摘要: 排序算法最能体现算法的多样性。
1. 代码先上代码, 再说废话.
/**
* Hash table.
*
* @author Fan Min minfanphd@163.com.
*/
#include
#include
#define TABLE_SIZE 19
/**
* pair.
*/
typedef struct Node{
int key;
char value;
}Node, *NodePtr;
/**
* pair.
*/
typedef struct SequentialList{
int length;
NodePtr elements;
}SequentialList, *ListPtr;
/**
* Initialize a data array.
*/
ListPtr initList(int* paraKeys, char* paraValues, int paraLength){
int i;
ListPtr resultPtr = (ListPtr)malloc(sizeof(struct SequentialList));
resultPtr->length = paraLength;
resultPtr->elements = (NodePtr)malloc(paraLength * sizeof(struct Node));
for (i = 0; i < paraLength; i ++){
//printf("setting key for index %d: %d and value: %c\r\n", i, paraKeys[i], paraValues[i]);
resultPtr->elements[i].key = paraKeys[i];
resultPtr->elements[i].value = paraValues[i];
}//Of for i
return resultPtr;
}//Of initList
/**
* Print the list.
*/
void printList(ListPtr paraPtr) {
int i;
printf("(Keys, values)\r\n");
for (i = 0; i < paraPtr->length; i ++) {
printf("%d\t", paraPtr->elements[i].key);
}//Of for i
printf("\r\n");
for (i = 0; i < paraPtr->length; i ++) {
printf("%c\t", paraPtr->elements[i].value);
}//Of for i
}//Of printList
/**
* Insertion sort. paraPtr->elements[0] does not store a valid data. paraPtr->elements[0].key should
* be smaller than any valid key.
*/
void insertionSort(ListPtr paraPtr) {
Node tempNode;
int j;
for (int i = 2; i < paraPtr->length; i++) {
tempNode = paraPtr->elements[i];
//Find the position to insert.
//At the same time, move other nodes.
for (j = i - 1; paraPtr->elements[j].key > tempNode.key; j--) {
paraPtr->elements[j + 1] = paraPtr->elements[j];
} // Of for j
//Insert.
paraPtr->elements[j + 1] = tempNode;
} // Of for i
}// Of insertionSort
/**
* Test the method.
*/
void insertionSortTest() {
int tempUnsortedKeys[] = { -100, 5, 3, 6, 10, 7, 1, 9 };
char tempContents[] = { 'n', 'i', 't', 'e', 's', 'c', 'f', 'w' };
ListPtr tempList = initList(tempUnsortedKeys, tempContents, 8);
printf("\r\nBefore insertion sort:\r\n");
printList(tempList);
insertionSort(tempList);
printf("\r\nAfter insertion sort:\r\n");
printList(tempList);
}// Of insertionSortTest
/**
* Shell sort.
*/
void shellSort(ListPtr paraPtr) {
Node tempNode;
int tempJumpArray[] = { 5, 3, 1 };
int tempJump;
int p, i, j, k;
for (i = 0; i < 3; i++) {
tempJump = tempJumpArray[i];
for (j = 0; j < tempJump; j++) {
for (k = j + tempJump; k < paraPtr->length; k += tempJump) {
tempNode = paraPtr->elements[k];
// Find the position to insert.
// At the same time, move other nodes.
for (p = k - tempJump; p >= 0; p -= tempJump) {
if (paraPtr->elements[p].key > tempNode.key) {
paraPtr->elements[p + tempJump] = paraPtr->elements[p];
} else {
break;
} // Of if
} // Of for p
// Insert.
paraPtr->elements[p + tempJump] = tempNode;
} // Of for k
} // Of for j
} // Of for i
}// Of shellSort
/**
* Test the method.
*/
void shellSortTest() {
int tempUnsortedKeys[] = {5, 3, 6, 10, 7, 1, 9 };
char tempContents[] = {'i', 't', 'e', 's', 'c', 'f', 'w' };
ListPtr tempList = initList(tempUnsortedKeys, tempContents, 7);
printf("\r\nBefore shell sort:\r\n");
printList(tempList);
shellSort(tempList);
printf("\r\nAfter shell sort:\r\n");
printList(tempList);
}// Of shellSortTest
/**
* Bubble sort.
