c++ - Winner of a tournament in O(N) and rank of the players in O(NLogN) -

in tennis tournament of n players every player plays every other player. following condition hold- if player p1 has won match p2 , player p2 has won p3, player p1 has defeated p3. find winner of tournament in o(n) time , o(1) space. find rank of players in o(nlogn) time. my solution : input boolean matrix element matrix[i][j] indicates whether player wins player j.

bool win[][]= {     {0, 0, 1, 1, 1, 0, 1},     {1, 0, 1, 1, 1, 1, 1},     {0, 0, 0, 1, 1, 0, 0},     {0, 0, 0, 0, 1, 0, 0},     {0, 0, 0, 0, 0, 0, 0},     {1, 0, 1, 1, 1, 0, 1},     {0, 0, 1, 1, 1, 0, 0} }; 

so winner found like,

int winner = 0; (int = 1; < player_count; ++i) {     if (win[i][winner])         winner = i; } return winner; 

for getting rank of players, guess topological sorting one. if player 1 wins player 2, edge added lke p1-> p2. if player 1 winner here, have edges other players. topological sorting winner source vertex, give rank of player. solution correct ? there other efficient solution ? great, in advance.

the condition

if player p1 has won match p2 , player p2 has won p3

is defining total ordering, i.e. if define p1 < p2 "p2 defeated p1", have transitive ordering relation <, can used regular less-than relation in either sorting or finding maximum. implementation can define predicate bool lessthan(int p1, int p2) p1 , p2 relation in matrix in o(1). , use predicate "maximum" search, linear (o(n)), or sorting (ranking), o(n log n).