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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.
1#include <vector>
2#include <string>
3
4struct TreeNode {
5 int val;
6 TreeNode* left;
7 TreeNode* right;
8 TreeNode(int x) : val(x), left(NULL), right(NULL) {}
9};
10
11void dfs(TreeNode* node, std::string path, std::vector<std::string>& paths) {
12 if (!node) return;
13 path += std::to_string(node->val);
14 if (!node->left && !node->right) {
15 paths.push_back(path);
16 } else {
17 path += "->";
18 dfs(node->left, path, paths);
19 dfs(node->right, path, paths);
20 }
21}
22
23std::vector<std::string> binaryTreePaths(TreeNode* root) {
24 std::vector<std::string> paths;
25 dfs(root, "", paths);
26 return paths;
27}This C++ solution recursively constructs paths by accumulating node values in a string. The current path is added to the list when a leaf is reached. Backtracking is naturally handled by recursion since we use the same path string at each recursive depth.
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
This iterative C solution uses a stack to hold nodes and their accumulated paths. When processing each node, its path is updated and child nodes are added to the stack along with updated paths. Leaf nodes are treated as path endpoints.