Problem 037——UVa 207 - PGA Tour Prize Money

PGA Tour Prize Money

A PGA (Professional Golf Association) Tour event is a golf tournament in which prize money is awarded to the best players. The tournament is broken into four rounds of 18 holes apiece. All players are eligible to play the first two rounds. Only those with the best scores from those 36 holes ``make the first cut" to play the final two rounds and qualify for prize money. Players with the best 72-hole aggregate scores (the lowest scores) earn prize money.

You must write a program to determine how the total prize money (called the tournament ``purse") is to be allocated for a tournament. Specifications are as follows.

1)

All players will play at least two 18-hole rounds (36 holes in all) unless they are disqualified for some reason.

2)

Any player who is disqualified stops playing at the time of the disqualification. Players who are disqualified during the first two rounds are ineligible to make the cut. Players who are disqualified during either of the last two rounds are ineligible to win prize money.

3)

At the end of the first two rounds, the field of players is cut to the 70 players with the lowest 36-hole scores plus ties. So if 10 players are tied for 70th place, then 79 players make the 36-hole cut. Players who do not make the 36-hole cut are eliminated from the playing field and do not win any prize money.

4)

The players who do make the 36-hole cut play an additional 36 holes (two 18-hole rounds) and are paid a percentage of the total prize money depending on their 72-hole aggregate score. The lower the score, the more prize money a player wins.

5)

Players are paid percentages of the the tournament purse according to their final standings. For example, if the tournament purse were $1,000,000 and the winner's share were 18%, the winner would earn $180,000.

6)

There will be only one winner of this tournament. (In an actual golf tournament, when there is a tie for the low 72-hole score, there is be a play-off among the tied players. We will ignore that situation.)

7)

There may be a tie for any or all of the positions between 2 and 70. If there is a tie among  n players for position  k, the money designated for positions  k through  n +  k - 1 is pooled and allocated equally among