*/
void bubbleSort(ListPtr paraPtr) {
bool tempSwapped;
Node tempNode;
int i, j;
for (i = paraPtr->length - 1; i > 0; i--) {
tempSwapped = false;
for (j = 0; j < i; j++) {
if (paraPtr->elements[j].key > paraPtr->elements[j + 1].key) {
// Swap.
tempNode = paraPtr->elements[j + 1];
paraPtr->elements[j + 1] = paraPtr->elements[j];
paraPtr->elements[j] = tempNode;
tempSwapped = true;
} // Of if
} // Of for j
// No swap in this round. The data are already sorted.
if (!tempSwapped) {
printf("Premature.\r\n");
break;
} // Of if
} // Of for i
}// Of bubbleSort
/**
* Test the method.
*/
void bubbleSortTest() {
int tempUnsortedKeys[] = {5, 3, 6, 10, 7, 1, 9 };
char tempContents[] = {'i', 't', 'e', 's', 'c', 'f', 'w' };
ListPtr tempList = initList(tempUnsortedKeys, tempContents, 7);
printf("\r\nBefore bubble sort:\r\n");
printList(tempList);
shellSort(tempList);
printf("\r\nAfter bubble sort:\r\n");
printList(tempList);
}// Of bubbleSortTest
/**
* Quick sort recursive.
*/
void quickSortRecursive(ListPtr paraPtr, int paraStart, int paraEnd) {
int tempPivot, tempLeft, tempRight;
Node tempNodeForSwap;
// Nothing to sort.
if (paraStart >= paraEnd) {
return;
} // Of if
tempPivot = paraPtr->elements[paraEnd].key;
tempLeft = paraStart;
tempRight = paraEnd - 1;
// Find the position for the pivot.
// At the same time move smaller elements to the left and bigger one to the
// right.
while (true) {
while ((paraPtr->elements[tempLeft].key < tempPivot) && (tempLeft < tempRight)) {
tempLeft++;
} // Of while
while ((paraPtr->elements[tempRight].key >= tempPivot) && (tempLeft < tempRight)) {
tempRight--;
} // Of while
if (tempLeft < tempRight) {
// Swap.
//System.out.println("Swapping " + tempLeft + " and " + tempRight);
tempNodeForSwap = paraPtr->elements[tempLeft];
paraPtr->elements[tempLeft] = paraPtr->elements[tempRight];
paraPtr->elements[tempRight] = tempNodeForSwap;
} else {
break;
} // Of if
} // Of while
// Swap
if (paraPtr->elements[tempLeft].key > tempPivot) {
tempNodeForSwap = paraPtr->elements[paraEnd];
paraPtr->elements[paraEnd] = paraPtr->elements[tempLeft];
paraPtr->elements[tempLeft] = tempNodeForSwap;
} else {
tempLeft++;
} // Of if
//System.out.print("From " + paraStart + " to " + paraEnd + ": ");
//System.out.println(this);
quickSortRecursive(paraPtr, paraStart, tempLeft - 1);
quickSortRecursive(paraPtr, tempLeft + 1, paraEnd);
}// Of quickSortRecursive
/**
* Quick sort.
*/
void quickSort(ListPtr paraPtr) {
quickSortRecursive(paraPtr, 0, paraPtr->length - 1);
}// Of quickSort
/**
* Test the method.
*/
void quickSortTest() {
int tempUnsortedKeys[] = {5, 3, 6, 10, 7, 1, 9 };
char tempContents[] = {'i', 't', 'e', 's', 'c', 'f', 'w' };
ListPtr tempList = initList(tempUnsortedKeys, tempContents, 7);
printf("\r\nBefore quick sort:\r\n");
printList(tempList);
quickSort(tempList);
printf("\r\nAfter quick sort:\r\n");
printList(tempList);
}// Of quickSortTest
/**
* Selection sort.
*/
void selectionSort(ListPtr paraPtr) {
Node tempNode;
int tempIndexForSmallest, i, j;
for (i = 0; i < paraPtr->length - 1; i++) {
// Initialize.
tempNode = paraPtr->elements[i];
tempIndexForSmallest = i;
for (j = i + 1; j < paraPtr->length; j++) {
if (paraPtr->elements[j].key < tempNode.key) {
tempNode = paraPtr->elements[j];
tempIndexForSmallest = j;
} // Of if
} // Of for j
// Change the selected one with the current one.
paraPtr->elements[tempIndexForSmallest] = paraPtr->elements[i];
paraPtr->elements[i] = tempNode;
} // Of for i
}// Of selectionSort
/**
* Test the method.
