Implement unique-binary-search-trees

name: unique-binary-search-trees
url: https://leetcode.com/problems/unique-binary-search-trees
difficulty: 2

time: 100.0 ms
time-rank: -1 %
time-complexity: O(N)

space: 5.9 MB
space-rank: 92.28 %
space-complexity: O(N)

Fixes #155

Signed-off-by: Christopher Friedt <[email protected]>

Author: cfriedt

unique-binary-search-trees-test.cpp

@@ -0,0 +1,27 @@
+/*
+ * Copyright (c) 2021, Christopher Friedt
+ *
+ * SPDX-License-Identifier: MIT
+ */
+
+#include <gtest/gtest.h>
+
+#include "unique-binary-search-trees.cpp"
+
+using namespace std;
+
+TEST(UniqueBinarySearchTrees, 1) {
+  EXPECT_EQ(1, Solution().numTrees(1));
+}
+
+TEST(UniqueBinarySearchTrees, 2) {
+  EXPECT_EQ(2, Solution().numTrees(2));
+}
+
+TEST(UniqueBinarySearchTrees, 3) {
+  EXPECT_EQ(5, Solution().numTrees(3));
+}
+
+TEST(UniqueBinarySearchTrees, 4) {
+  EXPECT_EQ(5, Solution().numTrees(3));
+}

unique-binary-search-trees.cpp

@@ -0,0 +1,51 @@
+/*
+ * Copyright (c) 2021, Christopher Friedt
+ *
+ * SPDX-License-Identifier: MIT
+ */
+
+// clang-format off
+// name: unique-binary-search-trees
+// url: https://leetcode.com/problems/unique-binary-search-trees
+// difficulty: 2
+// clang-format on
+
+#include <vector>
+
+using namespace std;
+
+class Solution {
+public:
+    int helper(vector<int>& dp, int n) {
+        if (dp[n] != 0) {
+            return dp[n];
+        }
+
+        int m = 0;
+        for(int root = 1; root <= n; ++root) {
+            int before = root - 1;
+            int after = n - root;
+
+            m += helper(dp, before) * helper(dp, after);
+        }
+        
+        dp[n] = m;
+        return m;
+    }
+
+    int numTrees(int n) {
+        // the solution is structurally recursive
+        // n | root | numTrees(n)
+        // ---------------
+        // 0 |      | 1
+        // 1 |      | 1
+        // 2 |   1  |  1
+        //   |   2  | +1 = 2
+        // 3 |   1  |   numTress(0) * numTrees(2)
+        //   |   2  | + numTrees(1) * numTrees(1)
+        //   |   3  | + numTrees(2) * numTrees(0) = 5
+        vector<int> dp(n + 1, 0);
+        dp[0] = 1;
+        return helper(dp, n);
+    }
+};