前言
算法是一门十分重要的必修课，近来有些空余时间，故温习一下几种排序算法，希望也对你有益。
环境： MinGW w64 6.0 / C99 / CLion 2018.1
排序算法
共用部分
#include <stdio.h>
typedef struct {
int len;
int *ary;
} array;
void vSwap(int *a, int *b) {
int t = *a;
*a = *b;
*b = t;
}
冒泡排序
从左到右，两两比较，
array tBubbleSort(array tAry) {
for (int i = 0; i < tAry.len; i++) {
for (int j = 1; j < tAry.len - i; j++) {
if (tAry.ary[j - 1] > tAry.ary[j]) {
vSwap(tAry.ary + (j - 1), tAry.ary + j);
}
}
}
return tAry;
}
插入排序
-
直接插入
array tInsertionSort(array tAry) {
for (int i = 1; i < tAry.len; i++) {
for (int j = i; j >= 1; j--) {
if (tAry.ary[j - 1] > tAry.ary[j]) {
vSwap(tAry.ary + (j - 1), tAry.ary + j);
} else {
break;
}
}
}
return tAry;
}
-
二分插入
array tBinaryInsertionSort(array tAry) {
for (int i = 0; i < tAry.len; i++) {
int st = 0, ed = i;
while (st != ed) {
int j = (st + ed) / 2;
if (tAry.ary[i] > tAry.ary[j]) {
st = j += (st == j);
} else {
ed = j;
}
}
for (int now = i; now > st; now--) {
vSwap(tAry.ary + now, tAry.ary + (now - 1));
}
}
return tAry;
}
选择排序
-
简单选择
array tSelectSort(array tAry) {
for (int i = 0; i < tAry.len; i++) {
for (int j = i; j < tAry.len; j++) {
if (tAry.ary[j] < tAry.ary[i]) {
vSwap(tAry.ary + i, tAry.ary + j);
}
}
}
return tAry;
}
-
优化选择
array tSelectSortPlus(array tAry) {
for (int i = 0; i < tAry.len / 2; i++) {
for (int st = i, ed = tAry.len - i - 1; st <= ed; st++) {
if (tAry.ary[st] < tAry.ary[i]) {
vSwap(tAry.ary + st, tAry.ary + i);
}
if (tAry.ary[st] > tAry.ary[ed]) {
vSwap(tAry.ary + st, tAry.ary + ed);
}
}
}
return tAry;
}
希尔排序
array tShellSort(array tAry) {
int step = tAry.len;
while (step > 1) {
step = step / 3 + 1;
for (int i = step; i < tAry.len; i++) {
int j = i - step, k = tAry.ary[i];
while (j >= 0) {
if (k < tAry.ary[j])
vSwap(tAry.ary + j, tAry.ary + j + step);
j = j - step;
}
}
}
return tAry;
}
快速排序
分享一个关于快速排序的演示视频，可以帮助理解。
void vQuickSortSubFun(int *ary, int low, int high) {
if (high <= low)
return;
int lowRaw = low, highRaw = high;
int temp = ary[low];
while (low < high) {
while (low < high) {
if (temp > ary[high]) {
ary[low] = ary[high];
break;
}
high--;
}
while (low < high) {
if (ary[low] > temp) {
ary[high] = ary[low];
break;
}
low++;
}
}
ary[low] = temp;
vQuickSortSubFun(ary, lowRaw, low - 1);
vQuickSortSubFun(ary, low + 1, highRaw);
}
array tQuickSort(array tAry) {
vQuickSortSubFun(tAry.ary, 0, tAry.len - 1);
return tAry;
}
堆排序
不是真的去构造二叉树，算法在于意而不在于形。
节点的两个子节点是
和
我网上找到一张动图，可以帮助理解。
堆排序 gif
array tHeapSort(array tAry) {
for (int last = tAry.len; last > 1; last--) {
int *ary = tAry.ary;
if (last % 2 == 0) {
if (ary[last - 1] > ary[last / 2 - 1])
vSwap(ary + (last - 1), ary + (last / 2 - 1));
}
