1823. Find the Winner of the Circular Game
Description
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 ith
friend brings you to the (i+1)th
friend for 1 <= i < n
, and moving clockwise from the nth
friend brings you to the 1st
friend.
The rules of the game are as follows:
- Start at the
1st
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
Follow up:
Could you solve this problem in linear time with constant space?
Solutions
Solution 1
1 2 3 4 5 6 |
|
1 2 3 4 5 6 7 8 9 |
|
1 2 3 4 5 6 7 8 |
|
1 2 3 4 5 6 7 8 9 10 |
|
1 2 3 4 5 6 7 |
|
1 2 3 4 5 6 7 8 9 |
|
1 2 3 4 5 6 7 8 9 10 11 12 |
|
Solution 2: Simulation
1 2 3 4 5 6 7 8 9 10 11 |
|
1 2 3 4 5 6 7 8 9 10 11 |
|