*/
void selectionSortTest() {
int tempUnsortedKeys[] = {5, 3, 6, 10, 7, 1, 9 };
char tempContents[] = {'i', 't', 'e', 's', 'c', 'f', 'w' };
ListPtr tempList = initList(tempUnsortedKeys, tempContents, 7);
printf("\r\nBefore selection sort:\r\n");
printList(tempList);
selectionSort(tempList);
printf("\r\nAfter selection sort:\r\n");
printList(tempList);
}// Of selectionSortTest
/**
* Adjust heap.
*/
void adjustHeap(ListPtr paraPtr, int paraStart, int paraLength) {
Node tempNode = paraPtr->elements[paraStart];
int tempParent = paraStart;
int tempKey = paraPtr->elements[paraStart].key;
for (int tempChild = paraStart * 2 + 1; tempChild < paraLength; tempChild = tempChild * 2 + 1) {
// The right child is bigger.
if (tempChild + 1 < paraLength) {
if (paraPtr->elements[tempChild].key < paraPtr->elements[tempChild + 1].key) {
tempChild++;
} // Of if
} // Of if
//System.out.println("The parent position is " + tempParent + " and the child is " + tempChild);
if (tempKey < paraPtr->elements[tempChild].key) {
// The child is bigger.
paraPtr->elements[tempParent] = paraPtr->elements[tempChild];
//System.out.println("Move " + paraPtr->elements[tempChild].key + " to position " + tempParent);
tempParent = tempChild;
} else {
break;
} // Of if
} // Of for tempChild
paraPtr->elements[tempParent] = tempNode;
}// Of adjustHeap
/**
* Heap sort.
*/
void heapSort(ListPtr paraPtr) {
Node tempNode;
int i;
// Step 1. Construct the initial heap.
for (i = paraPtr->length / 2 - 1; i >= 0; i--) {
adjustHeap(paraPtr, i, paraPtr->length);
} // Of for i
// Step 2. Swap and reconstruct.
for (i = paraPtr->length - 1; i > 0; i--) {
tempNode = paraPtr->elements[0];
paraPtr->elements[0] = paraPtr->elements[i];
paraPtr->elements[i] = tempNode;
adjustHeap(paraPtr, 0, i);
//System.out.println("Round " + (length - i) + ": " + this);
} // Of for i
}// Of heapSort
/**
* Test the method.
*/
void heapSortTest() {
int tempUnsortedKeys[] = {5, 3, 6, 10, 7, 1, 9 };
char tempContents[] = {'i', 't', 'e', 's', 'c', 'f', 'w' };
ListPtr tempList = initList(tempUnsortedKeys, tempContents, 7);
printf("\r\nBefore heap sort:\r\n");
printList(tempList);
heapSort(tempList);
printf("\r\nAfter heap sort:\r\n");
printList(tempList);
}// Of heapSortTest
/**
* Selection sort.
*/
void mergeSort(ListPtr paraPtr) {
// 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;
int i;
int tempSize;
/*
ListPtr tempMatrix[2];
int* tempIntArray = (int*)malloc(paraPtr->length * sizeof(int));
char* tempCharArray = (char*)malloc(paraPtr->length * sizeof(char));
tempMatrix[0] = paraPtr;
tempMatrix[1] = initList(tempIntArray, tempCharArray, paraPtr->length);
*/
Node** tempMatrix = (Node**)malloc(2 * sizeof(Node*));
tempMatrix[0] = (Node*)malloc(paraPtr->length * sizeof(Node));
tempMatrix[1] = (Node*)malloc(paraPtr->length * sizeof(Node));
for (i = 0; i < paraPtr->length; i ++) {
tempMatrix[0][i] = paraPtr->elements[i];
}//Of for i
/*
Node tempMatrix[2][length];
// Step 2. Copy data.
for (i = 0; i < length; i++) {
tempMatrix[0][i] = data[i];
} // Of for i
*/
// Step 3. Merge. log n rounds
tempRow = -1;
for (tempSize = 1; tempSize <= paraPtr->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 = paraPtr->length / (tempSize * 2);
if (paraPtr->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 > paraPtr->length - 1) {
// Copy the first part.
for (i = tempFirstStart; i < paraPtr->length; i++) {
tempMatrix[tempNextRow][i] = tempMatrix[tempActualRow][i];
} // Of for i
continue;
} // Of if
tempSecondEnd = tempGroupNumber * tempSize * 2 + tempSize * 2 - 1;
if (tempSecondEnd > paraPtr->length - 1) {
tempSecondEnd = paraPtr->length - 1;
} // Of if
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
} // Of for tempStepSize
for (i = 0; i < paraPtr->length; i ++) {
paraPtr->elements[i] = tempMatrix[tempNextRow][i];
}//Of for i
}// Of mergeSort
/**
* Test the method.
