Array Element Moved by K Using Single Moves

Suppose we have an array that has n elements from 1 to n in shuffled order. Another integer K is given. There are N peoples they are standing in a queue to play badminton. The first two players will go for playing, then the loser will go and place at the end of the queue. The winner will play with the next person from the queue and so on. They will play until someone wins K times consecutively. Then that player becomes the winner.

If the queue is like [2, 1, 3, 4, 5] and K = 2, then output will be 5. Now see the explanation −

(2, 1) plays, 2 wins, so 1 will be added into the queue, Queue is like [3, 4, 5, 1] (2, 3) plays, 3 wins, so 2 will be added into the queue, Queue is like [4, 5, 1, 2] (3, 4) plays, 4 wins, so 3 will be added into the queue, Queue is like [5, 1, 2, 3] (4, 5) plays, 5 wins, so 4 will be added into the queue, Queue is like [1, 2, 3, 4] (5, 1) plays, 5 wins, so 3 will be added into the queue, Queue is like [2, 3, 4, 1]

(2, 1) plays, 2 wins, so 1 will be added into the queue, Queue is like [3, 4, 5, 1]

(2, 3) plays, 3 wins, so 2 will be added into the queue, Queue is like [4, 5, 1, 2]

(3, 4) plays, 4 wins, so 3 will be added into the queue, Queue is like [5, 1, 2, 3]

(4, 5) plays, 5 wins, so 4 will be added into the queue, Queue is like [1, 2, 3, 4]

(5, 1) plays, 5 wins, so 3 will be added into the queue, Queue is like [2, 3, 4, 1]

as 5 wins two consecutive matches, then output is 5.

Algorithm

winner(arr, n, k)

Begin
   if k >= n-1, then return n
   best_player := 0
   win_count := 0
   for each element e in arr, do
      if e > best_player, then
         best_player := e
         if e is 0th element, then
            win_count := 1
         end if
      else
         increase win_count by 1
      end if
      if win_count >= k, then
         return best player
     done
   return best player
End

Example

#include <iostream>
using namespace std;
int winner(int arr[], int n, int k) {
   if (k >= n - 1) //if K exceeds the array size, then return n
      return n;
   int best_player = 0, win_count = 0; //initially best player and win count is not set
   for (int i = 0; i < n; i++) { //for each member of the array
      if (arr[i] > best_player) { //when arr[i] is better than the best one, update best
         best_player = arr[i];
         if (i) //if i is not the 0th element, set win_count as 1
         win_count = 1;
      }else //otherwise increase win count
      win_count += 1;
      if (win_count >= k) //if the win count is k or more than k, then we have got result
         return best_player;
   }
   return best_player; //otherwise max element will be winner.
}
main() {
   int arr[] = { 3, 1, 2 };
   int n = sizeof(arr) / sizeof(arr[0]);
   int k = 2;
   cout << winner(arr, n, k);
}

Output

3