Create all-possible-full-binary-trees.cpp

Author: kamyu104

C++/all-possible-full-binary-trees.cpp

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+// Time:  O(n * 4^n / n^(3/2)) ~= sum of Catalan numbers from 1 .. N
+// Space: O(n * 4^n / n^(3/2)) ~= sum of Catalan numbers from 1 .. N
+
+/**
+ * Definition for a binary tree node.
+ * struct TreeNode {
+ *     int val;
+ *     TreeNode *left;
+ *     TreeNode *right;
+ *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
+ * };
+ */
+class Solution {
+public:
+    vector<TreeNode*> allPossibleFBT(int N) {
+        if (!memo_.count(N)) {
+            vector<TreeNode*> result;
+            if (N == 1) {
+                result.emplace_back(new TreeNode(0));
+            } else if (N % 2 == 1) {
+                for (int i = 0; i < N; ++i) {
+                    for (const auto& left: allPossibleFBT(i)) {
+                        for (const auto& right: allPossibleFBT(N - 1 - i)) {
+                            auto node = new TreeNode(0);
+                            node->left = left;
+                            node->right = right;
+                            result.emplace_back(node);
+                        }
+                    }
+                }
+            }
+            memo_[N] = move(result);
+        }
+        return memo_[N];
+    }
+
+private:
+    unordered_map<int, vector<TreeNode*>> memo_;
+};