From c8960f3096b8c0801135f081e29d855a56b1370f Mon Sep 17 00:00:00 2001
From: Lam Haoyin <root@eatswap.org>
Date: Tue, 22 Feb 2022 15:41:22 +0800
Subject: [PATCH] add: 220222-CN [cpp]

---
 cpp/2202/220222-CN.cpp  | 94 +++++++++++++++++++++++++++++++++++++++++
 cpp/2202/CMakeLists.txt |  2 +-
 2 files changed, 95 insertions(+), 1 deletion(-)
 create mode 100644 cpp/2202/220222-CN.cpp

diff --git a/cpp/2202/220222-CN.cpp b/cpp/2202/220222-CN.cpp
new file mode 100644
index 0000000..6c009e6
--- /dev/null
+++ b/cpp/2202/220222-CN.cpp
@@ -0,0 +1,94 @@
+#include <vector>
+#include <iostream>
+
+class Solution {
+private:
+	inline static const int primes[] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29};
+	inline static const int MOD = 1000000007;
+public:
+	static int numberOfGoodSubsets(const std::vector<int>& nums) {
+		int cnt[31]{};
+		for (int i : nums)
+			++cnt[i];
+		// 2 x 3 = 6
+		// 2 x 5 = 10
+		// 2 x 7 = 14
+		// 2 x 11 = 22
+		// 2 x 13 = 26
+		// 3 x 5 = 15
+		// 3 x 7 = 21
+		long long ret = 0;
+		for (int i = 1; i < 1024; ++i) {
+			// Original numbers
+			long long now = 1;
+			for (int j = 0; j < 10; ++j)
+				if (i & (1 << j))
+					now = (now * cnt[primes[j]]) % MOD;
+			ret = (ret + now) % MOD;
+
+			if (i & 1) {
+				// 2-related numbers
+				for (int j = 1; j <= 5; ++j) {
+					if ((i & (1 << j)) && (now = cnt[primes[j] << 1])) {
+						// Now, there is no 2, no primes[j], but (primes[j] << 1).
+						for (int k = 1; k < 10; ++k)
+							if (k != j && (i & (1 << k)))
+								now = (now * cnt[primes[k]]) % MOD;
+						ret = (ret + now) % MOD;
+					}
+				}
+			}
+
+			if (i & 2) {
+				// 3-related numbers
+				// Only 5 (indexed 2) and 7 (indexed 3) is valid.
+				if ((i & 4) && (now = cnt[15])) {
+					for (int k = 0; k < 10; ++k)
+						if (k != 1 && k != 2 && (i & (1 << k)))
+							now = (now * cnt[primes[k]]) % MOD;
+					ret = (ret + now) % MOD;
+				}
+				if ((i & 8) && (now = cnt[21])) {
+					for (int k = 0; k < 10; ++k)
+						if (k != 1 && k != 3 && (i & (1 << k)))
+							now = (now * cnt[primes[k]]) % MOD;
+					ret = (ret + now) % MOD;
+				}
+			}
+
+			if ((now = cnt[30]) && ((i & 7) == 7)) {
+				// 2 * 3 * 5 == 30
+				for (int j = 3; j < 10; ++j)
+					if (i & (1 << j))
+						now = (now * cnt[primes[j]]) % MOD;
+				ret = (ret + now) % MOD;
+			}
+
+			// 2 - (11, 13) + 3 - (5, 7)
+			if (((i & 3) == 3) && (i & 61)) {
+				for (int j2 = 2; j2 <= 5; ++j2) {
+					for (int j3 = 2; j3 <= 3; ++j3) {
+						if (j2 != j3 && (i & (1 << j2)) && (i & (1 << j3))) {
+							now = (cnt[primes[j2] << 1] * cnt[primes[j3] * 3]) % MOD;
+							for (int k = 2; k < 10; ++k) {
+								if (k != j2 && k != j3 && (i & (1 << k))) {
+									now = (now * cnt[primes[k]]) % MOD;
+								}
+							}
+							ret = (ret + now) % MOD;
+						}
+					}
+				}
+			}
+		}
+		while (cnt[1]--) {
+			ret = (ret << 1) % MOD;
+		}
+		return ret % MOD;
+	}
+};
+
+int main() {
+	std::cout << Solution::numberOfGoodSubsets({5, 10, 1, 26, 24, 21, 24, 23, 11, 12, 27, 4, 17, 16, 2, 6, 1, 1, 6, 8, 13, 30, 24, 20, 2, 19});
+	return 0;
+}
diff --git a/cpp/2202/CMakeLists.txt b/cpp/2202/CMakeLists.txt
index 0f423ba..541a88c 100644
--- a/cpp/2202/CMakeLists.txt
+++ b/cpp/2202/CMakeLists.txt
@@ -3,4 +3,4 @@ PROJECT(2202)
 
 SET(CMAKE_CXX_STANDARD 23)
 
-ADD_EXECUTABLE(2202 220221.cpp)
+ADD_EXECUTABLE(2202 220222-CN.cpp)