import java.util.ArrayList;import java.util.List;import java.util.Map;import java.util.HashMap;public class TSP { private double[][] dArray; //距离矩阵 private int length; //距离矩阵的长度 private int lengthOfLength; //距离矩阵长度字符串的长度 private String allzero = ""; //0组成的字符串 最大值是length个(length - 1)连接起来的字符串，同样最小值是length个0连接起来 private String biggest =""; private List<String> list = new ArrayList<String>(); //城市流列表 private Map<String, Double> store; //存储中间数据 private String notExist = "不存在"; private String firnalRoad = notExist; //最终的路径，即距离矩阵的列号取值 private String firnalCityFlow = ""; //最终形成的城市流 private String min = notExist; //最终求得的最小值 private String allFlowTime = notExist; //求解所有城市流的时间 private String guihuaTime = notExist; //动态规划的时间 /** Creates a new instance of TwentyTwo */ public TSP(double[][] dArray) { if (this.check(dArray)) { this.dArray = dArray; this.length = dArray.length; this.lengthOfLength = (length - 1 + "").length(); for (int zeroLength = 0; zeroLength < (length * lengthOfLength);) { allzero += 0; zeroLength = allzero.length(); } for(int i = this.length; i > 0; i--){ this.biggest += this.toLengthOfLength(i - 1); } long start = System.currentTimeMillis(); this.allFlow(); long end = System.currentTimeMillis(); this.allFlowTime = end - start + "毫秒"; start = System.currentTimeMillis(); this.initstoreMap(); this.guihua(this.length - 2); end = System.currentTimeMillis(); this.guihuaTime = end - start + "毫秒"; } } public String getFirnalRoad() { return this.firnalRoad; } public String getFirnalCityFlow() { if ("".equals(this.firnalCityFlow)) { return this.notExist; } return this.firnalCityFlow; } public String getMin() { return this.min; } public String getAllFlowTime() { return this.allFlowTime; } public String getGuihuaTime() { return this.guihuaTime; } //输入距离矩阵的有效性判读 private boolean check(double[][] dArray) { if (dArray.length < 3) { System.out.println("错误信息：距离矩阵长度过小"); return false; } for (int i = 0; i < dArray.length; i++) { // 每个double[]的长度都进行判断 if (dArray.length != dArray[i].length) { System.out.println("错误信息：距离数组长度不合法"); return false; } } for (int i = 0; i < dArray.length; i++) { if (!oneZero(dArray[i], i)) { System.out.println("错误信息：距离数组顺序或元素值设置不合法"); return false; } } return true; } //对于一个doulbe类型的数组，只有第i个元素为0的判断 private boolean oneZero(double[] dArray, int i) { int numOfZero = 0; for (double d : dArray) { if (d == 0.0) { numOfZero++; } } if (numOfZero == 1 && (dArray[i] == 0)) { return true; } else { return false; } } //判断一个城市流是否合法 private boolean oneFlow(String str) { //将一个字符串更改为一个字符链表 List<String> listString = new ArrayList<String>(); for (int i = 0; i < (this.length * this.lengthOfLength);) { listString.add(str.substring(i, i + this.lengthOfLength)); i += this.lengthOfLength; } //如果有相同的元素，则false for (int i = 0; i < (this.length - 1); i++) { for (int j = i + 1; j < this.length; j++) { if (listString.get(i * this.lengthOfLength).equals(listString.get(j * this.lengthOfLength))) { return false; } } } //如果有距离矩阵全0对角线上的元素，则false for (int i = 0; i < listString.size(); i++) { if (Integer.parseInt(listString.get(i)) == i) { return false; } } //排除没有遍历所有城市的情况（从0点出发到达0点） Map<Integer, Integer> map = new HashMap<Integer, Integer>(); for (int i = 0; i < this.length;) { map.put(i, Integer.parseInt(str.substring(i, i + this.lengthOfLength))); i += this.lengthOfLength; } int allcity = 0; for (int i = 0;;) { i = map.get(i); allcity++; if (i == 0) { break; } } if (allcity < this.length) { return false; } return true; } //初始化存储map private void initstoreMap() { this.store = new HashMap<String, Double>(); //存距离矩阵最后一行可能的列号 for (int i = 0; i < this.length - 1; i++) { this.store.put(this.toLengthOfLength(i), this.dArray[this.length - 1][i]); } //存距离矩阵倒数两行可能的列号 