// Source : https://leetcode.com/problems/find-the-winner-of-the-circular-game/
// Author : Hao Chen
// Date   : 2021-04-11

/***************************************************************************************************** 
 *
 * There are n friends that are playing a game. The friends are sitting in a circle and are numbered 
 * from 1 to n in clockwise order. More formally, moving clockwise from the i^th friend brings you to 
 * the (i+1)^th friend for 1 <= i < n, and moving clockwise from the n^th friend brings you to the 
 * 1^st friend.
 * 
 * The rules of the game are as follows:
 * 
 * 	Start at the 1^st friend.
 * 	Count the next k friends in the clockwise direction including the friend you started at. 
 * The counting wraps around the circle and may count some friends more than once.
 * 	The last friend you counted leaves the circle and loses the game.
 * 	If there is still more than one friend in the circle, go back to step 2 starting from the 
 * friend immediately clockwise of the friend who just lost and repeat.
 * 	Else, the last friend in the circle wins the game.
 * 
 * Given the number of friends, n, and an integer k, return the winner of the game.
 * 
 * Example 1:
 * 
 * Input: n = 5, k = 2
 * Output: 3
 * Explanation: Here are the steps of the game:
 * 1) Start at friend 1.
 * 2) Count 2 friends clockwise, which are friends 1 and 2.
 * 3) Friend 2 leaves the circle. Next start is friend 3.
 * 4) Count 2 friends clockwise, which are friends 3 and 4.
 * 5) Friend 4 leaves the circle. Next start is friend 5.
 * 6) Count 2 friends clockwise, which are friends 5 and 1.
 * 7) Friend 1 leaves the circle. Next start is friend 3.
 * 8) Count 2 friends clockwise, which are friends 3 and 5.
 * 9) Friend 5 leaves the circle. Only friend 3 is left, so they are the winner.
 * 
 * Example 2:
 * 
 * Input: n = 6, k = 5
 * Output: 1
 * Explanation: The friends leave in this order: 5, 4, 6, 2, 3. The winner is friend 1.
 * 
 * Constraints:
 * 
 * 	1 <= k <= n <= 500
 ******************************************************************************************************/

class Solution {
public:
    int findTheWinner(int n, int k) {
        vector<int> persons(n);
        for(int i=0; i<n; i++) persons[i] = i + 1;
        
        for(int start=0; n>1; n--){
            start = (start + k -1) % n;
            persons.erase(persons.begin() + start);
            start = start %(n-1);
        }
        return persons[0];
    }
};