Coding style: Should I use keyword mutable to give intuitive signatures to member methods?

Question

For example, consider the following Disjoint Set data structure with path compression (https://en.wikipedia.org/wiki/Disjoint-set_data_structure):

struct DisjointSet {
        /* Other stuff*/
        int find(int x) {
                if(parent[x] != x) {
                    parent[x] = find(parent[x]);
                }
                return parent[x];
        }
        private:
        std::vector<int> parent;
};

The method find() does not modify the implicit data represented by the data structure. Should I instead use the following implementation which lets find() be const?

struct DisjointSet {
        /* Other stuff*/
        int find(int x) const {
                if(parent[x] != x) {
                    parent[x] = find(parent[x]);
                }
                return parent[x];
        }
        private:
        mutable std::vector<int> parent;
};