for (int cur = last % 2 == 0 ? (last - 1) / 2 : last / 2; cur > 0; cur--) {
if (ary[cur - 1] < ary[cur * 2 - 1]) { //比较左节点
vSwap(ary + (cur - 1), ary + (cur * 2 - 1));
}
if (ary[cur - 1] < ary[cur * 2]) { //比较右节点
vSwap(ary + (cur - 1), ary + (cur * 2));
}
}
vSwap(ary + 0, ary + (last - 1));
}
return tAry;
}
归并排序
合并时是先复制两个子数组，在往目标数组里顺序放置元素。
void vMerge(int *ary, int left, int centre, int right) {
int lLen = centre - left + 1;
int rLen = right - centre;
int *lAry = (int *) malloc(sizeof(int) * lLen);
int *rAry = (int *) malloc(sizeof(int) * rLen);
for (int tm = 0; tm < lLen; tm++) {
lAry[tm] = ary[left + tm];
}
for (int i = 0; i < rLen; i++) {
rAry[i] = ary[centre + 1 + i];
}
int lFlag = 0, rFlag = 0, curFlag = left;
while (1) {
if (lFlag < lLen && rFlag < rLen) {
if (lAry[lFlag] <= rAry[rFlag]) {
ary[curFlag] = lAry[lFlag];
lFlag++;
curFlag++;
} else {
ary[curFlag] = rAry[rFlag];
rFlag++;
curFlag++;
}
} else if (lFlag >= lLen) {
ary[curFlag] = rAry[rFlag];
rFlag++;
curFlag++;
} else {
ary[curFlag] = lAry[lFlag];
lFlag++;
curFlag++;
}
if (curFlag > right)
break;
}
}
void vMergeSortSubFun(int *arr, int left, int right) {
if (right <= left)
return;
int centre = (left + right) / 2;
vMergeSortSubFun(arr, left, centre);
vMergeSortSubFun(arr, centre + 1, right);
vMerge(arr, left, centre, right);
}
array tMergeSort(array tAry) {
vMergeSortSubFun(tAry.ary, 0, tAry.len - 1);
return tAry;
}
测试正确性
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <stdbool.h>
//创建数值和长度随机的数组
array tCreateRandomAry() {
int aryLenMax = 20, numMax = 100;
int aryLen = rand() % aryLenMax;
int *ary = (int *) malloc(sizeof(int) * aryLen);
for (int i = 0; i < aryLen; i++) {
ary[i] = rand() % (numMax + 1);
}
array tAry;
tAry.len = aryLen;
tAry.ary = ary;
return tAry;
}
//测试排序函数正确性（升序）
bool bVerifySortFunc(array (*sort)(array), array tAry) {
array tResult = sort(tAry);
for (int i = 1; i < tResult.len; i++) {
if (tResult.ary[i - 1] > tResult.ary[i])
return false;
}
return true;
}
//批量测试
void test(array (*sort)(array), char *description) {
int m = 0; //错误标记
int t = 1000; //测试次数
for (int i = 0; i < t; i++) {
if (!bVerifySortFunc(sort, tCreateRandomAry())) {
m = 1;
break;
}
}
if (m) printf("%s: Error\n", description); else printf("%s: OK\n", description);
}
int main() {
srand((unsigned int) time(NULL));
test(tBubbleSort,"冒泡排序");
test(tInsertionSort,"插入排序");
test(tBinaryInsertionSort,"二分排序");
test(tSelectSort,"选择排序");
test(tSelectSortPlus,"优化选择排序");
test(tShellSort,"希尔排序");
test(tQuickSort,"快速排序");
test(tHeapSort,"堆排序");
test(tMergeSort,"归并排序");
return 0;
}
结束
以上，纰漏之处请指正。
图片如有侵权请告知，将尽快删除。
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