背景
考虑一个循环锦标赛,其中每个参赛者与其他参赛者进行一场比赛。没有平局,因此每场比赛都有赢家和输家。如果对其他每位竞争者B来说,A击败B或A击败另一位竞争者C,而竞争者C又击败B,那么竞争者A是比赛的王者。可以证明,每场比赛都有至少一位国王(尽管可能有几位)。在这个挑战中,您的任务是找到给定锦标赛的国王。
输入输出
您输入的是N × N
布尔矩阵T
,还可以N ≥ 2
是参赛者人数。每个条目T[i][j]
代表选手之间的比赛的胜负i
和j
,值为1代表一胜i
0一胜j
。请注意,T[i][j] == 1-T[j][i]
如果i != j
。的对角线T
包括0。
您的输出应为T
代表比赛的国王列表,使用基于0或基于1的索引。国王的顺序无关紧要,但不应重复。
输入和输出都可以采用任何合理的格式。
规则和计分
您可以编写完整的程序或函数。最低字节数获胜,并且不允许出现标准漏洞。
测试用例
这些测试用例使用基于0的索引。对于基于1的索引,增加每个输出值。
2 [[0,0],[1,0]] -> [1]
3 [[0,1,0],[0,0,0],[1,1,0]] -> [2]
3 [[0,1,0],[0,0,1],[1,0,0]] -> [0,1,2]
4 [[0,1,1,1],[0,0,1,0],[0,0,0,0],[0,1,1,0]] -> [0]
4 [[0,1,1,0],[0,0,1,0],[0,0,0,1],[1,1,0,0]] -> [0,2,3]
5 [[0,1,0,0,1],[0,0,0,0,1],[1,1,0,0,0],[1,1,1,0,1],[0,0,1,0,0]] -> [3]
5 [[0,1,0,1,0],[0,0,1,1,1],[1,0,0,0,0],[0,0,1,0,1],[1,0,1,0,0]] -> [0,1,4]
5 [[0,0,0,0,0],[1,0,1,1,0],[1,0,0,0,1],[1,0,1,0,1],[1,1,0,0,0]] -> [1,3,4]
6 [[0,0,0,0,0,0],[1,0,1,1,0,0],[1,0,0,1,1,0],[1,0,0,0,1,1],[1,1,0,0,0,1],[1,1,1,0,0,0]] -> [1,2,3,4,5]
6 [[0,0,1,1,1,0],[1,0,0,1,1,1],[0,1,0,0,1,0],[0,0,1,0,0,1],[0,0,0,1,0,1],[1,0,1,0,0,0]] -> [0,1,2,3,5]
6 [[0,1,1,0,0,1],[0,0,0,1,0,1],[0,1,0,1,1,0],[1,0,0,0,1,1],[1,1,0,0,0,0],[0,0,1,0,1,0]] -> [0,1,2,3,4,5]
8 [[0,0,1,1,0,1,1,1],[1,0,1,0,1,1,0,0],[0,0,0,1,1,0,0,0],[0,1,0,0,0,1,0,0],[1,0,0,1,0,1,0,0],[0,0,1,0,0,0,1,0],[0,1,1,1,1,0,0,1],[0,1,1,1,1,1,0,0]] -> [0,1,4,6,7]
20 [[0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,1,1,0,1],[1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,1],[0,0,0,1,0,0,0,1,1,0,1,0,1,0,0,0,0,0,1,1],[0,0,0,0,1,1,1,1,1,1,1,1,0,0,1,0,0,1,1,1],[1,0,1,0,0,0,0,1,1,0,1,1,1,0,1,1,1,1,0,1],[0,1,1,0,1,0,1,1,1,1,1,0,1,1,1,0,1,1,0,1],[0,0,1,0,1,0,0,1,1,0,1,0,1,1,1,1,1,0,1,0],[1,0,0,0,0,0,0,0,1,0,1,1,1,1,0,0,1,1,1,0],[1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,1,1],[1,0,1,0,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,1],[1,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0],[0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,1,0,1,1],[0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,1,0,1,1,1],[1,0,1,1,1,0,0,0,0,1,0,0,1,0,1,1,1,1,1,1],[0,0,1,0,0,0,0,1,0,1,1,0,0,0,0,1,1,0,0,1],[0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1],[0,0,1,1,0,0,0,0,0,1,1,0,1,0,0,1,0,0,1,1],[0,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1],[1,0,0,0,1,1,0,0,0,0,1,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0]] -> [0,1,3,4,5,7,8,11,15,17,18]