第 34 天: 图的深度优先遍历
- 与二叉树的深度优先遍历类似. 但要难一点.
- while (true)退出条件是栈为空.
- 需要在前面 import ObjectStack.
- 按例子自己理一遍逻辑会清晰很多.
package day30; import day30.IntMatrix; import day20.ObjectStack; import day20.CircleObjectQueue;; public class Graph { IntMatrix connectivityMatrix; public Graph(int paraNumbers) { connectivityMatrix = new IntMatrix(paraNumbers,paraNumbers); }// Of the first constructor public Graph(int[][] paraMatrix) { connectivityMatrix = new IntMatrix(paraMatrix); }// Of the second constructor public String toString() { String resultString = "This is the connectivity matrix of the graph.\r\n" + connectivityMatrix; return resultString; }//Of toString public boolean getConnectivity()throws Exception{ IntMatrix tempConnectivityMatrix = IntMatrix.getIdentityMatrix(connectivityMatrix.getData().length); IntMatrix tempMultipliedMatrix = new IntMatrix(connectivityMatrix); for(int i = 0; i < connectivityMatrix.getData().length - 1; i++) { tempConnectivityMatrix.add(tempMultipliedMatrix); tempMultipliedMatrix = IntMatrix.multiply(tempMultipliedMatrix, connectivityMatrix); }//Of for i System.out.println("The connectivity matrix is: " + tempConnectivityMatrix); int[][] tempData = tempConnectivityMatrix.getData(); for(int i = 0; i < tempData.length; i++) { for(int j = 0; j < tempData.length; j++) { if(tempData[i][j] == 0) { System.out.println("Node " + i + " cannot reach " + j); return false; }// Of if } // Of for j } // Of for i return true; }// Of getConnectivity public static void getConnectivityTest() { int[][] tempMatrix = { { 0, 1, 0 }, { 1, 0, 1 }, { 0, 1, 0 } }; Graph tempGraph2 = new Graph(tempMatrix); System.out.println(tempGraph2); boolean tempConnected = false; try { tempConnected = tempGraph2.getConnectivity(); } catch (Exception ee) { System.out.println(ee); } // Of try System.out.println("Is the graph connected? " + tempConnected); tempGraph2.connectivityMatrix.setValue(1, 0, 0); tempConnected = false; try { tempConnected = tempGraph2.getConnectivity(); } catch (Exception ee) { System.out.println(ee); }//Of try System.out.println("Is the graph connected? " + tempConnected); }// Of getConnectivityTest public String breadthFirstTraversal(int paraStartIndex) { CircleObjectQueue tempQueue = new CircleObjectQueue(); String resultString = ""; int tempNumNodes = connectivityMatrix.getRows(); boolean[] tempVisitedArray = new boolean[tempNumNodes]; tempVisitedArray[paraStartIndex] = true; resultString += paraStartIndex; tempQueue.enqueue(new Integer(paraStartIndex)); int tempIndex; Integer tempInteger = (Integer)tempQueue.dequeue(); while (tempInteger != null) { tempIndex = tempInteger.intValue(); for(int i = 0; i < tempNumNodes; i++) { if(tempVisitedArray[i]) { continue; }//Of if if(connectivityMatrix.getData()[tempIndex][i] == 0) { continue; }//Of if tempVisitedArray[i] = true; resultString += i; tempQueue.enqueue(new Integer(i)); }//Of for i tempInteger = (Integer)tempQueue.dequeue(); }//Of while return resultString; }//Of breadthFirstTraversal public static void breadthFirstTraversalTest() { 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 String depthFirstTraversal(int paraStartIndex) { ObjectStack tempStack = new ObjectStack(); String resultString = ""; int tempNumNodes = connectivityMatrix.getRows(); boolean[] tempVisitedArray = new boolean[tempNumNodes]; tempVisitedArray[paraStartIndex] = true; resultString += paraStartIndex; tempStack.push(new Integer(paraStartIndex)); System.out.println("Push " + paraStartIndex); System.out.println("Visited " + resultString); int tempIndex = paraStartIndex; int tempNext; Integer tempInteger; while(true) { tempNext = -1; for(int i = 0; i < tempNumNodes; i++) { if(tempVisitedArray[i]) { continue; //Already visited. }//Of if if (connectivityMatrix.getData()[tempIndex][i] == 0) { continue; //Not directly connected. }//Of if tempVisitedArray[i] = true; resultString += i; tempStack.push(new Integer(i)); System.out.println("Push " + i); tempNext = i; break; }//Of for i if(tempNext == -1) { tempInteger = (Integer) tempStack.pop(); System.out.println("Pop " + tempInteger); if (tempStack.isEmpty()) { break; }else { tempInteger = (Integer) tempStack.pop(); tempIndex = tempInteger.intValue(); tempStack.push(tempInteger); }// Of if } else { tempIndex = tempNext; } // Of if }//Of while return resultString; }//Of depthFirstTraversal public static void