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 Problem Statement for CheeseRolling

Problem Statement


N people (where N is a power of 2) are taking part in a single-elimination tournament in cheese rolling. The diagram below illustrates the structure of the tournament bracket.

The people entering the tournament are numbered from 0 to N-1. For each potential cheese rolling match you know who would win the match. You are given this information encoded as a String[] wins with N elements, each containing N characters. For each valid i and j, wins[i][j] is 'Y' if person i beats person j. Otherwise, wins[i][j] is 'N'. The relation is not necessarily transitive: it may be the case that person i beats person j, person j beats person k, and person k beats person i.

There are N! (N factorial) ways to assign the people to positions in the bracket. Different assignments may produce a different winner of the tournament. Return a long[] with N elements. For each valid i, element i of the return value should be the exact number of assignments for which person i wins the tournament.



Method signature:long[] waysToWin(String[] wins)
(be sure your method is public)


-N will be between 2 and 16, inclusive.
-N will be a power of 2.
-wins will contain exactly N elements.
-Each element of wins will have a length of exactly N.
-Each element of wins will be composed of the characters 'Y' and 'N'.
-For each i from 0 to N-1, wins[i][i] = 'N'.
-For all distinct integers i and j from 0 to N-1, exactly one of wins[i][j] and wins[j][i] will be 'Y'.


Returns: {0, 2 }
There are 2 ways to assign the players:
  • Player 0 goes to position 0 and player 1 goes to position 1.
  • Player 1 goes to position 0 and player 0 goes to position 1.
In both assignments, player 1 will win the match against player 0 because wins[1][0] = 'Y'.
Returns: {8, 0, 16, 0 }
Returns: {4096, 8960, 0, 2048, 23808, 0, 1408, 0 }
{331616878592, 37267079168, 2426798866432, 2606831599616, 994941665280, 1162501849088, 1888166674432, 4632734203904, 832881524736, 84707409920, 3007127748608, 55490052096, 17818550272, 254672666624, 629921447936, 1959311671296 }
Returns: {20922789888000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }
Player 0 wins no matter how the positions are assigned, so the answer is 16! = 20922789888000.

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This problem was used for:
       Single Round Match 663 Round 1 - Division II, Level Three