插入排序
// 插入排序
//時間復雜度:
//最壞是O(N^2),順序逆序
//最好是O(N),順序有序
void InsertSort(int* a, int n)
{
//多趟排序
for (int i = 0; i < n - 1; i++)
{
int end = i;
int tmp = a[end + 1];
while (end >= 0)
{
if (tmp < a[end])
{
a[end + 1] = a[end];
end--;
}
else
{
break;
}
}
a[end + 1] = tmp;
}
}
希爾排序
// 希爾排序
//預排序->接近有序
//直接插入排序
//間隔為gap分成一組,對每組進行插入排序
//平均O(N^1.3)
//最壞:O(log3(N)*N)
void ShellSort(int* a, int n)
{
//gap > 1 的時候,預排序
//gap == 1 的時候,直接插入排序 O(N)
int gap = n;
while (gap > 1)
{
gap = (gap / 3 + 1);
for (int i = 0; i < n - gap; i++)
{
int end = i;
int tmp = a[end + gap];
while (end >= 0)
{
if (tmp < a[end])
{
a[end + gap] = a[end];
end -= gap;
}
else
{
break;
}
}
a[end + gap] = tmp;
}
}
}
選擇排序
// 選擇排序
void Swap(int* p1, int* p2)
{
int tmp = *p1;
*p1 = *p2;
*p2 = tmp;
}
void SelectSort(int* a, int n)
{
int left = 0;
int right = n - 1;
while (left < right)
{
int minIndex = left, maxIndex = left;
for (int i = left; i <= right; i++)
{
if (a[i] < a[minIndex])
minIndex = i;
if (a[i] > a[maxIndex])
maxIndex = i;
}
Swap(&a[left], &a[minIndex]);
//如果max和left位置重疊,max
if (left == maxIndex)
{
maxIndex = minIndex;
}
Swap(&a[right], &a[maxIndex]);
++left;
--right;
}
}
堆排序
// 堆排序
void AdjustDwon(int* a, int n, int root)
{
int parent = root;
int child = parent * 2 + 1;
while (child < n)
{
if (child+1 < n && a[child + 1] > a[child])
{
++child;
}
if (a[child] > a[parent])
{
Swap(&a[child], &a[parent]);
parent = child;
child = parent * 2 + 1;
}
else
{
break;
}
}
}
//O(N*logN)
void HeapSort(int* a, int n)
{
//升序 建大堆
for (int i = (n - 1 - 1) / 2; i >= 0; i--)
{
AdjustDwon(a, n, i);
}
int end = n - 1;
while (end > 0)
{
Swap(&a[0], &a[end]);
AdjustDwon(a, end, 0);
end--;
}
}
冒泡排序
//冒泡和插入相比,誰更好
//順序有序,一樣好
//接近有序,插入好
//
// 冒泡排序
//最壞:O(N^2)
//最好:O(N)
void BubbleSort(int* a, int n)
{
for (int end = n; end > 0; end--)
{
int exchange = 0;
for (int i = 1; i < end; i++)
{
if (a[i - 1] > a[i])
{
Swap(&a[i - 1], &a[i]);
exchange = 1;
}
}
if (exchange == 0)
break;
}
}
快速排序(遞回和非遞回)
//快速排序優化
//三數取中
int GetMidIndex(int* a, int left, int right)
{
int mid = (left + right) >> 1;
//left mid right
if (a[left] < a[mid])
{
if (a[mid] < a[right])
{
return mid;
}
else if(a[left] > a[right])
{
return a[left];
}
else
{
return right;
}
}
else //a[left] > a[mid]
{
if (a[mid] > a[right])
{
return mid;
}
else if (a[left] < a[right])
{
return left;
}
else
{
return right;
}
}
}
// 快速排序遞回實作
// 快速排序hoare版本
int PartSort1(int* a, int left, int right)
{
int midIndex = GetMidIndex(a, left, right);
Swap(&a[left], &a[midIndex]);
int keyi = left;
while (left < right)
{
//找小
while (left < right && a[right] >= a[keyi])
