36.1 相当于图的压缩存储. 每一行数据用一个单链表存储。
36.2 重写了广度优先遍历. 可以发现, 使用队列的机制不变. 仅仅是把其中的 for 循环换成了 while, 避免检查不存在的边. 如果图很稀疏的话, 可以降低时间复杂度。
36.3 深度优先遍历可以当作作业, 这里不写了。
代码：
package 日撸Java300行_31_40;
public class AdjacencyList {
class AdjacencyNode {
int column;
AdjacencyNode next;
public AdjacencyNode(int paraColumn) {
column = paraColumn;
next = null;
} // Of AdjacencyNode
} // Of class AdjacencyNode
int numNodes;
AdjacencyNode[] headers;
public AdjacencyList(int[][] paraMatrix) {
numNodes = paraMatrix.length;
// Step 1. Initialize. The data in the headers are not meaningful.
AdjacencyNode tempPreviousNode, tempNode;
headers = new AdjacencyNode[numNodes];
for (int i = 0; i < numNodes; i++) {
headers[i] = new AdjacencyNode(-1);
tempPreviousNode = headers[i];
for (int j = 0; j < numNodes; j++) {
if (paraMatrix[i][j] == 0) {
continue;
} // Of if
// Create a new node.
tempNode = new AdjacencyNode(j);
//Link
tempPreviousNode.next = tempNode;
tempPreviousNode = tempNode;
} // Of for j
} // Of for i
} // Of class AdjacenTable
public String toString() {
String resultString = "";
AdjacencyNode tempNode;
for (int i = 0; i < numNodes; i++) {
tempNode = headers[i].next;
while (tempNode != null) {
resultString += " (" + i + ", " + tempNode.column + ")";
tempNode = tempNode.next;
} // Of while
resultString += "rn";
} // Of for i
return resultString;
} // Of toString
public String breadthFirstTraversal(int paraStartIndex) {
CircleObjectQueue tempQueue = new CircleObjectQueue();
String resultString = "";
boolean[] tempVisitedArray = new boolean[numNodes];
tempVisitedArray[paraStartIndex] = true;
// Initialize the queque.
// Visit before enqueue.
tempVisitedArray[paraStartIndex] = true;
resultString += paraStartIndex;
tempQueue.enqueue(new Integer(paraStartIndex));
// Now visit the rest of the graph.
int tempIndex;
Integer tempInteger = (Integer)tempQueue.dequeue();
AdjacencyNode tempNode;
while (tempInteger != null) {
tempIndex = tempInteger.intValue();
// Enqueue all its unvisited neighbors. The neighbor are linked
// already.
tempNode = headers[tempIndex].next;
while (tempNode != null) {
if (!tempVisitedArray[tempNode.column]) {
// Viisit before enqueue.
tempVisitedArray[tempNode.column] = true;
resultString += tempNode.column;
tempQueue.enqueue(new Integer(tempNode.column));
} // Of if
tempNode = tempNode.next;
} // Of for i
//Take out one from the head.
tempInteger = (Integer) tempQueue.dequeue();
} // Of while
return resultString;
} // Of breadthFirstTraversal
public static void breadthFirstTraversalTest() {
// Test an undirected graph.
int[][] tempMatrix = { { 0, 1, 1, 0 }, { 1, 0, 0, 1 }, { 1, 0, 0, 1}, { 0, 1, 1, 0 } };
Graph tempGraph = new Graph(tempMatrix);
System.out.println(tempGraph);
String tempSequence = "";
try {
tempSequence = tempGraph.breadthFirstTraversal(2);
} catch (Exception ee) {
System.out.println(ee);
} // Of try.
System.out.println("The breadth first order of visit " + tempSequence);
} // Of breadthFirstTraversalTest
public static void main(String[] args) {
int[][] tempMatrix = { { 0, 1, 0 }, { 1, 0, 1 }, { 0, 1, 0} };
AdjacencyList tempTable = new AdjacencyList(tempMatrix);
System.out.println("The data are: rn" + tempTable);
breadthFirstTraversalTest();
}// Of main
} // Of class AdjacencyList
截图：
37 十字链表
37.1 比邻接表难一点点, 毕竟多一个指针域。
37.2 为控制代码量, 只做了建表和 toString。
代码：
package 日撸Java300行_31_40;
public class OrthogonalList {
class OrthogonalNode {
int row;
int column;
OrthogonalNode nextOut;
OrthogonalNode nextIn;
public OrthogonalNode(int paraRow, int paraColumn) {
row = paraRow;
column = paraColumn;
nextOut = null;
nextIn = null;
} // Of OrthogonalNode
}// Of class OrthogonalNode
int numNodes;
OrthogonalNode[] headers;
public OrthogonalList(int[][] paraMatrix) {
numNodes = paraMatrix.length;
// Step 1. Initialize. The data in the headers are not meaningful.
