Problem

https://leetcode.com/problems/unique-binary-search-trees-ii/description/

Given an integer 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 3

Idea: Recursion

for i in 1..n: pick i as root,
left subtrees can be generated in the same way for n_l = 1 … i – 1,
right subtrees can be generated in the same way for n_r = i + 1, …, n
def gen(s, e):
return [tree(i, l, r) for l in gen(s, i – 1) for r in gen(i + 1, e) for i in range(s, e+1)

# of trees:

n = 0: 1
n = 1: 1
n = 2: 2
n = 3: 5
n = 4: 14
n = 5: 42
n = 6: 132
…
Trees(n) = Trees(0)*Trees(n-1) + Trees(1)*Trees(n-2) + … + Tress(n-1)*Trees(0)

Time complexity: O(3^n)

Space complexity: O(3^n)

C++

// Author: Huahua

// Running time: 16 ms

class Solution {

public:

vector<TreeNode*> generateTrees(int n) {

if (n == 0) return {};

const auto& ans = generateTrees(1, n);

cout << ans.size() << endl;

return ans;

}

private:

vector<TreeNode*> generateTrees(int l, int r) {

if (l > r) return { nullptr };

vector<TreeNode*> ans;

for (int i = l; i <= r; ++i)

for (TreeNode* left : generateTrees(l, i - 1))

for (TreeNode* right : generateTrees(i + 1, r)) {

ans.push_back(new TreeNode(i));

ans.back()->left = left;

ans.back()->right = right;

}

return ans;

}

};

Java

// Author: Huahua 4 ms

class Solution {

public List<TreeNode> generateTrees(int n) {

if (n == 0) return new ArrayList<TreeNode>();

return generateTrees(1, n);

}

private List<TreeNode> generateTrees(int l, int r) {

List<TreeNode> ans = new ArrayList<>();

if (l > r) {

ans.add(null);

return ans;

}

for (int i = l; i <= r; ++i)

for (TreeNode left : generateTrees(l, i - 1))

for (TreeNode right: generateTrees(i + 1, r)) {

TreeNode root = new TreeNode(i);

root.left = left;

root.right = right;

ans.add(root);

}

return ans;

}

Python 3

"""

Author: Huahua

Running time: 84 ms

"""

class Solution:

def generateTrees(self, n):

def newTree(x, l, r):

t = TreeNode(x)

t.left = l

t.right = r

return t

def gen(s, e):

return [newTree(i, l, r) for i in range(s, e + 1) for l in gen(s, i - 1) for r in gen(i + 1, e)] or [None]

return gen(1, n) if n > 0 else []

Solution 2: DP

Java

// Author: Huahua, 3 ms

class Solution {

public List<TreeNode> generateTrees(int n) {

if (n == 0) return new ArrayList<TreeNode>();

List<TreeNode>[] dp = new List[n + 1];

dp[0] = new ArrayList<TreeNode>();

dp[0].add(null);

for (int i = 1; i <= n; ++i) {

dp[i] = new ArrayList<TreeNode>();

for (int j = 0; j < i; ++j)

for (TreeNode left : dp[j])

for (TreeNode right: dp[i - j - 1]) {

TreeNode root = new TreeNode(j + 1);

root.left = left;

root.right = clone(right, j + 1);

dp[i].add(root);

}

return dp[n];

}

private TreeNode clone(TreeNode root, int delta) {

if (root == null) return root;

TreeNode node = new TreeNode(root.val + delta);

node.left = clone(root.left, delta);

node.right = clone(root.right, delta);

return node;

}

花花酱 LeetCode 95. Unique Binary Search Trees II

Problem

Idea: Recursion

C++

Java

Python 3

Solution 2: DP

Java

Related Problems

Be First to Comment

Leave a Reply Cancel reply