[LeetCode] Problem 894 - All Possible Full Binary Trees

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A full binary tree is a binary tree where each node has exactly 0 or 2 children.

Return a list of all possible full binary trees with N nodes. Each element of the answer is the root node of one possible tree.

Each node of each tree in the answer must have node.val = 0.

You may return the final list of trees in any order.

Example

Input: 7

Output: [[0,0,0,null,null,0,0,null,null,0,0],[0,0,0,null,null,0,0,0,0],[0,0,0,0,0,0,0],[0,0,0,0,0,null,null,null,null,0,0],[0,0,0,0,0,null,null,0,0]]

Explanation:

m9spdS.png

Note

  • 1 <= N <= 20

Code

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public class TreeNode {
    int val;
    TreeNode left;
    TreeNode right;
    TreeNode(int x) { val = x; }
}
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private Map<Integer, List<TreeNode>> map = new HashMap<>();

public List<TreeNode> allPossibleFBT(int N) {
    List<TreeNode> result = new ArrayList<>();

    if (N == 1) {
        result.add(new TreeNode(0));
        return result;
    }
    else if (N % 2 == 0)
        return result;

    if (map.containsKey(N))
        return map.get(N);
    
    for (int i = 1; i < N; i += 2) {
        List<TreeNode> left = allPossibleFBT(i);
        List<TreeNode> right = allPossibleFBT(N - i - 1);

        for (TreeNode l : left) {
            for (TreeNode r : right) {
                TreeNode root = new TreeNode(0);
                root.left = l;
                root.right = r;
                result.add(root);
            }
        }
    }
    
    map.put(N, result);
    
    return result;
}