for (int i = 0; i < this.length; i++) { if(i == this.length -2) continue; for (int j = 0; j < this.length - 1; j++) { if (i == j) { continue; } store.put(this.toLengthOfLength(i) + this.toLengthOfLength(j), this.dArray[this.length - 2][i] + store.get(this.toLengthOfLength(j))); } } } //两个相近的城市流，前length - 2 - temp个数相同，后面不同，用动态规划实现 private void guihua(int temp) { if (list.size() == 1) { this.firnalRoad = list.get(0); this.thePrint(list.get(0)); this.min = this.store.get(list.get(0)) + ""; return; } for (int i = 0; i < (list.size() - 1); i++) { int next = (i + 1); if (list.get(i).substring(0, temp * this.lengthOfLength).equals(list.get(next).substring(0, temp * this.lengthOfLength))) { double iValue = 0; double nextValue = 0; iValue = this.dArray[temp][Integer.parseInt(list.get(i).substring(temp, temp + this.lengthOfLength))] + store.get(list.get(i).substring((temp + 1) * this.lengthOfLength)); nextValue = this.dArray[temp][Integer.parseInt(list.get(next).substring(temp, temp + this.lengthOfLength))] + store.get(list.get(next).substring((temp + 1) * this.lengthOfLength)); this.store.put(list.get(i).substring(temp * this.lengthOfLength), iValue); this.store.put(list.get(next).substring(temp * this.lengthOfLength), nextValue); if (iValue >= nextValue) { list.remove(i); } else { list.remove(next); } i--; } } this.guihua(temp - 1); } //组成所有的城市流 private void allFlow() { while (!this.biggest.equals(this.allzero)) { this.allzero = this.addone(this.allzero); if (this.oneFlow(this.allzero)) { this.list.add(this.allzero); } } } //将length进制的字符串加1操作 private String addone(String str) { List<String> listString = new ArrayList<String>(); for (int i = 0; i < (this.length * this.lengthOfLength);) { listString.add(str.substring(i, i + this.lengthOfLength)); i += this.lengthOfLength; } for (int i = (length - 1); i > -1; i--) { int last = Integer.parseInt(listString.get(i)); if (last == (length - 1)) { last = 0; String strLast = this.toLengthOfLength(last); listString.set(i, strLast); } else { last++; String strLast = this.toLengthOfLength(last); listString.set(i, strLast); break; } } String ret = ""; for (String s : listString) { ret += s; } return ret; } //如果一个int字符串长度不够lengthOfLength 则补足 private String toLengthOfLength(Object i) { String returnString = i.toString(); while (returnString.length() < this.lengthOfLength) { returnString = (0 + returnString); } return returnString; } //将一个字符串键值映射，并标准输出 private void thePrint(String str) { Map<Integer, Integer> map = new HashMap<Integer, Integer>(); for (int i = 0; i < this.length;) { map.put(i, Integer.parseInt(str.substring(i, i + this.lengthOfLength))); i += this.lengthOfLength; } String cityFlow = this.toLengthOfLength(0); for (int i = 0;;) { i = map.get(i); cityFlow += this.toLengthOfLength(i); if (i == 0) { break; } } for (int i = 0; i < this.length + 1;) { if (i < (this.length)) { this.firnalCityFlow += Integer.parseInt(cityFlow.substring(i, i + this.lengthOfLength)) + "->"; } else { this.firnalCityFlow += Integer.parseInt(cityFlow.substring(i, i + this.lengthOfLength)); } i += this.lengthOfLength; } } public static void main(String[] args) { double[][] first = {//各个节点之间路径长度的二维数组 {0, 2, 1, 3, 4, 5, 5, 6}, {1, 0, 4, 4, 2, 5, 5, 6}, {5, 4, 0, 2, 2, 6, 5, 6}, {5, 2, 2, 0, 3, 2, 5, 6}, {4, 2, 4, 2, 0, 3, 5, 6}, {4, 2, 4, 2, 3, 0, 5, 6}, {4, 2, 4, 2, 4, 3, 0, 6}, {4, 2, 4, 2, 8, 3, 5, 0}}; long start = System.currentTimeMillis(); TSP ff = new TSP(first); System.out.println("路径是：" + ff.getFirnalRoad()); System.out.println("城市顺序：" + ff.getFirnalCityFlow()); System.out.println("最小值：" + ff.getMin()); System.out.println("生成所有合法城市流用时：" + ff.getAllFlowTime()); System.out.println("动态规划求解过程用时：" + ff.getGuihuaTime()); }}
