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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.
1using System;
2using System.Collections.Generic;
3
4public class TreeNode {
5 public int val;
6 public TreeNode left;
7 public TreeNode right;
8 public TreeNode(int x) { val = x; }
9}
10
11public class Solution {
12 public IList<string> BinaryTreePaths(TreeNode root) {
13 List<string> paths = new List<string>();
14 if (root != null) Dfs(root, "", paths);
15 return paths;
16 }
17
18 private void Dfs(TreeNode node, string path, List<string> paths) {
19 if (node != null) {
20 path += node.val;
21 if (node.left == null && node.right == null) { // Leaf node
22 paths.Add(path);
23 } else {
24 path += "->";
25 Dfs(node.left, path, paths);
26 Dfs(node.right, path, paths);
27 }
28 }
29 }
30}This C# approach utilizes a recursive method for generating paths similar to other languages. Each path is built from the root to the leaves, utilizing a recursive call stack to track the depth and path.
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.
1#include <string>
#include <stack>
struct TreeNode {
int val;
TreeNode* left;
TreeNode* right;
TreeNode(int x) : val(x), left(NULL), right(NULL) {}
};
std::vector<std::string> binaryTreePaths(TreeNode* root) {
std::vector<std::string> paths;
if (!root) return paths;
std::stack<std::pair<TreeNode*, std::string>> stack;
stack.push({root, std::to_string(root->val)});
while (!stack.empty()) {
auto [node, path] = stack.top(); stack.pop();
if (!node->left && !node->right) {
paths.push_back(path);
}
if (node->right) {
stack.push({node->right, path + "->" + std::to_string(node->right->val)});
}
if (node->left) {
stack.push({node->left, path + "->" + std::to_string(node->left->val)});
}
}
return paths;
}In this C++ solution, a stack simulates the recursive call stack by holding nodes and path strings. On processing nodes, if they are leaves, the path is added to the result. Otherwise, child nodes are stacked with updated paths.