add: 220522-CN [cpp]

cpp/2205/220522-CN.cpp

@@ -0,0 +1,54 @@
+#include <bitset>
+#include <functional>
+
+/**
+ * 464. Can I Win
+ * In the "100 game" two players take turns adding, to a running total, any integer from 1 to 10. The player who first causes the running total to reach or exceed 100 wins.
+ * What if we change the game so that players cannot re-use integers?
+ * For example, two players might take turns drawing from a common pool of numbers from 1 to 15 without replacement until they reach a total >= 100.
+ * Given two integers maxChoosableInteger and desiredTotal, return true if the first player to move can force a win, otherwise, return false. Assume both players play optimally.
+ */
+
+class Solution {
+public:
+	static bool canIWin(int maxChoosableInteger, int desiredTotal) {
+		if (!desiredTotal)
+			return true;
+		if (maxChoosableInteger * (maxChoosableInteger + 1) / 2 < desiredTotal)
+			return false;
+
+		// ans Key -> bit 19-0: chosen, bit 20: moving | 0 = me, bit -21: cur
+		// ans[state] -> Can I (moves first) win with this state?
+		std::bitset<1048576> s, vis;
+
+		std::function<bool(int)> dp = [&](int state) {
+			if (vis[state])
+				return s.test(state);
+
+			int sum = 0;
+			for (int i = 0; i < maxChoosableInteger; ++i)
+				if (state & (1 << i))
+					sum += 1 + i;
+
+			vis.set(state);
+			if (sum >= desiredTotal)
+				return bool(s[state] = false);
+
+			for (int i = 0; i < maxChoosableInteger; ++i) {
+				if (state & (1 << i))
+					continue;
+				if (!dp(state | (1 << i)))
+					return bool(s[state] = true);
+			}
+			return bool(s[state] = false);
+		};
+
+		return dp(0);
+	}
+};
+
+int main() {
+	std::printf("%s\n", Solution::canIWin(6, 16) ? "yes" : "false");
+	return 0;
+}
+

cpp/2205/CMakeLists.txt

@@ -3,4 +3,4 @@ PROJECT(2205)
 
 SET(CMAKE_CXX_STANDARD 23)
 
-ADD_EXECUTABLE(2205 220521-CN.cpp)
+ADD_EXECUTABLE(2205 220522-CN.cpp)