacci came up with something similar $-$ but I think mine is much more better...$)$

As you can see, I have a couple problems:

For some reason, the number got real big $-$ it was approaching $2,147,483,647$ at

goldRabbits$(45)-($Actual value was $1,836,311,903$ when it suddenly went negative at

goldRabbits$(46)...$ That's weird. Am I right? What is going on$????$

It's taking a long, long time to calculate. At this rate, I will be retired before the

calculation is complete...

Your assignment is to solve these problems for me:

Rewrite the goldRabbits$($int n $)$ function so that it throws an exception if it detects integer

overflow. The exception will throw a string that indicates the input number $($n$)$ which

caused the overflow.

Speed up the goldRabbits function so that it is very fast. You can use a static map to

accomplish this.

Keep track of how many times the goldRabbits function is called. You did something

similar in Prog $4$ to track of global swaps.

The fibo values are stored in a map in the goldRabbits function. If the incoming parameter

is $-1,$ then the function will print the contents of the map. Example: goldRabbits$(-1)$ will

print the map. Both $$ first$>$ and values will be printed $-$ refer to the sample

output below.