depthFirstTraversalTest() { // Test an undirected graph. int[][] tempMatrix = { { 0, 1, 1, 0 }, { 1, 0, 0, 1 }, { 1, 0, 0, 0}, { 0, 1, 0, 0} }; Graph tempGraph = new Graph(tempMatrix); System.out.println(tempGraph); String tempSequence = ""; try { tempSequence = tempGraph.depthFirstTraversal(0); } catch (Exception ee) { System.out.println(ee); } // Of try. System.out.println("The depth first order of visit: " + tempSequence); }//Of depthFirstTraversalTest public static void main(String[] args) { System.out.println("Hello!"); Graph tempGraph = new Graph(3); System.out.println(tempGraph); getConnectivityTest(); breadthFirstTraversalTest(); depthFirstTraversalTest(); }//Of main }// Of class Graph运行截图：
35 天: 图的 m 着色问题
package day30;
import day30.IntMatrix;
import day20.ObjectStack;
import java.util.Arrays;
import day20.CircleObjectQueue;;
public class Graph {
IntMatrix connectivityMatrix;
public Graph(int paraNumbers) {
connectivityMatrix = new IntMatrix(paraNumbers,paraNumbers);
}// Of the first constructor
public Graph(int[][] paraMatrix) {
connectivityMatrix = new IntMatrix(paraMatrix);
}// Of the second constructor
public String toString() {
String resultString = "This is the connectivity matrix of the graph.\r\n" + connectivityMatrix;
return resultString;
}//Of toString
public boolean getConnectivity()throws Exception{
IntMatrix tempConnectivityMatrix = IntMatrix.getIdentityMatrix(connectivityMatrix.getData().length);
IntMatrix tempMultipliedMatrix = new IntMatrix(connectivityMatrix);
for(int i = 0; i < connectivityMatrix.getData().length - 1; i++) {
tempConnectivityMatrix.add(tempMultipliedMatrix);
tempMultipliedMatrix = IntMatrix.multiply(tempMultipliedMatrix, connectivityMatrix);
}//Of for i
System.out.println("The connectivity matrix is: " + tempConnectivityMatrix);
int[][] tempData = tempConnectivityMatrix.getData();
for(int i = 0; i < tempData.length; i++) {
for(int j = 0; j < tempData.length; j++) {
if(tempData[i][j] == 0) {
System.out.println("Node " + i + " cannot reach " + j);
return false;
}// Of if
} // Of for j
} // Of for i
return true;
}// Of getConnectivity
public static void getConnectivityTest() {
int[][] tempMatrix = { { 0, 1, 0 }, { 1, 0, 1 }, { 0, 1, 0 } };
Graph tempGraph2 = new Graph(tempMatrix);
System.out.println(tempGraph2);
boolean tempConnected = false;
try {
tempConnected = tempGraph2.getConnectivity();
} catch (Exception ee) {
System.out.println(ee);
} // Of try
System.out.println("Is the graph connected? " + tempConnected);
tempGraph2.connectivityMatrix.setValue(1, 0, 0);
tempConnected = false;
try {
tempConnected = tempGraph2.getConnectivity();
} catch (Exception ee) {
System.out.println(ee);
}//Of try
System.out.println("Is the graph connected? " + tempConnected);
}// Of getConnectivityTest
public String breadthFirstTraversal(int paraStartIndex) {
CircleObjectQueue tempQueue = new CircleObjectQueue();
String resultString = "";
int tempNumNodes = connectivityMatrix.getRows();
boolean[] tempVisitedArray = new boolean[tempNumNodes];
tempVisitedArray[paraStartIndex] = true;
resultString += paraStartIndex;
tempQueue.enqueue(new Integer(paraStartIndex));
int tempIndex;
Integer tempInteger = (Integer)tempQueue.dequeue();
while (tempInteger != null) {
tempIndex = tempInteger.intValue();
for(int i = 0; i < tempNumNodes; i++) {
if(tempVisitedArray[i]) {
continue;
}//Of if
if(connectivityMatrix.getData()[tempIndex][i] == 0) {
continue;
}//Of if
tempVisitedArray[i] = true;
resultString += i;
tempQueue.enqueue(new Integer(i));
}//Of for i
tempInteger = (Integer)tempQueue.dequeue();
}//Of while
return resultString;
}//Of breadthFirstTraversal
public static void breadthFirstTraversalTest() {
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 String depthFirstTraversal(int paraStartIndex) {
ObjectStack tempStack = new ObjectStack();
String resultString = "";
int tempNumNodes = connectivityMatrix.getRows();
boolean[] tempVisitedArray = new boolean[tempNumNodes];
tempVisitedArray[paraStartIndex] = true;
resultString += paraStartIndex;
tempStack.push(new Integer(paraStartIndex));
System.out.println("Push " + paraStartIndex);
System.out.println("Visited " + resultString);
int tempIndex = paraStartIndex;
int tempNext;
Integer tempInteger;
while(true) {
tempNext = -1;
for(int i = 0; i < tempNumNodes; i++) {
if(tempVisitedArray[i]) {
continue; //Already visited.
