学习来源：日撸 Java 三百行（41-50天，查找与排序）_闵帆的博客-CSDN博客
48 堆排序
48.1 堆排序可能是排序算法中最难的. 用到了二叉树.
48.2 建初始堆比较费劲.
48.3 调整堆的时间复杂度为O(logn), 所以总体时间复杂度只有 O(nlogn).
48.4 空间复杂度只有O(1).
代码：
/**
*******************
* Test the method.
*******************
*/
public static void selectionSortTest() {
int[] tempUnsortedKeys = { 5, 3, 6, 10, 7, 1, 9 };
String[] tempContents = { "if", "then", "else", "switch", "case", "for", "while" };
DataArray tempDataArray = new DataArray(tempUnsortedKeys, tempContents);
System.out.println(tempDataArray);
tempDataArray.selectionSort();
System.out.println("Result\r\n" + tempDataArray);
} //Of selectionSortTest
/**
*******************
* Heap sort. Maybe the most difficult sorting algorithm.
*******************
*/
public void heapSort() {
DataNode tempNode;
// Step 1. Construct the initial heap.
for (int i = length / 2; i >= 0; i--) {
adjustHeap(i, length);
} // Of for i
System.out.println("The initial heap: " + this + "\r\n");
// Step 2. Swap and reconstruct.
for (int i = length - 1; i > 0; i--) {
tempNode = data[0];
data[0] = data[i];
data[i] = tempNode;
adjustHeap(0,i);
System.out.println("Round " + (length - i) + ": " + this);
} // Of for i
} // Of heapSort
/**
*******************
* Adjust the heap.
*
* @param paraStart The start of the index.
* @param paraLength The length of the adjusted sequence.
*******************
*/
public void adjustHeap(int paraStart, int paraLength) {
DataNode tempNode = data[paraStart];
int tempParent = paraStart;
int tempKey = data[paraStart].key;
for (int tempChild = paraStart * 2 + 1; tempChild < paraLength; tempChild = tempChild * 2 + 1) {
// The right child is bigger.
if (tempChild + 1 < paraLength) {
if (data[tempChild].key < data[tempChild + 1].key) {
tempChild++;
} // Of if
} // Of if
System.out.println("The parent position is " + tempParent + " and the child is " + tempChild);
if (tempKey < data[tempChild].key) {
// The child is bigger.
data[tempParent] = data[tempChild];
System.out.println("Move " + data[tempChild].key + "to position " + tempParent);
tempParent = tempChild;
} else {
break;
} // Of if
} // Of for tempChild
data[tempParent] = tempNode;
System.out.println("Adjust " + paraStart + " to " + paraLength + ": " + this);
} // Of adjustHeap
/**
*******************
* Test the method.
*******************
*/
public static void heapSortTest() {
int[] tempUnsortedKeys = { 5, 3, 6, 10, 7, 1, 9 };
String[] tempContents = { "if", "then", "else", "switch", "case", "for", "while" };
DataArray tempDataArray = new DataArray(tempUnsortedKeys, tempContents);
System.out.println(tempDataArray);
tempDataArray.heapSort();
System.out.println("Result\r\n" + tempDataArray);
} // Of heapSortTest
/**
*********************
* The entrance of the program.
*
* @param args
* Not used now.
*********************
*/
public static void main(String[] args) {
System.out.println("\r\n-------------sequentialSearchTest-------------");
sequentialSearchTest();
System.out.println("\r\n-------------binarySearchTest-------------");
binarySearchTest();
System.out.println("\r\n-------------hashSearchTest-------------");
hashSearchTest();
System.out.println("\r\n-------------insertionSort-------------");
insertionSortTest();
System.out.println("\r\n-------------shellSort-------------");
shellSortTest();
System.out.println("\r\n-------------bubbleSort-------------");
bubbleSortTest();
System.out.println("\r\n-------------quickSort-------------");
quickSortTest();
System.out.println("\r\n-------------selectionSort-------------");
selectionSortTest();
System.out.println("\r\n-------------heapSort-------------");
heapSortTest();
} // Of main
截图：
49 天: 归并排序
49.1 logn 轮, 每轮O(n) 次拷贝. 因此时间复杂度为O(nlogn).
49.2 空间复杂度为O(n). 只需要一行辅助空间.
49.3 全都是在拷贝引用, 而不是数据本身. 这是 Java 的特性.
49.4 里面的两重循环总共只有O(n). 这里是分成了若干个小组.
49.5 归并两个有序小组的时候, 用了三个并列的循环.
49.6 涉及分组后尾巴的各种情况, 所以需要相应的 if 语句.
代码：
/**
*******************
* Merge Sort. Results are stored in the member variable data.
