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]);
    }

}