Path state (top-down) (Tree DFS Sub-pattern)

// Top-down: carry the path's state as a parameter; check it at the leaves.
// Here: every root-to-leaf path whose sum is target (Path Sum II).
void walk(TreeNode* node, int remaining, vector<int>& path, vector<vector<int>>& out) {
    if (!node) return;
    path.push_back(node->val);                           // enter: add this node to the path
    remaining -= node->val;
    if (!node->left && !node->right) {                   // a leaf: the path is complete
        if (remaining == 0) out.push_back(path);
    } else {
        walk(node->left, remaining, path, out);
        walk(node->right, remaining, path, out);
    }
    path.pop_back();                                     // leave: undo, so the parent's path is clean
}

vector<vector<int>> pathSum(TreeNode* root, int target) {
    vector<vector<int>> out;
    vector<int> path;
    walk(root, target, path, out);
    return out;
}