java - Time complexity analysis of minimum set cover solution -

for question

there n persons , k different type of dishes. each person has preference each dish. either likes or not. need feed people. every person should atleast 1 dish of chioce. minimum number of different type of dishes can order?

one of solution is,

  public class optimumdish {    private set<integer> result = new hashset<integer>();    public void print(){     for(int r:result)       system.out.print(r + " ");   }    // find optimum dish navigating available options   public void find(int[][] m, int r, int c, int mr, int mc, stack<integer> dishes) {      dishes.push(c);      if (r == mr) {       // reached last person. unique dishes       set<integer> d = new hashset<>(dishes);       if(result.size() == 0 || result.size() > d.size())         result = d;     }     else if (r < mr) {       // check next person's preferred dish       (int = 0; <= mc; i++) {         if (m[r + 1][i] == 1) {           find(m, r+1, i, mr, mc, dishes);           break;         }       }     }      dishes.pop();      // current dish may not optimum.     // check other dish same person     (int = c + 1; <= mc; i++) {       if (m[r][i] == 1) {         find(m, r, i, mr, mc, dishes);       }     }   }    public static void main(string[] args) {      int[][] m = {          { 0, 1, 1, 0, 0, 0, 0 },         { 0, 1, 0, 1, 0, 0, 0 },         { 0, 1, 1, 0, 0, 1, 0 },         { 1, 0, 0, 1, 0, 0, 0 },         { 0, 0, 1, 0, 1, 0, 0 },         { 0, 0, 0, 1, 0, 0, 1 }         };      int mr = m.length - 1;     int mc = m[0].length - 1;     int c = 0;      (int = 0; <= mr; i++) {       if (m[0][i] == 1) {         c = i;         break;       }     }      optimumdish od = new optimumdish();     stack<integer> dishes = new stack<>();     od.find(m, 0, c, mr, mc, dishes);     od.print();   } } 

this problem of type 'minimum set cover'. since np-complete problem, can't solved in polynomial time. per solution can solved in polynomial time?

please let me know time complexity of solution? o(n^4)?. thanks.