Apparently it means to swap the left and right subtrees. How's that "inversion"? I'd call it "flipping" or "mirroring" or something... If this is the case, then it's a trivial solution: invert(left_child); invert(right_child);

Or, if the structure is this:

    struct node {
            struct node *left_node;
            struct node *right_node;
            int val;
    };

    struct reversed_node {
            struct reversed_node *right_node;
            struct reversed_node *left_node;
            int val;
    };

No? You then just have a different mapping for the exact same data, no traversal needed.