You are a contestant on a TV quiz show.
Throughout the game, you and your 2 opponents have accumulated points by answering trivia questions.
At the end of the game, the three of you are given one final question.
Before you hear the question, each contestant must decide how many points he or she wishes to wager.
Each contestant who answers the question correctly will gain a number of points equal to his or her wager,
while the others will lose a number of points equal to their respective wagers.
The contestant who ends up with the highest score after the final question wins the game.
It has come to the point in the game where you must select your wager.
You can bet any amount between zero and your current score, inclusive.
Given your current score, the scores of your two opponents, and how much you believe each of your opponents will wager,
compute how much you should wager in order to have the highest probability of winning the game. Assume that you and your opponents each independently have a 50% chance of answering the final question correctly.
You will be given the three scores as a int[], scores.
The first element is your score,
the next element is your first opponent's score,
and the last element is your second opponent's score.
You will also be given wager1 and wager2,
the amount of your first and second opponents' wagers, respectively.
Your goal is to maximize your chance of winning uncontested.
As far as you're concerned, ending in a tie is as bad as losing.
If there are multiple wagers that give you the same highest probability of winning, return the smallest such wager.
If you have no chance of winning, return zero.
|