动态规划算法的java实现

一：动态规划

1）动态规划的向前处理法

java中没有指针，所以邻接表的存储需要转化一中形式，用数组存储邻接表

用三个数组u,v,w存储边，u数组代表起点，v数组代表终点，w代表权值;例如：1-->2 权值为9 存为：u[i]=1,v[i]=2,w[i]=9,如果该边为第一条边则i=1;

　

 package dynamicProgramming;

 public class FGRAPH {

     public static void main(String[] args) {
         // TODO Auto-generated method stub
         int i;
         int first[],next[];
         int n=12;
         int m=21;
         int[] u={0,1,1,1,1,2,2,2,3,3,4,5,5,6,6,7,7,8,8,9,10,11};
         int[] v={0,2,3,4,5,6,7,8,6,7,8,7,8,9,10,9,10,10,11,12,12,12};
         int[] w={0,9,7,3,2,4,2,1,2,7,11,11,8,6,5,4,3,5,6,4,2,5};
         first=new int[n+2];
         next=new int[m+1];
         for(i=1;i<n+2;i++)
             first[i]=-1;
         for(i=1;i<m+1;i++){
             next[i]=first[u[i]];
             first[u[i]]=i;
             System.out.println(i+" u,v,w: "+u[i]+" "+v[i]+"  "+w[i]);
         }
         //遍历
         int k;
         int[] cost=new int[n+1];
         int[] d=new int[n+1];
         for(i=1;i<n+1;i++){
             cost[i]=9999;
             d[i]=-1;
         }
         cost[n]=0;
         for(i=n-1;i>0;i--){
             k=first[i];
             while(k!=-1){
                 //System.out.println(u[k]+" "+v[k]+" "+w[k]);
                 if(w[k]+cost[v[k]]<cost[u[k]]){
                     cost[u[k]]=w[k]+cost[v[k]];
                     d[u[k]]=v[k];
                 }
                 k=next[k];
             }
         }
         i=1;
         System.out.println();
         System.out.print("1");
         while(d[i]!=-1){
             System.out.print("->"+d[i]);
             d[i]=d[d[i]];
         }
         System.out.println("    cost[1]:"+cost[1]);
     }

 }

2)动态规划的向后处理法

 package dynamicProgramming;

 public class BGRAPH {

     public static void main(String[] args) {
         // TODO Auto-generated method stub
         int i;
         int first[],next[];
         int n=12;
         int m=21;
         int[] u={0,1,1,1,1,2,2,2,3,3,4,5,5,6,6,7,7,8,8,9,10,11};
         int[] v={0,2,3,4,5,6,7,8,6,7,8,7,8,9,10,9,10,10,11,12,12,12};
         int[] w={0,9,7,3,2,4,2,1,2,7,11,11,8,6,5,4,3,5,6,4,2,5};
         first=new int[n+1];
         next=new int[m+1];
         for(i=1;i<n+1;i++)
             first[i]=-1;
         for(i=1;i<m+1;i++){
             next[i]=first[u[i]];
             first[u[i]]=i;
             System.out.println(i+" u,v,w: "+u[i]+" "+v[i]+"  "+w[i]);
         }
         //遍历
         int k;
         int[] cost=new int[n+1];
         int[] d=new int[n+1];
         for(i=1;i<n+1;i++){
             cost[i]=9999;
             d[i]=-1;
         }
         cost[1]=0;
         for(i=1;i<n+1;i++){
             k=first[i];
             while(k!=-1){
                 if(w[k]+cost[u[k]]<cost[v[k]]){
                     cost[v[k]]=w[k]+cost[u[k]];
                     d[v[k]]=u[k];
                 }
                 k=next[k];
             }
         }
         i=12;
         System.out.println();
         System.out.print("12");
         while(d[i]!=-1){
             System.out.print(" <-- "+d[i]);
             d[i]=d[d[i]];
         }
         System.out.println("    cost[1]:"+cost[12]);
     }

 }