问题描述：给定一个钢条的长度，求最大效益和切割方法
长度和价格的关系如下：
length  1  2  3  4  5  6  7  8  9  10
price   1  5  8  9  10 17 17 20 24 30
package com.dynamic;

public class CutRod {
  private int []price;
  private int length;
  private int []r;
  private int []s;
  public CutRod(int []price){
    this.price=price;
  }
  /**
   *自顶向下递归 
   * @param length
   * @return
   */
  public int momoizedCutRod(int length){
    r=new int[length+1];
    for(int i=0;i<=length;i++){
      r[i]=-1;
    }
    return memoizedCutRodAux(length,r);
  }
  private int memoizedCutRodAux(int length,int []r){
    if(r[length]>=0){
      return r[length];
    }
    int q;
    if(length==0){
      q=0;
    }else{
      if(length>=price.length){
        q=price[price.length-1];
      }else{
        q=price[length];
      }
      if(length>price.length){
        for(int i=1;i<=price.length-1;i++){
          q=Math.max(q, price[i]+memoizedCutRodAux(length-i,r));
        }
      }else{
        for(int i=1;i<=length-1;i++){
          q=Math.max(q, price[i]+memoizedCutRodAux(length-i,r));
        }
      }
    }
    r[length]=q;
    return q;
  }
  
  public int bottomUpCutRod(int length){
    r=new int[length+1];
    r[0]=0;
    for(int j=1;j<=length;j++){
      int q=0;
      if(j>=price.length){
        q=price[price.length-1];
      }else{
        q=price[j];
      }
      for(int i=1;i<=j;i++){
        q=Math.max(q, price[i]+r[j-i]);
      }
      r[j]=q;
      
    }
    return r[length];
  }
  
  public int extendBottomUpCutRod(int length){
    r=new int[length+1];
    s=new int[length+1];
    r[0]=0;
    for(int j=1;j<=length;j++){
      int q=0;
      if(j>=price.length){
        q=price[price.length-1];
      }else{
        q=price[j];
      }
      for(int i=1;i<=j;i++){
        if(q<=price[i]+r[j-i]){
          q=price[i]+r[j-i];
          s[j]=i;
        }
      }
      r[j]=q;
      
    }
    return r[length];
  }
  
  public void printSolution(int length){
    extendBottomUpCutRod(length);
    int n=length;
    while(n>0){
      System.out.print(s[n]+" ");
      n=n-s[n];
    }
    System.out.println();
  }
  
  public static void main(String[] args) {
    int []price=new int[]{0,1,5,8,9,10,17,17,20,24,30};
    CutRod cut=new CutRod(price);
    System.out.println(cut.extendBottomUpCutRod(3));
    cut.printSolution(3);
    System.out.println(cut.extendBottomUpCutRod(4));
    cut.printSolution(4);
    System.out.println(cut.extendBottomUpCutRod(5));
    cut.printSolution(5);
    System.out.println(cut.extendBottomUpCutRod(10));
    cut.printSolution(10);
    System.out.println("===========");
    System.out.println(cut.bottomUpCutRod(5));
    System.out.println("===========");
    System.out.println(cut.momoizedCutRod(4));
  }

}