solution 292-Nim-Game

Author: andy6804tw

Algorithms/C/292-Nim-Game.md

@@ -0,0 +1,48 @@
+# 292. Nim Game (C Language)
+
+## Problem
+
+You are playing the following Nim Game with your friend: There is a heap of stones on the table, each time one of you take turns to remove 1 to 3 stones. The one who removes the last stone will be the winner. You will take the first turn to remove the stones.
+
+Both of you are very clever and have optimal strategies for the game. Write a function to determine whether you can win the game given the number of stones in the heap.
+
+For example, if there are 4 stones in the heap, then you will never win the game: no matter 1, 2, or 3 stones you remove, the last stone will always be removed by your friend.
+
+Credits:
+Special thanks to @jianchao.li.fighter for adding this problem and creating all test cases.
+
+
+
+
+##### Solution 1.
+
+這題是在兩個玩家情況下輪流拿石頭，拿到最後一個獲勝，題目有說到剩 4 顆石頭必輸，所以要盡可能想辦法讓對方拿到 4 顆(4的倍數)，以下舉幾個所有可能情況。
+- 1~3顆全拿(獲勝)
+- 4顆(輸)
+  - 我方拿1、2、3顆對方都獲勝
+- 5顆(獲勝)
+  - 我方拿1顆對方剩4顆情況
+- 6顆(獲勝)
+  - 我方拿2顆對方剩4顆情況
+- 7顆(獲勝)
+  - 我方拿3顆對方剩4顆情況
+- 8顆(輸)
+  - 我方拿1、2、3顆對方都獲勝
+.
+.
+.
+重複
+
+- 數學解法
+- Run Time: 0 ms
+- 時間複雜度: O(1)
+- 空間複雜度: O(1)
+
+```c
+bool canWinNim(int n) {
+    if(n<4)
+        return 1;
+    else
+        return (n%4)!=0;
+}
+```

Algorithms/Java/292-Nim-Game.md

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+# 292. Nim Game (Java)
+
+## Problem
+
+You are playing the following Nim Game with your friend: There is a heap of stones on the table, each time one of you take turns to remove 1 to 3 stones. The one who removes the last stone will be the winner. You will take the first turn to remove the stones.
+
+Both of you are very clever and have optimal strategies for the game. Write a function to determine whether you can win the game given the number of stones in the heap.
+
+For example, if there are 4 stones in the heap, then you will never win the game: no matter 1, 2, or 3 stones you remove, the last stone will always be removed by your friend.
+
+Credits:
+Special thanks to @jianchao.li.fighter for adding this problem and creating all test cases.
+
+
+
+
+##### Solution 1.
+
+這題是在兩個玩家情況下輪流拿石頭，拿到最後一個獲勝，題目有說到剩 4 顆石頭必輸，所以要盡可能想辦法讓對方拿到 4 顆(4的倍數)，以下舉幾個所有可能情況。
+- 1~3顆全拿(獲勝)
+- 4顆(輸)
+  - 我方拿1、2、3顆對方都獲勝
+- 5顆(獲勝)
+  - 我方拿1顆對方剩4顆情況
+- 6顆(獲勝)
+  - 我方拿2顆對方剩4顆情況
+- 7顆(獲勝)
+  - 我方拿3顆對方剩4顆情況
+- 8顆(輸)
+  - 我方拿1、2、3顆對方都獲勝
+.
+.
+.
+重複
+
+- 數學解法
+- Run Time: 0 ms
+- 時間複雜度: O(1)
+- 空間複雜度: O(1)
+
+```java
+class Solution {
+    public boolean canWinNim(int n) {
+        if(n<4)
+        		return true;
+        else
+        		return (n%4)!=0;
+    }
+}
+```

README.md

@@ -15,6 +15,7 @@
 53.|[Maximum Subarray](https://leetcode.com/problems/maximum-subarray/description/)|Array|Easy|[C](/Algorithms/C/53-Maximum-Subarray.md) [Java](/Algorithms/Java/53-Maximum-Subarray.md)|
 69.|[Sqrt(x)](https://leetcode.com/problems/sqrtx/description/)|Math|Easy|[C](/Algorithms/C/69-Sqrt(x).md) [Java](/Algorithms/Java/69-Sqrt(x).md)|
 242.|[Valid Anagram](https://leetcode.com/problems/valid-anagram/description/)|String|Easy|[C](/Algorithms/C/242-Valid-Anagram.md) [Java](/Algorithms/Java/242-Valid-Anagram.md)|
+292.|[Nim Game](https://leetcode.com/problems/nim-game/description/)|Math|Easy|[C](/Algorithms/C/292-Nim-Game.md) [Java](/Algorithms/Java/292-Nim-Game.md)|
 344.|[Reverse String](https://leetcode.com/problems/reverse-string/description/)|String |Easy|[C](/Algorithms/C/344-Reverse-String.md) [Java](/Algorithms/Java/344-Reverse-String.md)