OrthogonalNode tempPreviousNodes,tempNode;
headers = new OrthogonalNode[numNodes];
// Step 2. Link to its out nodes.
for (int i = 0; i < numNodes; i++) {
headers[i] = new OrthogonalNode(i, -1);
tempPreviousNodes = headers[i];
for (int j = 0; j < numNodes; j++) {
if (paraMatrix[i][j] == 0) {
continue;
} // Of if
// Create a new node.
tempNode = new OrthogonalNode(i, j);
// Link.
tempPreviousNodes.nextOut = tempNode;
tempPreviousNodes = tempNode;
} // Of for j
} // Of for i
// Step 3. Link to its in nodes. This step is harder.
OrthogonalNode[] tempColumnNodes = new OrthogonalNode[numNodes];
for (int i = 0; i < numNodes; i++) {
tempColumnNodes[i] = headers[i];
} // Of for i
for (int i = 0; i < numNodes; i++) {
tempNode = headers[i].nextOut;
while (tempNode != null) {
tempColumnNodes[tempNode.column].nextIn = tempNode;
tempColumnNodes[tempNode.column] = tempNode;
tempNode = tempNode.nextOut;
} // Of while
} // Of for i
} // Of the constructor
public String toString() {
String resultString = "Out arcs: ";
OrthogonalNode tempNode;
for (int i = 0; i < numNodes; i++) {
tempNode = headers[i].nextOut;
while (tempNode != null) {
resultString += " (" + tempNode.row + ", " + tempNode.column + ")";
tempNode = tempNode.nextOut;
} // Of while
resultString += "rn";
} // Of for i
resultString += "rnIn arcs:";
for (int i = 0; i < numNodes; i++) {
tempNode = headers[i].nextIn;
while (tempNode !=null) {
resultString += " (" + tempNode.row + ", " + tempNode.column + ")";
tempNode = tempNode.nextIn;
} // Of while
resultString += "rn";
} // Of for i
return resultString;
} // Of toString
public static void main(String[] args) {
int[][] tempMatrix = { { 0, 1, 0, 0 }, { 0, 0, 0, 1 }, { 1, 0, 0, 0}, { 0, 1, 1, 0 } };
OrthogonalList tempList = new OrthogonalList(tempMatrix);
System.out.println("The data ars: rn" + tempList);
} // Of main
} // Of class OrthogonalList
截图：
38 Dijkstra 算法与 Prim 算法
38.1 Dijkstra 算法需要有向图, Prim 算法需要无向图. 代码中也需要更换后者。
38.2 两个算法的结构相同. 不同之处是比较距离的时候, 是用累计的 (Dijkstra) 还是当前边的 (Prim). 建议先写 Dijkstra, 然后拷贝、修改变成 Prim. 到这个阶段, 应该已经具备这样的能力。
代码：
package 日撸Java300行_31_40;
import java.util.Arrays;
public class Net {
public static final int MAX_DISTANCE = 10000;
int numNodes;
IntMatrix weightMatrix;
public Net(int paraNumNodes) {
numNodes = paraNumNodes;
weightMatrix = new IntMatrix(numNodes,numNodes);
for (int i = 0; i < numNodes; i++) {
// For better readability, you may need to write fill() in class
// IntMatrix.
Arrays.fill(weightMatrix.getData()[i], MAX_DISTANCE);
} // Of for i
} // Of the first constructor
public Net(int[][] paraMatrix) {
weightMatrix = new IntMatrix(paraMatrix);
numNodes = weightMatrix.getRows();
} // Of the second constructor
public String toString() {
String resultString = "This is the weight matrix of the graph.rn" + weightMatrix;
return resultString;
} // Of toString
public int[] dijkstra(int paraSource) {
// Step 1. Initialize.
int[] tempDistanceArray = new int[numNodes];
for (int i = 0; i < numNodes; i++) {
tempDistanceArray[i] = weightMatrix.getValue(paraSource, i);
} // Of for i
int[] tempParentArray = new int[numNodes];
Arrays.fill(tempParentArray, paraSource);
// -1 for no parent.
tempParentArray[paraSource] = -1;
// Visited nodes will not be considered further.
boolean[] tempVisitedArray = new boolean[numNodes];
tempVisitedArray[paraSource] = true;
// Step 2. Main loops.
int tempMinDistance;
int tempBestNode = -1;
for (int i = 0; i < numNodes; i++) {
// Step 2.1 Find out the best next node.
tempMinDistance = Integer.MAX_VALUE;
for (int j = 0; j < numNodes; j++) {
// This node is visited.
if (tempVisitedArray[j]) {
continue;
} // Of if
if (tempMinDistance > tempDistanceArray[j]) {
tempMinDistance = tempDistanceArray[j];
tempBestNode = j;
} // Of if
} // Of for j
tempVisitedArray[tempBestNode] = true;
// Step 2.2 Prepare for the next round.
for (int j = 0; j < numNodes; j++) {
//This node is visited.
