Create subtree-removal-game-with-fibonacci-tree.cpp

Author: kamyu104

C++/subtree-removal-game-with-fibonacci-tree.cpp

@@ -0,0 +1,22 @@
+// Time:  O(1)
+// Space: O(1)
+
+class Solution {
+public:
+    bool findGameWinner(int n) {
+        return n % 6 != 1;  // the cycle period is 6 observed from solution2, which could be proved by mathematical induction
+    }
+};
+
+// Time:  O(n)
+// Space: O(1)
+class Solution2 {
+public:
+    bool findGameWinner(int n) {
+        vector<int> grundy = {0, 1};
+        for (int i = 2; i < n; ++i) {
+            grundy[i % 2] = (grundy[(i - 1) % 2] + 1) ^ (grundy[(i - 2) % 2] + 1);
+        }
+        return grundy[(n - 1) % 2];  // colon principle, replace the branches by a non-branching stalk of length equal to their nim sum
+    }
+};