--right;
//找大
while (left < right && a[left] <= a[keyi])
++left;
Swap(&a[left], &a[right]);
}
Swap(&a[keyi], &a[left]);
return left;
}
// 快速排序挖坑法
int PartSort2(int* a, int left, int right)
{
int midIndex = GetMidIndex(a, left, right);
Swap(&a[left], &a[midIndex]);
int key = a[left];
while (left < right)
{
//找小
while (left < right && a[right] >= key)
{
--right;
}
//放到左邊的坑位中,右邊就形成新的坑
a[left] = a[right];
//找大
while (left < right && a[left] <= key)
{
++left;
}
//放到右邊的坑位中,左邊就形成了新的坑
a[right] = a[left];
}
a[left] = key;
return left;
}
// 快速排序前后指標法
//[begin, end]
int PartSort3(int* a, int left, int right)
{
int midIndex = GetMidIndex(a, left, right);
Swap(&a[left], &a[midIndex]);
int keyi = left;
int prev = left;
int cur = left + 1;
while (cur <= right)
{
if (a[cur] < a[keyi] && ++prev != cur)
{
Swap(&a[cur], &a[prev]);
}
++cur;
}
Swap(&a[keyi], &a[prev]);
return prev;
}
void QuickSort(int* a, int begin, int end)
{
if (begin >= end)
return;
//int keyi = PartSort1(a, begin, end);
//int keyi = PartSort2(a, begin, end);
//小區間優化
//1.如果這個子區間是資料較多,繼續選key單趟,分割子區間分治遞回
//2.如果這個子區間是資料較少,再去分治遞回不太劃算
if (end-begin > 20)
{
int keyi = PartSort3(a, begin, end);
//[begin, keyi-1] meeti [keyi+1, end]
QuickSort(a, begin, keyi - 1);
QuickSort(a, keyi + 1, end);
}
else
{
InsertSort(a + begin, end - begin + 1);
}
}
// 快速排序 非遞回實作
//最大的問題->遞回深度太深,程式本身沒問題,但是堆疊空間不夠,導致堆疊溢位
//只能改成非遞回,改成非遞回有兩種方式:
//1.直接改回圈->斐波那契數列求解
//2.樹遍歷非遞回和快排非遞回等等,只能用Stack存盤資料模擬遞回程序
#include "Stack.h"
void QuickSortNonR(int* a, int begin, int end)
{
Stack st;
StackInit(&st);
StackPush(&st, begin);
StackPush(&st, end);
while (!StackEmpty(&st))
{
int left, right;
right = StackTop(&st);
StackPop(&st);
left = StackTop(&st);
StackPop(&st);
int keyi = PartSort1(a, left, right);
if (left < keyi - 1)
{
StackPush(&st, left);
StackPush(&st, keyi - 1);
}
if (keyi+1 < right)
{
StackPush(&st, keyi+1);
StackPush(&st, right);
}
}
StackDestory(&st);
}
歸并排序(遞回和非遞回)
void _Merge(int* a, int* tmp, int begin1, int end1, int begin2, int end2)
{
int i = begin1;
int j = begin1;
while (begin1 <= end1 && begin2 <= end2)
{
if (a[begin1] < a[begin2])
tmp[i++] = a[begin1++];
else
tmp[i++] = a[begin2++];
}
while (begin1 <= end1)
tmp[i++] = a[begin1++];
while (begin2 <= end2)
tmp[i++] = a[begin2++];
//歸并完成后,拷回原陣列
for (; j <= end2; j++)
{
a[j] = tmp[j];
}
}
void _MergeSort(int* a, int left, int right, int* tmp)
{
if (left >= right)
return;
int mid = (left + right) >> 1;
// [left, mid][mid+1,right]
_MergeSort(a, left, mid, tmp);
_MergeSort(a, mid + 1, right, tmp);
int begin1 = left, end1 = mid;
