From 92baff81df67c18a94951ff790372f22c9ac8ddf Mon Sep 17 00:00:00 2001
From: Lam Haoyin <root@eatswap.org>
Date: Sat, 1 Jan 2022 13:08:06 +0800
Subject: [PATCH] add: 220101, I am vegetable

---
 2201/220101.cpp     | 95 +++++++++++++++++++++++++++++++++++++++++++++
 2201/CMakeLists.txt |  2 +-
 2 files changed, 96 insertions(+), 1 deletion(-)
 create mode 100644 2201/220101.cpp

diff --git a/2201/220101.cpp b/2201/220101.cpp
new file mode 100644
index 0000000..f2a2e10
--- /dev/null
+++ b/2201/220101.cpp
@@ -0,0 +1,95 @@
+#include <iostream>
+#include <vector>
+#include <map>
+#include <cstring>
+
+/**
+ * Usage of dynamic programming
+ *
+ * Initial attempt:
+ * try to merge 2 arrays which is calculated before.
+ * [3, 1, 7] => 49; [5, 8] => 48
+ * [3, 1, 7, 5, 8] => 501
+ * dp[L][R] <- max{merge(dp[L][L + i], dp[L + i + 1][R])}
+ *
+ * Why it fails:
+ * Since the solution might be in a completely shuffled
+ * order, making the previous results useless.
+ *
+ * How the solution solved it:
+ * The solution iterates from smaller intervals to
+ * larger intervals.
+ * dp[L][R] <- max{dp[L][L + i - 1] + dp[L + i + 1][R] + n[L + i] * n[L - 1] * n[R + 1]}
+ *
+ * Why solution works?
+ * In my previous attempt, There is no information such as
+ * *Which one is eliminated the first [Elimination Order]?*
+ * thus the order to eliminate remains unknown.
+ * The solution iterates *the last number to eliminate*,
+ * avoided to consider the order. (by brute force)
+ *
+ */
+
+class Solution {
+public:
+	static int maxCoins(const std::vector<int>& nums) {
+		const auto n = nums.size();
+		int num[n + 2];
+		std::memcpy(num + 1, &nums[0], n * sizeof(int));
+		num[0] = num[n + 1] = 1;
+
+		int dp[n + 2][n + 2];
+		std::memset(dp, 0, sizeof dp);
+		for (int i = 1; i <= n; ++i)
+			dp[i][i] = num[i - 1] * num[i] * num[i + 1];
+		dp[0][0] = num[1];
+		dp[n + 1][n + 1] = num[n];
+
+		for (int interval = 2; interval <= n; ++interval)
+			for (int L = 1, R = interval; R <= n; ++L, ++R)
+				for (int M = L; M <= R; ++M)
+					dp[L][R] = std::max(dp[L][R], dp[L][M - 1] + dp[M + 1][R] + num[M] * num[L - 1] * num[R + 1]);
+
+		return dp[1][n];
+	}
+};
+
+std::map<std::vector<int>, int> m;
+int cnt = 0;
+
+int bruteForce(const std::vector<int>& nums) {
+	if (m[nums]) { return m[nums]; }
+	++cnt;
+	if (nums.size() == 1)
+		return nums[0];
+	else if (nums.empty())
+		return 0;
+	int ret = -1;
+	for (auto it = nums.begin(); it != nums.end(); ++it) {
+		std::vector<int> d(nums.begin(), it);
+		d.insert(d.end(), it + 1, nums.end());
+		int t = (*it * (it == nums.begin() ? 1 : *(it - 1)) * ((it + 1 == nums.end()) ? 1 : *(it + 1))) + bruteForce(d);
+		ret = (t > ret) ? t : ret;
+	}
+	return m[nums] = ret;
+}
+
+int betterBruteForce(const std::vector<int>& nums, int append) {
+	return 0;
+}
+
+int main() {
+	// 3, 1, 5, 87, 9 --> 4101
+	// 3, 1, 5, 87, 9, 51 --> 63102
+	srand(time(nullptr));
+	const int LIM = 15;
+	std::vector<int> s;
+	s.reserve(LIM);
+	for (int i = 0; i < LIM; ++i) {
+		s.push_back(rand() % 100 + 1);
+	}
+	std::printf("%d\n", Solution::maxCoins(s));
+	std::printf("%d\n", bruteForce(s));
+	std::printf("Count = %d\n", cnt);
+	return 0;
+}
\ No newline at end of file
diff --git a/2201/CMakeLists.txt b/2201/CMakeLists.txt
index 5e425c3..b367a11 100644
--- a/2201/CMakeLists.txt
+++ b/2201/CMakeLists.txt
@@ -3,4 +3,4 @@ PROJECT(2201)
 
 SET(CMAKE_CXX_STANDARD 23)
 
-ADD_EXECUTABLE(2201 220101-CN.cpp)
\ No newline at end of file
+ADD_EXECUTABLE(2201 220101.cpp)
\ No newline at end of file