Unique Binary Search Trees II
Given n, generate all structurally unique BST's (binary search trees) that store values 1...n.
For example,
Given n = 3, your program should return all 5 unique BST's shown below.
1 3 3 2 1
\ / / / \ \
3 2 1 1 3 2
/ / \ \
2 1 2
Solution
- DFS directly. (from the Internet)
- DP + DFS. (my solution)
- Generate trees for 'n' from 1 to n. (DP)
- When generate trees for n = i, get the left and right subtrees by copying tree structures of dp[1...i-1]. (copy tree uses DFS)
Code
/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode(int x) { val = x; }
* }
*/
public class Solution {
public List<TreeNode> generateTrees(int n) {
return generateTreesRe(1, n);
}
public List<TreeNode> generateTreesRe(int l, int r) {
ArrayList<TreeNode> res = new ArrayList<TreeNode>();
if (l > r) {
res.add(null);
return res;
}
for (int k = l; k <= r; ++k) {
List<TreeNode> leftTrees = generateTreesRe(l, k-1);
List<TreeNode> rightTrees = generateTreesRe(k+1, r);
for (int i = 0; i < leftTrees.size(); i++) {
for (int j = 0; j < rightTrees.size(); j++) {
TreeNode root = new TreeNode(k);
root.left = leftTrees.get(i);
root.right = rightTrees.get(j);
res.add(root);
}
}
}
return res;
}
}