int begin2 = mid + 1, end2 = right;
//兩段有序子區間歸并到tmp,并拷貝回去
_Merge(a, tmp, left, mid, mid + 1, right);
}
// 歸并排序遞回實作
// 時間復雜度:O(N*logN)
// 空間復雜度:O(N)
void MergeSort(int* a, int n)
{
int* tmp = (int*)malloc(sizeof(int) * n);
if (tmp == NULL)
{
printf("malloc fail\n");
exit(-1);
}
_MergeSort(a, 0, n - 1, tmp);
free(tmp);
}
// 歸并排序非遞回實作
void MergeSortNonR(int* a, int n)
{
int* tmp = (int*)malloc(sizeof(int) * n);
if (tmp == NULL)
{
printf("malloc fail\n");
exit(-1);
}
int gap = 1;
while (gap < n)
{
for (int i = 0; i < n; i += 2 * gap)
{
//[i,i+gap-1][i+gap, i+2*gap-1]
int begin1 = i, end1 = i + gap - 1, begin2 = i + gap, end2 = i + 2 * gap - 1;
//如果第二個小區間不存在,結束本次回圈
if (begin2 >= n)
break;
//如果第二個小區間存在,但是不夠gap個,結束位置越界了,修正
if (end2 >= n)
end2 = n - 1;
_Merge(a, tmp, begin1, end1, begin2, end2);
}
gap *= 2;
}
free(tmp);
}
計數排序
//計數排序
//時間復雜度:O(N+range)
//空間復雜度:O(range)
//只適合,一組資料,資料的范圍比較集中,那么效率很高,局限性也在這里
//并且只適合整數,如果是浮點數、字串等等就不行了
void CountSort(int* a, int n)
{
int max = a[0], min = a[0];
for (int i = 0; i < n; i++)
{
if (a[i] > max)
max = a[i];
if (a[i] < min)
min = a[i];
}
int range = max - min + 1;
int* count = malloc(sizeof(int) * range);
memset(count, 0, sizeof(int)*range);
for (int i = 0; i < n; i++)
{
count[a[i] - min]++;
}
int i = 0;
for (int j = 0; j < range; j++)
{
while (count[j]--)
{
a[i++] = j + min;
}
}
free(count);
}
Sort.c
#include "Sort.h"
void PrintArray(int* a, int n)
{
for (int i = 0; i < n; i++)
{
printf("%d ", a[i]);
}
puts("\n---------------------------------");
}
// 插入排序
//時間復雜度:
//最壞是O(N^2),順序逆序
//最好是O(N),順序有序
void InsertSort(int* a, int n)
{
//多趟排序
for (int i = 0; i < n - 1; i++)
{
int end = i;
int tmp = a[end + 1];
while (end >= 0)
{
if (tmp < a[end])
{
a[end + 1] = a[end];
end--;
}
else
{
break;
}
}
a[end + 1] = tmp;
}
}
// 希爾排序
//預排序->接近有序
//直接插入排序
//間隔為gap分成一組,對每組進行插入排序
//平均O(N^1.3)
//最壞:O(log3(N)*N)
void ShellSort(int* a, int n)
{
//gap > 1 的時候,預排序
//gap == 1 的時候,直接插入排序 O(N)
int gap = n;
while (gap > 1)
{
gap = (gap / 3 + 1);
for (int i = 0; i < n - gap; i++)
{
int end = i;
int tmp = a[end + gap];
while (end >= 0)
{
if (tmp < a[end])
{
a[end + gap] = a[end];
end -= gap;
}
else
{
break;
}
}
a[end + gap] = tmp;
}
}
}
// 選擇排序
void Swap(int* p1, int* p2)
{
int tmp = *p1;
*p1 = *p2;
*p2 = tmp;
}
void SelectSort(int* a, int n)
{
int left = 0;
int right = n - 1;
while (left < right)
{
int minIndex = left, maxIndex = left;
for (int i = left; i <= right; i++)
{
if (a[i] < a[minIndex])
minIndex = i;
if (a[i] > a[maxIndex])
maxIndex = i;
}
Swap(&a[left], &a[minIndex]);
//如果max和left位置重疊,max
if (left == maxIndex)
{
maxIndex = minIndex;
