## Facebook Interview Question

**Country:**United States

P1>P2 and P2>P3 implies P1>P3

The first question is basically finding the max in an array. First compare between P1 and P2, store the bigger one and then match the result with P3. This process goes on till PN.

The second question is basically sorting the players. This is merge sort where the results of the pairwise matches determine which element is larger.

```
// players: [0, n-1]
// w[0] wins w[1]
func Question1(n int, wins [][]int) int {
// Two iteration, but strictly O(1) space
var loser int
for _, w := range wins {
loser = w[1]
// mark loser's index using negative value
wins[loser][0] = math.MinInt32 + abs(wins[loser][0])
}
for i := 0; i < n; i++ {
// winner never loses
if wins[i][0] > 0 {
return i
}
}
return -1
}
func Question2(n int, wins [][]int) []int {
// topological sort
// O(n) time, O(n) space
games := make(map[int][]int)
ans, degrees := make([]int, n), make([]int, n)
for _, w := range wins {
games[w[1]] = append(games[w[1]], w[0])
degrees[w[0]]++
}
// there should always be all-game losers, otherwise the deadlock occurs
var queue []int
for i, in := range degrees {
if in == 0 {
queue = append(queue, i)
}
}
for len(queue) > 0 {
size := len(queue)
for i := 0; i < size; i++ {
cur := queue[i]
n--
ans[n] = queue[i]
for _, winner := range games[cur] {
degrees[winner]--
if degrees[winner] == 0 {
queue = append(queue, winner)
}
}
}
queue = queue[size:]
}
return ans
}
```

- yp November 25, 2021