if (tempVisitedArray[j]) {
continue;
} // Of if
if (tempMinDistance > tempDistanceArray[j]) {
tempMinDistance = tempDistanceArray[j];
tempBestNode = j;
} // Of if
} // Of for j
tempVisitedArray[tempBestNode] = true;
// Step 2.2 Prepare for the next round.
for (int j = 0; j < numNodes; j++) {
// This node is visited.
if (tempVisitedArray[j]) {
continue;
} // Of if
// This node cannot be reached.
if (weightMatrix.getValue(tempBestNode, j) >= MAX_DISTANCE) {
continue;
} // Of if
if (tempDistanceArray[j] > tempDistanceArray[tempBestNode]
+ weightMatrix.getValue(tempBestNode, j)) {
// Change the distance.
tempDistanceArray[j] = tempDistanceArray[tempBestNode]
+ weightMatrix.getValue(tempBestNode, j);
// Change the parent.
tempParentArray[j] = tempBestNode;
} // Of if
} // Of for j
// For test
System.out.println("The distance to each node: " + Arrays.toString(tempDistanceArray));
System.out.println("The parent of each node: " + Arrays.toString(tempParentArray));
} // Of for j
// Step 3. Output for debug.
System.out.println("Finally");
System.out.println("The distance to each node: " + Arrays.toString(tempDistanceArray));
System.out.println("The parent of each node: " + Arrays.toString(tempParentArray));
return tempDistanceArray;
} // Of dijksta
public int prim() {
// Step 1. Initialize.
// Any node can be the source.
int tempSource = 0;
int[] tempDistanceArray = new int[numNodes];
for (int i = 0; i < numNodes; i++) {
tempDistanceArray[i] = weightMatrix.getValue(tempSource, i);
} // Of for i
int[] tempParentArray = new int[numNodes];
Arrays.fill(tempParentArray, tempSource);
// -1 for no parent.
tempParentArray[tempSource] = -1;
// Visited nodes will not be considered further.
boolean[] tempVisitedArray = new boolean[numNodes];
tempVisitedArray[tempSource] =true;
// Step 2. Main loops.
int tempMinDistance;
int tempBestNode = -1;
for (int i = 0; i < numNodes; i++) {
// Step 2.1 Find out the best next node.
tempMinDistance = Integer.MAX_VALUE;
for (int j = 0; j < numNodes; j++) {
// This node is visited.
if (tempVisitedArray[j]) {
continue;
} // Of if
if (tempMinDistance > tempDistanceArray[j]) {
tempMinDistance = tempDistanceArray[j];
tempBestNode = j;
} // Of if
} // Of for j
tempVisitedArray[tempBestNode] = true;
// Step 2.2 Prepare for the next round.
for (int j = 0; j < numNodes; j++) {
// This node is visited.
if (tempVisitedArray[j]) {
continue;
} // Of if
// This node cannot be reached.
if (weightMatrix.getValue(tempBestNode, j) >= MAX_DISTANCE) {
continue;
} // Of if
//Attention the difference from the Dijkstra algorithm.
if (tempDistanceArray[j] > weightMatrix.getValue(tempBestNode, j)) {
// Change the distance.
tempDistanceArray[j] = weightMatrix.getValue(tempBestNode, j);
// Change the parent.
tempParentArray[j] = tempBestNode;
} // Of if
} // Of for j
// For test
System.out.println("The selected disatnce to each node: " + Arrays.toString(tempDistanceArray));
System.out.println("The parent of each node: " + Arrays.toString(tempParentArray));
} // Of for i
int resultCost = 0;
for (int i = 0; i < numNodes; i++) {
resultCost += tempDistanceArray[i];
}
// Step 3. Output for debug.
System.out.println("Finally");
System.out.println("The distance to each node: " + Arrays.toString(tempDistanceArray));
System.out.println("The total cost: " + resultCost);
return resultCost;
} // Of prim
public static void main(String[] args) {
Net tempNet0 = new Net(3);
System.out.println(tempNet0);
int[][] tempMatrix1 = { { 0, 9, 3, 6 }, { 5, 0, 2, 4 }, { 3, 2, 0, 1}, { 2, 8, 7, 0 } };
Net tempNet1 = new Net(tempMatrix1);
System.out.println(tempNet1);
// Dijkstra
tempNet1.dijkstra(1);
// An undirected net is required
int[][] tempMatrix2 = { { 0, 7, MAX_DISTANCE, 5, MAX_DISTANCE }, { 7, 0, 8, 9, 7 },
{ MAX_DISTANCE, 8, 0, MAX_DISTANCE, 5 }, { 5, 9, MAX_DISTANCE, 0, 15 },
{ MAX_DISTANCE, 7, 5, 15, 0 } };
Net tempNet2 = new Net(tempMatrix2);
tempNet2.prim();
} // Of main
} // Of class Net
截图：
