動態規劃之零件加工

• 動態規劃
• 有n個工件，j1, j2, …, jn, 每個工件有一個給定的最小加工時間pj , 以及一個權重wj
  1 j n。有一個用來加工這些工件的機器。假設這個機器一次可以加工任意多的工件，　同時加工的工件組成一個批Ｂ。
  在同一批B里加工的工件必須同時開始，同時結束，即它們有同樣的開始時間sj, 同樣的結束時間Ｃj = sj + p(B)jB，
  這裏 。 從一批工件開始加工到結束中間不允許中斷。
  請問：如何給這些工件分批，以及如何對這些批進行排序使得所有工件的加權完成時間之和最小。
  這是代碼：
  用三個一維數組來記錄，分別爲 前i個點的完成時間:finish[i],前i個點的總權重result[i], 第i個點的前一批的最後一個，用於分批

ps:代碼和註釋感覺挺清楚了，如果還有疑問，請在底下留言

public class Fifth {
    //time;
int a[]={1,5,2,4,5,9,5,10,5,6,6,7,8,7,11,6,6,7,11,10,7,12,8,8,8,6,5,13,14,9,8,
        9,3,3,11,2,9,13,4,6,4,4,8,9,6,15,5,7,9,3};
 //value
int b[]={2,3,2,5,4,4,6,8,5,7,7,4,6,9,12,4,
        4,3,5,5,3,6,9,5,9,12,3,7,12,11,11,3,4,5,3,12,
        2,6,6,4,9,15,12,4,8,31,1,12,3,4};
static int [][] res;
static int [][] fin;
static int [][] pre; 
Workpiece all[];
void Create() {
    all=new Workpiece[50];
    res =new int[all.length][all.length]; //記錄權重結果
    fin = new int[all.length][all.length];//每個工件的完成時間
    pre=new int [all.length][all.length];//每個工件前一個的時間
    for (int i = 0; i < a.length; i++) {
        all[i]=new Workpiece();
       all[i].setTime(a[i]);
       all[i].setWeight(b[i]);
       all[i].setFinish(0);
    }
    for (int i = 0; i < all.length; i++) {
        int sum=0;
        Workpiece temp=new Workpiece();
        temp.setTime(100);
        for (int j = i; j < all.length; j++) {
            if (all[j].getTime()<temp.getTime()) {
                temp=all[j];
                sum=j;
            }
        }
        Workpiece temps=new Workpiece();
          temps=all[i];
        all[i]=all[sum];
        all[sum]=temps;
    }
}
void cal() {
    //前一個的標號
    int index[]=new int [50];
    //all數組有每個工件的時間.finsh爲每個工件的完成時間
    int finish[]=new int [50];
    int result[]=new int [50];//每一步的最優結果
    for (int i = 0; i < finish.length; i++) {
        index[i]=0;
        finish[i]=0;
       result[i]=0;
    }
    finish[0]=all[0].getTime();
    index[0]=0;
    result[0]=all[0].getTime()*all[0].getWeight();
    //從一開始更新並記錄
for (int i = 1; i < result.length; i++) {
    //最後一個和之前的分開的時間
     result[i]=(finish[i-1]+all[i].getTime())*(all[i].getWeight())+result[i-1];
     finish[i]=finish[i-1]+all[i].getTime();
     index[i]=i-1;
     //逐漸合併更新
     int all_weight=all[i].getWeight();
     for (int j = i-1; j>0; j--) {
         all_weight+=all[j].getWeight();
        int results=(finish[j-1]+all[i].getTime())*(all_weight)+result[j-1];
        //成功和j合併
        if (results<result[i]) {
            result[i]=results;
            index[i]=j-1;
            //index[j]=j-1;
            //更新合併後的合併點的finish時間
            for (int k = j; k <=i; k++) {
                finish[k]=finish[j-1]+all[i].getTime();
            }
        }
    }
//      和0合併
        int result_0=(all_weight+all[0].getWeight())*all[i].getTime();
        if (result_0<result[i]) {
            index[i]=0;
            result[i]=result_0;
            finish[i]=all[i].getTime();
            for (int j_2 = 0; j_2 <i; j_2++) {
                finish[j_2]=all[i].getTime();
            }
        }
}   
for (int k = 0; k < result.length; k++) {
    System.out.print(finish[k]+" ");
}
System.out.println();
for (int i = 0; i < result.length; i++) {
    //System.out.print(index[i]+" ");
    System.out.print(result[i]+" ");
}
}
class Workpiece{
    public int getFinish() {
        return finish;
    }
    public void setFinish(int finish) {
        this.finish = finish;
    }
    public int getWeight() {
        return weight;
    }
    public void setWeight(int weight) {
        this.weight = weight;
    }
    public int getTime() {
        return time;
    }
    public void setTime(int time) {
        this.time = time;
    }
    int weight;
    int time; 
    int finish;//完成時間
}
public static void main(String[] args) {
    Fifth aFifth=new Fifth();
    aFifth.Create();
    aFifth.cal();
}
}