poscores

Combine match scores into systems.

Introduction

Purpose of the program is to combine match scores into combinations of scores. A combination is defined as set of values for each score so that a cartesian product will generate only valid match scores.

Example:

• 3 matches
• score 1: 2-1, 0-0, 3-0
• score 2: 3-1, 0-0, 3-0
• score 3: 4-1, 1-0, 3-0

Scores 1 and 2 can be combined, so the output will contain two score combinations.

• {2,3}-1, 0-0, 3-0
• 4-1, 1-0, 3-0

Score 3 cannot be combined since the result of the 2nd match differs from the two other scores.

Match score

Match scores are handled as individual goal counts. This is equivalent and simpler when searching for possible combinations.

Terminology

Term	Explanation	Example w/ 2 matches
pts	Number of goals / points scored by one team	"1"
score	Points for each team	("1", "2", "0", "3")
combo	Score combination	("1","2") or ("2",)
scores	All scores / combos. Each value maybe a point or a combo	(("1","2"), ("2",), "0", ("3",))

Example:

➜ python poscores/main.py input/2310.txt
Summary:
Input 2310 scores, generated 1328 coupons
top 20 coupon sizes: 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 4, 4, 4
5.24 % of scores covered by first 20 coupons