write this in java he foundation of the Elo system is the probability of a given player beating another. This probability then serves as a weight to determine the impact of a win or loss on that players Elo.

First, we must calculate the R values from both player$$s Elo:

R$($Player$1)=10^\{(\backslash$frac$\{$Player$1$Elo$\}\{400\})\}$ Note : this is $10^($Player$1$Elo $/400)$

R$($Player$2)=10^\{(\backslash$frac$\{$Player$2$Elo$\}\{400\})\}$

If Player$1\text{'}$s Elo was $1200$ and Player$2\text{'}$s Elo was $1000,$ their R values would be $1000$ and $316\mathrm{.}227766$ respectively.

The R value is then used to calculate the probability that that player would win, this is called the expected score.

E$($Player$1)=\backslash$frac$\{$R$($Player$1)\}\{[$R$($Player$1)+$R$($Player$(2)]\}=\backslash$frac$\{1000\}\{1000+316\mathrm{.}227766\}\backslash$approx~$0\mathrm{.}76$

E$($Player$2)=\backslash$frac$\{$R$($Player$2)\}\{[$R$($Player$1)+$R$($Player$(2)]\}=\backslash$frac$\{316\mathrm{.}227766\}\{1000+316\mathrm{.}227766\}\backslash$approx~$0\mathrm{.}24$

As you can see the expected scores will always sum to $1.$

Using these probabilities, we can then calculate the updated Elo from the result of using the following equations.

New Elo of Winning Player $=$PlayerElo$+$K$*[1-$E$($Player$)]$

New Elo of Losing Player $=$PlayerElo$+$K$*[0-$E$($Player$)]$

Note K is a constant, a K$-$factor, that is used to control how much change will happen to a players Elo after a match. Low values of K result in Elo ratings that do not move much after a match while higher K values result in major swings in Elo ratings after a match. For this assignment we will be using a constant K value of $25.$

Assuming Player$1$ wins the updated Elo for each player would be:

Player$1$NewElo $=$P$1$Elo$+$K$*[1-$E$($P$1)]=1200+25*(1-\mathrm{.}76)=1206$

Player$2$NewElo $=$P$2$Elo$+$K$*[0-$E$($P$2)]=1000+25*(0-\mathrm{.}24)=993$

Both player$$s Elo should have changed by and equal amount, but because of Integer truncation the values are not rounded so Player$2$ lost $7$ Elo while Player$1$ gained $6.$ Now what happens if the lower rated player wins?

Player$1$NewElo $=$P$1$Elo$+$K$*[0-$E$($P$1)]=1200+25*(0-\mathrm{.}76)=1181$

Player$2$NewElo $=$P$2$Elo$+$K$*[1-$E$($P$2)]=1000+25*(1-\mathrm{.}24)=1018$

Player $1$ lost $19$ points of Elo while Player$2$ gained $18.$ Player $2$ is rewarded more for winning since they were at a statistical disadvantage.

Due to the complexity of calculating draws, we will assume that every game has a winner.

The above equations use rounded E values for simplicity only. Keep in mind to not round during calculations and to only truncate the value at the end.

Instructions

For this project you will be implementing an interactive menu using the provided Strings in the starter code. Failure to use the provided Strings may result in a loss of points. For this assignment you may not use Lists, ArrayLists, or String.split$().$ Specific Implementation requirements include:

The program will greet the user with a one time WELCOME$\_$MESSAGE before printing the MAIN$\_$MENU.

The user will then select $1$ of $4$ options.

Your program must handle invalid inputs on the MENU by printing INVALID$\_$INPUT and reprinting the MAIN$\_$MENU.

Option $1-$ Single Match:

Prompt the user with the SINGLE$\_$MATCH prompt.

The user will input a single match in the format of $[$Play$1$Elo$]-[$W$/$L$][$Player$2$Elo$]$ Examples $1$: $1200-$W$1000(1200$ wins vs $1000).$ Example$2$: $1350-$L$1224(1350$ loses to $1224)$

The program should print the MATCH$\_$OUTCOME prompt followed by the new Elo for the players in the order entered separated by a hyphen $\text{'}-\text{'}.$ Example Output$1$: "The Result of the Single Match is $1206-993".$ Example Output$2$: "The Result of the Single Match is $1333-1240"$

The program should then return to the MAIN$\_$MENU.

You can assume the user will enter a valid parsable input.

Option $2-$ Tournament Results:

Prompt the user with the TOURNAMENT$\_$RESULTS prompt.

The user will input a single line in the format of $[$CompetitorElo$]-$Result$[$OpponentElo$]-$Result$2[$Opponent$2$Elo$]-...$ ResultN$[$OpponentNElo$].$ Example Input: $1350-$L$1500-$W$1200-$L$1480-$W$1415-$L$1520$

Note that the length of the string is not set, your program should handle all result strings of $1$ or greater.

Note: A players Elo changes after EVERY match played. Which will impact the next match's calculation.

The program should print the TOURNAMENT$\_$OUTCOME prompt followed by competitor Elo then each of the opponents' Elo. Example Output: "The Final Tournament Results are $1348-1507-1192-1487-1399-1527".1348$ is the final Elo for the competitor, and the following Elo values are the updated Elo of the opponents after their match.

The program should then return to the MAIN$\_$MENU.

You can assume the user will enter a valid parsabl