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: 0int 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rint[] 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 + " ");}
}