How to resolve the algorithm World Cup group stage step by step in the Python programming language
How to resolve the algorithm World Cup group stage step by step in the Python programming language
Table of Contents
Problem Statement
It's World Cup season (or at least it was when this page was created)! The World Cup is an international football/soccer tournament that happens every 4 years. Countries put their international teams together in the years between tournaments and qualify for the tournament based on their performance in other international games. Once a team has qualified they are put into a group with 3 other teams. For the first part of the World Cup tournament the teams play in "group stage" games where each of the four teams in a group plays all three other teams once. The results of these games determine which teams will move on to the "knockout stage" which is a standard single-elimination tournament. The two teams from each group with the most standings points move on to the knockout stage. Each game can result in a win for one team and a loss for the other team or it can result in a draw/tie for each team.
Don't worry about tiebreakers as they can get complicated. We are basically looking to answer the question "if a team gets x standings points, where can they expect to end up in the group standings?". Hint: there should be no possible way to end up in second place with less than two points as well as no way to end up in first with less than three. Oddly enough, there is no way to get 8 points at all.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm World Cup group stage step by step in the Python programming language
The code starts by importing three functions:
product: It generates Cartesian products, which are all possible tuples of length 6 from the set {0, 1, 2}. combinations: It generates combinations, which are all possible tuples of length 2 from the set {0, 1, 2, 3}. izip: It generates tuples by iterating over two iterables with the same length. The code then initializes a list scoring with three values [0, 1, 3] and a list histo with four lists, each containing 10 zeros.
The main loop iterates over all possible outcomes of six dice rolls, where each roll can be 0, 1, or 2.
For each outcome, it calculates the score for each player.
Player 0 gets points for rolling 0 and player 2 gets points for rolling 2.
Player 1 and player 3 get points for rolling 1 or 2.
The code then increments the count in the histo list for the corresponding score.
After all the outcomes have been processed, the code prints the histo list, which contains the distribution of the scores for each player.
Source code in the python programming language
from itertools import product, combinations, izip
scoring = [0, 1, 3]
histo = [[0] * 10 for _ in xrange(4)]
for results in product(range(3), repeat=6):
s = [0] * 4
for r, g in izip(results, combinations(range(4), 2)):
s[g[0]] += scoring[r]
s[g[1]] += scoring[2 - r]
for h, v in izip(histo, sorted(s)):
h[v] += 1
for x in reversed(histo):
print x
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