}//Of if
if (connectivityMatrix.getData()[tempIndex][i] == 0) {
continue; //Not directly connected.
}//Of if
tempVisitedArray[i] = true;
resultString += i;
tempStack.push(new Integer(i));
System.out.println("Push " + i);
tempNext = i;
break;
}//Of for i
if(tempNext == -1) {
tempInteger = (Integer) tempStack.pop();
System.out.println("Pop " + tempInteger);
if (tempStack.isEmpty()) {
break;
}else {
tempInteger = (Integer) tempStack.pop();
tempIndex = tempInteger.intValue();
tempStack.push(tempInteger);
}// Of if
} else {
tempIndex = tempNext;
} // Of if
}//Of while
return resultString;
}//Of depthFirstTraversal
public static void depthFirstTraversalTest() {
// Test an undirected graph.
int[][] tempMatrix = { { 0, 1, 1, 0 }, { 1, 0, 0, 1 }, { 1, 0, 0, 0}, { 0, 1, 0, 0} };
Graph tempGraph = new Graph(tempMatrix);
System.out.println(tempGraph);
String tempSequence = "";
try {
tempSequence = tempGraph.depthFirstTraversal(0);
} catch (Exception ee) {
System.out.println(ee);
} // Of try.
System.out.println("The depth first order of visit: " + tempSequence);
}//Of depthFirstTraversalTest
public void coloring(int paraNumColors) {
int tempNumNodes = connectivityMatrix.getRows();
int[] tempColorScheme = new int[tempNumNodes];
Arrays.fill(tempColorScheme, -1);
coloring(paraNumColors, 0, tempColorScheme);
}// Of coloring
public void coloring(int paraNumColors, int paraCurrentNumNodes, int[] paraCurrentColoring) {
// Step 1. Initialize.
int tempNumNodes = connectivityMatrix.getRows();
System.out.println("coloring: paraNumColors = " + paraNumColors + ", paraCurrentNumNodes = " + paraCurrentNumNodes + ", paraCurrentColoring" + Arrays.toString(paraCurrentColoring));
// A complete scheme.
if (paraCurrentNumNodes >= tempNumNodes) {
System.out.println("Find one:" + Arrays.toString(paraCurrentColoring));
return;
} // Of if
for(int i = 0; i < paraNumColors; i++) {
paraCurrentColoring[paraCurrentNumNodes] = i;
if (!colorConflict(paraCurrentNumNodes + 1, paraCurrentColoring)) {
coloring(paraNumColors, paraCurrentNumNodes + 1, paraCurrentColoring);
} // Of if
} // Of for i
}// Of coloring
public boolean colorConflict(int paraCurrentNumNodes, int[] paraColoring) {
for (int i = 0; i < paraCurrentNumNodes - 1; i++) {
// No direct connection.
if (connectivityMatrix.getValue(paraCurrentNumNodes - 1, i) == 0) {
continue;
} // Of if
if (paraColoring[paraCurrentNumNodes - 1] == paraColoring[i]) {
return true;
} // Of if
} // Of for i
return false;
}// Of colorConflict
public static void coloringTest() {
int[][] tempMatrix = { { 0, 1, 1, 0 }, { 1, 0, 0, 1 }, { 1, 0, 0, 0 }, { 0, 1, 0, 0 } };
Graph tempGraph = new Graph(tempMatrix);
//tempGraph.coloring(2);
tempGraph.coloring(3);
}// Of coloringTest
public static void main(String[] args) {
System.out.println("Hello!");
Graph tempGraph = new Graph(3);
System.out.println(tempGraph);
getConnectivityTest();
breadthFirstTraversalTest();
depthFirstTraversalTest();
coloringTest();
}//Of main
}// Of class Graph运行截图：
图的代码一直都有点复杂，要多加练习和复习。
