Chapter 40. Bowling Scores
Bowling is played in ten frames, each of which allows one or two
deliveries. If all ten pins are bowled over in the first delivery, there
is no second delivery.
Each frame has a score based on the delivery in that frame, as well
as the next one or two deliveries. This means that the score for a frame
may not necessarily be posted at the end of the frame. It also means that
the tenth frame may require a total of three deliveries to resolve the
scoring.
-
Rule A. The score for a frame is the total pins bowled over during
that frame, if the number is less than ten (an open frame, or error
or split depending some other rules beyond the scope of this
problem).
-
Rule B. If all ten pins are bowled over on the first delivery (a
strike), the score for that frame is 10 + the next two
deliveries.
-
Rule C. If all ten pins are bowled over between the first two
deliveries (a spare), the score for that frame is 10 + the next
delivery.
A game can be as few as twelve deliveries: ten frames plus two
additional deliveries in the tenth frame to resolve the rule B scoring. A
game can be as many as twenty deliveries: ten open frames of less than 10
pins bowled over during the frame.
There is a relatively straight-forward annotation for play. Each
frame has two characters to describe the pins bowled during the delivery.
The final frame has three characters for a total of 21 characters.
Rule A: If the frame is open, the two characters are the two
deliveries; the total will be less than 10. If a delivery fails to bowl
over any pins, a - is used instead of a number.
Rule B: If the frame is strike, the two characters are
X␣. No second delivery was made.
Rule C: If the frame is a spare, the first character is the number
of pins on the first delivery. The second character is a
/.
For example:
8/9-X␣X␣6/4/X␣8-X␣XXX
This can be analyzed into ten frames as follows:
| Frame |
First delivery |
Second delivery |
Scoring rule |
Frame Score |
Total |
| 1 |
8 |
2 |
C- spare = 10 + next delivery |
19 |
19 |
| 2 |
9 |
- |
A- open = 9 |
9 |
28 |
| 3 |
10 |
(not taken) |
B- strike = 10 + next 2 deliveries |
26 |
54 |
| 4 |
10 |
(not taken) |
B- strike = 10 + next 2 deliveries |
20 |
74 |
| 5 |
6 |
4 |
C- spare = 10 + next delivery |
14 |
88 |
| 6 |
4 |
6 |
C- spare = 10 + next delivery |
20 |
108 |
| 7 |
10 |
(not taken) |
B- strike = 10 + next 2 deliveries |
18 |
126 |
| 8 |
8 |
- |
A- open = 8 |
8 |
134 |
| 9 |
10 |
(not taken) |
B- strike = 10 + next 2 deliveries |
30 |
164 |
| 10 |
10 |
10 and 10 |
B- strike = 10 + next 2 deliveries, two extra deliveries are
taken during this 10th frame. |
30 |
194 |
Each of the first nine frames has a two-character code for each
delivery. There are three forms:
The tenth frame has a three-character code for each of the
deliveries. There are three forms:
-
XXX
-
n
/
r
where
n
is -, 1-9 and
r
is X,
-, 1-9.
-
mm
␣
where
m
is - or 1-9. The two
values cannot total to 10.
Write a valid(
game
)
function that will validate a 21-character string as describing a legal
game.
Write a scoring function,
scores(
game
), that will
accept the 21-character scoring string and produce a sequence of
frame-by-frame totals.
Write a reporting function,
scoreCard(
game
) will use the
validation and scoring functions to produce a scorecard. The scorecard
shows three lines of output with 5 character positions for each
frame.
The top line has the ten frame numbers: 2 digits and 3 spaces for
each frame.
The second line has the character codes for the delivery: 2 or 3
characters and 3 or 2 spaces for each of the ten frames.
The third line has the cumulative score for each frame: 3 digit
number and 2 spaces.
The game shown above would have the following output.
1 2 3 4 5 6 7 8 9 10
8/ 9- X X 6/ 4/ X 8- X XXX
19 28 54 74 88 108 126 134 164 194
