There is an upcoming football tournament, and the n participating teams are labelled from 1 to n. Each pair of teams will play against each other exactly once. Thus, a total of [n(n-1)/2] matches will be held, and each team will compete in n − 1 of these matches. There are only two possible outcomes of a match: 1. The match ends in a draw, in which case both teams will get 1 point. 2. One team wins the match, in which case the winning team gets 3 points and the losing team gets 0 points. Design an algorithm which runs in O(n2 ) time and provides a list of results in all [n(n-1)/2] matches which: (a) ensures that all n teams finish with the same points total, and (b) includes the fewest drawn matches among all lists satisfying (a). Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain English list of results mean Any combination of wins, losses and draws. You may wish to view this as a mapping from the set of distinct unordered pairs of teams to the set of results {smaller labelled team wins, draw, larger labelled team wins}. Hint: Can you prove that for certain values of n, it is impossible for a tournament without draws to finish with all teams on the same points total?
There is an upcoming football tournament, and the n participating teams are labelled from 1 to n.
Each pair of teams will play against each other exactly once.
Thus, a total of [n(n-1)/2] matches will be held, and each team will compete in n − 1 of these matches. There are only two possible outcomes of a match:
1. The match ends in a draw, in which case both teams will get 1 point.
2. One team wins the match, in which case the winning team gets 3 points and the losing team gets 0 points.
Design an
(a) ensures that all n teams finish with the same points total, and
(b) includes the fewest drawn matches among all lists satisfying (a).
Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain English
list of results mean Any combination of wins, losses and draws. You may wish to view this as a mapping from the set of distinct unordered pairs of teams to the set of results
{smaller labelled team wins, draw, larger labelled team wins}.
Hint: Can you prove that for certain values of n, it is impossible for a tournament without draws to finish with all teams on the same points total?
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