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This approach uses Depth-First Search (DFS) to explore all paths from the root to the leaf nodes. Starting from the root, we recursively visit each node, accumulating the current path. When a leaf node is reached, we add the accumulated path to a list of paths. This can be implemented recursively and is optimal given the constraints.
Time Complexity: O(n), where n is the number of nodes in the tree, as we visit each node once.
Space Complexity: O(n), for the space used to store the recursion stack and the result paths.
1class TreeNode:
2 def __init__(self, val=0, left=None, right=None):
3 self.val = val
4 self.left = left
5 self.right = right
6
7class Solution:
8 def binaryTreePaths(self, root: TreeNode) -> List[str]:
9 def dfs(node, path):
10 if node:
11 path += str(node.val)
12 if not node.left and not node.right: # Leaf node
13 paths.append(path)
14 else:
15 path += '->'
16 dfs(node.left, path)
17 dfs(node.right, path)
18
19 paths = []
20 dfs(root, '')
21 return pathsThis Python solution leverages the recursive DFS approach to gather paths. Leaf nodes signal the end of a path, which is then appended to the results.
This approach utilizes an iterative Depth-First Search (DFS) with a stack. By storing the nodes and their paths on the stack, we can simulate the recursive DFS stack. This allows for constructing the paths through iterative backtracking.
Time Complexity: O(n), traversing each node once.
Space Complexity: O(n), as we maintain a stack proportional to the tree height.
1using System.Collections.Generic;
public class TreeNode {
public int val;
public TreeNode left;
public TreeNode right;
public TreeNode(int x) { val = x; }
}
public class Solution {
public IList<string> BinaryTreePaths(TreeNode root) {
List<string> paths = new List<string>();
if (root == null) return paths;
Stack<(TreeNode, string)> stack = new Stack<(TreeNode, string)>();
stack.Push((root, root.val.ToString()));
while (stack.Count > 0) {
var (node, path) = stack.Pop();
if (node.left == null && node.right == null) {
paths.Add(path);
}
if (node.right != null) {
stack.Push((node.right, path + "->" + node.right.val));
}
if (node.left != null) {
stack.Push((node.left, path + "->" + node.left.val));
}
}
return paths;
}
}This C# solution uses a stack to iteratively explore the tree, simulating recursive behavior through stack operations. The process accumulates paths, finalizing them once a leaf node is identified.