A and B are playing a game. At the beginning there are n coins. Given two more numbers x and y. In each move a player can pick x or y or l coins. A always starts the game. The player who picks the last coin wins the game. For a given value of n, find whether A will win the game or not if both are playing optimally.
Input : n = 5, x = 3, y = 4 Output : A There are 5 coins, every player can pick 1 or 3 or 4 coins on his/her turn. A can win by picking 3 coins in first chance. Now 2 coins will be left so B will pick one coin and now A can win by picking the last coin. Input : 2 3 4 Output : B
Let us take few example values of n for x = 3, y = 4.
n = 0 A can not pick any coin so he losses
n = 1 A can pick 1 coin and win the game
n = 2 A can pick only 1 coin. Now B will pick 1 coin and win the game
n = 3 4 A will win the game by picking 3 or 4 coins
n = 5, 6 A will choose 3 or 4 coins. Now B will have to choose from 2 coins so A will win.
We can observe that A wins game for n coins only when it loses for coins n-1, n-x and n-y.
This article is contributed by nuclode. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
- Predict the winner of the game | Sprague-Grundy
- Coin Change | DP-7
- Coin Change | BFS Approach
- Maximum games played by winner
- Understanding The Coin Change Problem With Dynamic Programming
- Optimal Strategy for a Game | DP-31
- Optimal Strategy for a Game | Set 2
- Optimal Strategy for a Game | Set 3
- Optimal strategy for a Game with modifications
- Count number of ways to reach a given score in a game
- Count ways to reach Nth Stairs by taking 1 and 2 steps with exactly one 3 step
- Number of subsequences with negative product
- Maximum number of multiples in an array before any element
- Maximum subsequence sum with adjacent elements having atleast K difference in index
Improved By : vt_m