*******************
*/
public void mergeSort() {
// Step 1. Allocate space.
int tempRow; // The current row
int tempGroups; // Number of groups
int tempActualRow; // Only 0 or 1
int tempNextRow = 0;
int tempGroupNumber;
int tempFirstStart, tempSecondStart, tempSecondEnd;
int tempFirstIndex, tempSecondIndex;
int tempNumCopied;
for (int i = 0; i < length; i++) {
System.out.println(data[i]);
} // Of for i
System.out.println();
DataNode[][] tempMatrix = new DataNode[2][length];
// Step 2. Copy data.
for (int i = 0; i < length; i++) {
tempMatrix[0][i] = data[i];
} // Of for i
// Step 3. Merge. log n rounds
tempRow = -1;
for (int tempSize = 1; tempSize <= length; tempSize *= 2) {
// Reuse the space of the two rows.
tempRow++;
System.out.println("Current row = " + tempRow);
tempActualRow = tempRow % 2;
tempNextRow = (tempRow + 1) % 2;
tempGroups = length / (tempSize * 2);
if (length % (tempSize * 2) != 0) {
tempGroups++;
} // Of if
System.out.println("tempSize = " + tempSize + ", numGroups = " + tempGroups);
for (tempGroupNumber = 0; tempGroupNumber < tempGroups; tempGroupNumber++) {
tempFirstStart = tempGroupNumber * tempSize * 2;
tempSecondStart = tempGroupNumber * tempSize * 2 + tempSize;
if (tempSecondStart > length - 1) {
// Copy the first part.
for (int i = tempFirstStart; i < length; i++) {
tempMatrix[tempNextRow][i] = tempMatrix[tempActualRow][i];
} // Of for i
continue;
} // Of if
tempSecondEnd = tempGroupNumber * tempSize * 2 + tempSize * 2 - 1;
if (tempSecondEnd > length - 1) {
tempSecondEnd = length - 1;
} // Of if
System.out
.println("Trying to merge [" + tempFirstStart + ", " + (tempSecondStart - 1)
+ "] with [" + tempSecondStart + ", " + tempSecondEnd + "]");
tempFirstIndex = tempFirstStart;
tempSecondIndex = tempSecondStart;
tempNumCopied = 0;
while ((tempFirstIndex <= tempSecondStart - 1)
&& (tempSecondIndex <= tempSecondEnd)) {
if (tempMatrix[tempActualRow][tempFirstIndex].key <= tempMatrix[tempActualRow][tempSecondIndex].key) {
tempMatrix[tempNextRow][tempFirstStart + tempNumCopied] = tempMatrix[tempActualRow][tempFirstIndex];
tempFirstIndex++;
System.out.println("Copying " + tempMatrix[tempActualRow][tempFirstIndex]);
} else {
tempMatrix[tempNextRow][tempFirstStart + tempNumCopied] = tempMatrix[tempActualRow][tempSecondIndex];
System.out.println("Copying " + tempMatrix[tempActualRow][tempSecondIndex]);
tempSecondIndex++;
} // Of if
tempNumCopied++;
} // Of while
while (tempFirstIndex <= tempSecondStart - 1) {
tempMatrix[tempNextRow][tempFirstStart + tempNumCopied] = tempMatrix[tempActualRow][tempFirstIndex];
tempFirstIndex++;
tempNumCopied++;
} // Of while
while (tempSecondIndex <= tempSecondEnd) {
tempMatrix[tempNextRow][tempFirstStart + tempNumCopied] = tempMatrix[tempActualRow][tempSecondIndex];
tempSecondIndex++;
tempNumCopied++;
} // Of while
} // Of for groupNumber
System.out.println("Round " + tempRow);
for (int i = 0; i < length; i++) {
System.out.println(tempMatrix[tempNextRow][i] + " ");
} // Of for i
System.out.println();
} // Of for tempSize
data = tempMatrix[tempNextRow];
} // Of mergeSort
/**
*******************
* Test the method.
*******************
*/
public static void mergeSortTest() {
int[] tempUnsortedKeys = { 5, 3, 6, 10, 7, 1, 9 };
String[] tempContents = { "if", "then", "else", "switch", "case", "for", "while" };
DataArray tempDataArray = new DataArray(tempUnsortedKeys, tempContents);
System.out.println(tempDataArray);
tempDataArray.mergeSort();
System.out.println("Result\r\n" + tempDataArray);
} // Of mergeSortTest
/**
*********************
* The entrance of the program.
*
* @param args
* Not used now.
*********************
*/
public static void main(String[] args) {
System.out.println("\r\n-------------sequentialSearchTest-------------");
sequentialSearchTest();
System.out.println("\r\n-------------binarySearchTest-------------");
binarySearchTest();
System.out.println("\r\n-------------hashSearchTest-------------");
hashSearchTest();
System.out.println("\r\n-------------insertionSort-------------");
insertionSortTest();
System.out.println("\r\n-------------shellSort-------------");
shellSortTest();
System.out.println("\r\n-------------bubbleSort-------------");
bubbleSortTest();
System.out.println("\r\n-------------quickSort-------------");
quickSortTest();
System.out.println("\r\n-------------selectionSort-------------");
selectionSortTest();
System.out.println("\r\n-------------heapSort-------------");
heapSortTest();
System.out.println("\r\n-------------mergeSort-------------");
mergeSortTest();
} // Of main
截图：
