被dynamic programming震慑到了

当年学习算法的时候 也没认真去实践dynamic programming. 今日一试,被震慑了. 不废话, 上代码, 比performance.

import java.util.TreeMap;/** * @author andrewMay 9, 2011 */public class Fib {private static TreeMap<Integer,Integer> m=new TreeMap<Integer, Integer>();public static int naiveFib(int n){if(n==1 || n==2) {return 1;}else{return naiveFib(n-1)+naiveFib(n-2);}}public static int dynamicFib(int n){if(n==1 || n==2){return 1;}else{if(m.containsKey(n)) {return m.get(n);}else{int tmp=dynamicFib(n-1)+dynamicFib(n-2);m.put(n, tmp);return tmp;}}}/** * @param args */public static void main(String[] args) {// TODO Auto-generated method stubif(args.length>0){int n=Integer.parseInt(args[0]);if(Integer.parseInt(args[1])==0){System.out.println(naiveFib(n));}else if(Integer.parseInt(args[1])==1){System.out.println(dynamicFib(n));}else{System.out.println("usage: Fib input choice(0 for naive, 1 for dynamic)");}}}}

 

为了防止桟溢出, 试了个fib 50

结果 naive 跑了40s, 而dynamic的只用0.2s.

 

分析:

Wiki上讲dynamic programming applicable的条件有两:

(1) optimal substructure

(2) overlapping subproblems (Fib就是个完美的例子涅)

 

naive算法:

Fib(n) : 被call 1次

Fib(n-1): 2

Fib(n-2): 3

....

Fib(2): Fib(n-1)

Fib(1): Fib(n)

So 总共递归调用了 Fib(1)+Fib(2)+...+Fib(n)次Fib 方法

 

而dynamic的却是linear的... 强大!