SICP习题 1.19(对数级?---斐波那契数的再一次优化!!!)

(define (fib n)
  (fib-iter 1 0 0 1 n))

(define (fib-iter a b p q n)
  (cond ((= n 0) b)
        ((even? n) (fib-iter a
                                 b
                                 (+ (square p) (square q))
                                 (+ (* 2 p q) (square q))
                                 (/ n 2)))
        (else (fib-iter (+ (* b q) (* a q) (* a p))
                         (+ (* b p) (* a q))
                         p
                         q
                         (- n 1)))))
(define (square x)
  (* x x))

 用java来跑一跑:

/**
 * Created by Ramble on 2017/11/22.
 */
public class Fib {
    public static long digui(long n) {
        if (n==0)
            return 0;
        if (n==1)
            return 1;
        else {
            return digui(n-1)+digui(n-2);
        }
    }

    public static long diedai(long n) {
        return diedai_iter(1, 0, n);
    }

    public static long diedai_iter(long a, long b, long count) {
        if (count==0)
            return b;
        else {
            return diedai_iter(a+b, a, count-1);
        }
    }


      public static long fib(long n) {
        return fib_iter(1, 0, 0, 1, n);
      }
      public static long fib_iter(long a,long b, long p,long q, long n) {
          if (n==0) {
              return b;
          }
          if (n%2==0) {
              return fib_iter(a,b,p*p+q*q,2*p*q+q*q, n/2);
          }
          else {
              return fib_iter(b*q+a*q+a*p,b*p+a*q,p,q,n-1);
          }
      }



    public static void main(String[] args) {
        long startTime = System.currentTimeMillis();//获取当前时间
//doSomeThing();   //要运行的java程序

//       System.out.println(digui(50L));
        for (long i=1000; i<5000; i++) {
            for(long j=1000;j<1200;j++) {
                long x = diedai(i);
                long y = diedai(j);
                long xy = x*y;
                System.out.println(xy);
            }
        }
//        程序运行时间：9324ms
//                for (long i=1000; i<5000; i++) {
//            for(long j=1000;j<1200;j++) {
//                long x = fib(i);
//                long y = fib(j);
//                long xy = x*y;
//                System.out.println(xy);
//            }
//        }
        //程序运行时间：4430ms

        long endTime = System.currentTimeMillis();
        System.out.println("程序运行时间："+(endTime-startTime)+"ms");
        //12586269025
    }
}

 经过我拙劣的比较,对数级比线性还是要好很多的.