一、上机目的

1、通过分支限界法的示例程序进一步理解分支限界法的基本思想；
2、运用分支限界法解决实际问题，进一步加深对分支限界法的理解和运用

二、上机内容与要求

1、分析并掌握“单源最短路径” 问题的分支限界法求解方法；
2、练习使用分支限界法求解“装载”问题；

三、上机步骤

1．理解分支限界法思想和算法示例；
2．上机输入和调试算法示例程序；
3．理解实验题的问题要求；
4．上机输入和调试自己所编的实验题程序；
5．验证并分析实验题的实验结果；
6．整理出实验报告；

四、上机结果

1、将课本6.2节单源最短路径算法改为程序，并进行测试和验证

import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;

class ArcCell {
    int adj;  // 保存权值
    int info; // 存储最短路径长度
}

public class GraphPath {

    static ArcCell[][] AdjMatrix = new ArcCell[100][100];
    static VerType[] vexs = new VerType[100];
    static int vexnum;
    static int arcnum;
    static Queue<Integer> q = new LinkedList<>();

    static class VerType {
        int data;
        int length;
    }

    static void CreateGraph() {
        Scanner scanner = new Scanner(System.in);
        int m, n, t;
        System.out.print("输入顶点数和弧数:");
        vexnum = scanner.nextInt();
        arcnum = scanner.nextInt();
        System.out.print("输入顶点:");
        for (int i = 1; i <= vexnum; i++) {
            vexs[i] = new VerType();
            vexs[i].data = scanner.nextInt();
            vexs[i].length = 10000;
        }

        for (int i = 1; i <= vexnum; i++)
            for (int j = 1; j <= vexnum; j++) {
                AdjMatrix[i][j] = new ArcCell();
                AdjMatrix[i][j].adj = 0;
            }

        System.out.println("输入弧及权重:");
        for (int i = 1; i <= arcnum; i++) {
            m = scanner.nextInt();
            n = scanner.nextInt();
            t = scanner.nextInt();
            AdjMatrix[m][n].adj = 1;
            AdjMatrix[m][n].info = t;
        }
    }

    static int NextAdj(int v, int w) {
        for (int i = w + 1; i <= vexnum; i++)
            if (AdjMatrix[v][i].adj != 0)
                return i;
        return 0; // not found;
    }

    static void ShortestPaths(int v) {
        int k = 0; // 从首个节点开始访问
        int t;
        vexs[v].length = 0;
        q.offer(vexs[v].data);
        while (!q.isEmpty()) {
            t = q.poll();
            k = NextAdj(t, k);
            while (k != 0) {
                if (vexs[t].length + AdjMatrix[t][k].info <= vexs[k].length) {
                    vexs[k].length = vexs[t].length + AdjMatrix[t][k].info;
                    q.offer(vexs[k].data);
                }
                k = NextAdj(t, k);
            }
        }
    }

    static void Print() {
        for (int i = 1; i <= vexnum; i++)
            System.out.println(vexs[i].data + "------" + vexs[i].length);
    }

    public static void main(String[] args) {
        CreateGraph();
        ShortestPaths(1);
        Print();
    }
}

2、将课本6.3节装载问题改为程序，并进行测试和验证。

import java.util.PriorityQueue;
import java.util.Scanner;

class MaxHeapQNode {
    MaxHeapQNode parent;  // 父节点
    int lchild;           // 左节点: 1; 右节点: 0
    int weight;           // 总重量
    int lev;              // 层次
}

class MaxLoading {
    static int n;
    static int c;
    static int bestw;
    static int[] w;
    static int[] bestx;

    public static void main(String[] args) {
        InPut();
        MaxLoading();
        OutPut();
    }

    static void InPut() {
        Scanner scanner = new Scanner(System.in);
        System.out.println("Input1:");
        n = scanner.nextInt();
        System.out.println("Input2:");
        c = scanner.nextInt();
        System.out.println("Input3:");
        w = new int[n + 1];
        bestx = new int[n + 1];
        for (int i = 1; i <= n; ++i)
            w[i] = scanner.nextInt();
    }

    static void AddAliveNode(PriorityQueue<MaxHeapQNode> q, MaxHeapQNode E, int wt, int i, int ch) {
        MaxHeapQNode p = new MaxHeapQNode();
        p.parent = E;
        p.lchild = ch;
        p.weight = wt;
        p.lev = i + 1;
        q.add(p);
    }

    static void MaxLoading() {
        PriorityQueue<MaxHeapQNode> q = new PriorityQueue<>((a, b) -> Integer.compare(b.weight, a.weight));
        // 定义剩余重量数组r
        int[] r = new int[n + 1];
        r[n] = 0;
        for (int j = n - 1; j > 0; --j)
            r[j] = r[j + 1] + w[j + 1];
        int i = 1;
        MaxHeapQNode E = new MaxHeapQNode();
        int Ew = 0;
        while (i != n + 1) {
            if (Ew + w[i] <= c) {
                AddAliveNode(q, E, Ew + w[i] + r[i], i, 1);
            }
            AddAliveNode(q, E, Ew + r[i], i, 0);

            // 取下一节点
            E = q.poll();
            i = E.lev;
            Ew = E.weight - r[i - 1];
        }
        bestw = Ew;
        for (int j = n; j > 0; --j) {
            bestx[j] = E.lchild;
            E = E.parent;
        }
    }

    static void OutPut() {
        System.out.println("最优装载量为 " + bestw);
        System.out.println("装载的物品为 ");
        for (int i = 1; i <= n; ++i)
            if (bestx[i] == 1)
                System.out.print(i + " ");
    }
}