*/
void mergeSortTest() {
int tempUnsortedKeys[] = {5, 3, 6, 10, 7, 1, 9 };
char tempContents[] = {'i', 't', 'e', 's', 'c', 'f', 'w' };
ListPtr tempList = initList(tempUnsortedKeys, tempContents, 7);
printf("\r\nBefore merge sort:\r\n");
printList(tempList);
mergeSort(tempList);
printf("\r\nAfter merge sort:\r\n");
printList(tempList);
}// Of mergeSortTest
/**
* The entrance of the program.
*/
int main() {
insertionSortTest();
//shellSortTest();
//bubbleSortTest();
//quickSortTest();
//selectionSortTest();
//heapSortTest();
//mergeSortTest();
return 1;
}// Of main
Before insertion sort:
(Keys, values)
-100 5 3 6 10 7 1 9
n i t e s c f w
After insertion sort:
(Keys, values)
-100 1 3 5 6 7 9 10
n f t i e c w s Press any key to continue
好几个算法.
3.1 插入排序- 插入排序是简单直接的排序方式之一. 代码非常短.
- 每次保证前 i 个数据是有序的.
- 先做简单的事情 (第 1 轮最多有 1 次移动), 再做麻烦的事情 (最后一轮最多有 n − 1 n - 1n−1 次移动).
- 下标 0 的数据为岗哨. 比其它排序方式多用一个空间.
- 多达 4 重循环, 但时间复杂度只有 O ( n 2 ) O(n^2 ) O(n2).
- 多次排序反正减少了平均排序时间. 神奇的脑回路.
- 有了昨天的程序铺垫, 本程序写起来也不难.
- 岗哨的个数与最初的步长相关, 我们的程序中为 5. 简便起见我就没用了.
- 可以改变 tempJumpArray.
- 每次确定当前最大值, 也就是确定一个位置的数据.
- 仅交换相邻数据.
- 如果某一趟没有交换, 就表示数据已经有序 (早熟, premature), 可以提前结束了.
- 平均时间复杂度为 O ( n log n ) O(n \log n ) O(nlogn), 但最坏情况还是 O ( n 2 ) O(n^2) O(n2).
- Pivot 应该选 (该子序列的) 最后一个元素.
- 递归算法, 每次只能确定 pivot 的位置.
- 判断条件 && (tempLeft < tempRight) 不能少.
- (paraPtr->elements[tempRight].key >= tempPivot) 不能写成 >, 否则出现两个相同 key 时可能出错.
- 又是一个基础 (简单) 算法.
- 与插入排序不同, 先做最麻烦的, 要进行 n − 1 n − 1 n−1 次比较才能获得最小的数据.
- 数据一旦被选择并确定位置, 就不再改变.
- 作为一种简单算法, 其时间复杂度为 O ( n 2 ) O(n^2) O(n2).
- 只需要两个额外的空间来存放最小数据的引用与下标, 因此空间复杂度为 O ( 1 ) O(1) O(1).
- 堆排序可能是排序算法中最难的. 用到了二叉树.
- 建初始堆比较费劲.
- 调整堆的时间复杂度为 O ( log n ) O(\log n) O(logn), 所以总体时间复杂度只有 O ( n log n ) O(n \log n) O(nlogn).
- 空间复杂度只有 O ( 1 ) O(1) O(1).
- log n \log n logn 轮, 每轮 O ( n ) O(n) O(n) 次拷贝. 因此时间复杂度为 O ( n log n ) O(n \log n) O(nlogn).
- 空间复杂度为 O ( n ) O(n) O(n). 只需要一行辅助空间.
- 全都是在拷贝引用, 而不是数据本身. 这是 Java 的特性.
- 里面的两重循环总共只有 O ( n ) O(n) O(n). 这里是分成了若干个小组.
- 归并两个有序小组的时候, 用了三个并列的循环.
- 涉及分组后尾巴的各种情况, 所以需要相应的 if 语句.
欢迎分享，转载请注明来源：内存溢出
微信扫一扫
支付宝扫一扫
评论列表（0条）