public class power_r {
 
  // there's another way to compute those powers!
  // let's see...

  // square -> same as in power_i
  public static int pow2(int x) {
    return x * x;
  }

  // cube -> look: x^3 = x * x^2, so we can make use of pow2()
  public static int pow3(int x) {
    return x * pow2(x);
  }

  // 4th power -> idem: x^4 = x * x^3
  public static int pow4(int x) {
    return x * pow3(x);
  }

  // generalization: n-th power -> x^n = x * x^(n - 1)
  // (works for n > 0)
  public static int pown(int x, int n) {
    if (n == 1) {
      return x;
    }
    return x * pown(x, n - 1);
  }

  /////////////////////////////////////////////////////////////////////
  // now, pown() doesn't contain any loops!                          //
  //                                                                 //
  // this is a RECURSIVE solution, whereas what we've done for       //
  // power_i.java is called an ITERATIVE solution.                   //
  //                                                                 //
  // as a matter of fact, every iterative procedure can be           //
  // written recursively and vice-versa -                            //
  // however, often one way to write a procedure is much more        //
  // easy than the other (see for example the flood-fill exercise    //
  // from the ITP labs)                                              //
  /////////////////////////////////////////////////////////////////////

  // test our methods -> still works ;-)
  public static void main(String a[]) {
    System.out.println(" 7^2 = " + pow2(7));
    System.out.println("10^3 = " + pow3(10));
    System.out.println(" 2^4 = " + pow4(2));
    System.out.println(" 2^5 = " + pown(2, 5));
  }

}