}
Swap(&a[right], &a[maxIndex]);
++left;
--right;
}
}
// 堆排序
void AdjustDwon(int* a, int n, int root)
{
int parent = root;
int child = parent * 2 + 1;
while (child < n)
{
if (child+1 < n && a[child + 1] > a[child])
{
++child;
}
if (a[child] > a[parent])
{
Swap(&a[child], &a[parent]);
parent = child;
child = parent * 2 + 1;
}
else
{
break;
}
}
}
//O(N*logN)
void HeapSort(int* a, int n)
{
//升序 建大堆
for (int i = (n - 1 - 1) / 2; i >= 0; i--)
{
AdjustDwon(a, n, i);
}
int end = n - 1;
while (end > 0)
{
Swap(&a[0], &a[end]);
AdjustDwon(a, end, 0);
end--;
}
}
//冒泡和插入相比,誰更好
//順序有序,一樣好
//接近有序,插入好
//
// 冒泡排序
//最壞:O(N^2)
//最好:O(N)
void BubbleSort(int* a, int n)
{
for (int end = n; end > 0; end--)
{
int exchange = 0;
for (int i = 1; i < end; i++)
{
if (a[i - 1] > a[i])
{
Swap(&a[i - 1], &a[i]);
exchange = 1;
}
}
if (exchange == 0)
break;
}
}
//快速排序優化
//三數取中
int GetMidIndex(int* a, int left, int right)
{
int mid = (left + right) >> 1;
//left mid right
if (a[left] < a[mid])
{
if (a[mid] < a[right])
{
return mid;
}
else if(a[left] > a[right])
{
return a[left];
}
else
{
return right;
}
}
else //a[left] > a[mid]
{
if (a[mid] > a[right])
{
return mid;
}
else if (a[left] < a[right])
{
return left;
}
else
{
return right;
}
}
}
// 快速排序遞回實作
// 快速排序hoare版本
int PartSort1(int* a, int left, int right)
{
int midIndex = GetMidIndex(a, left, right);
Swap(&a[left], &a[midIndex]);
int keyi = left;
while (left < right)
{
//找小
while (left < right && a[right] >= a[keyi])
--right;
//找大
while (left < right && a[left] <= a[keyi])
++left;
Swap(&a[left], &a[right]);
}
Swap(&a[keyi], &a[left]);
return left;
}
// 快速排序挖坑法
int PartSort2(int* a, int left, int right)
{
int midIndex = GetMidIndex(a, left, right);
Swap(&a[left], &a[midIndex]);
int key = a[left];
while (left < right)
{
//找小
while (left < right && a[right] >= key)
{
--right;
}
//放到左邊的坑位中,右邊就形成新的坑
a[left] = a[right];
//找大
while (left < right && a[left] <= key)
{
++left;
}
//放到右邊的坑位中,左邊就形成了新的坑
a[right] = a[left];
}
a[left] = key;
return left;
}
// 快速排序前后指標法
//[begin, end]
int PartSort3(int* a, int left, int right)
{
int midIndex = GetMidIndex(a, left, right);
Swap(&a[left], &a[midIndex]);
int keyi = left;
int prev = left;
int cur = left + 1;
while (cur <= right)
{
if (a[cur] < a[keyi] && ++prev != cur)
{
Swap(&a[cur], &a[prev]);
}
++cur;
}
Swap(&a[keyi], &a[prev]);
return prev;
}
void QuickSort(int* a, int begin, int end)
{
if (begin >= end)
return;
//int keyi = PartSort1(a, begin, end);
//int keyi = PartSort2(a, begin, end);
//小區間優化
//1.如果這個子區間是資料較多,繼續選key單趟,分割子區間分治遞回
//2.如果這個子區間是資料較少,再去分治遞回不太劃算
if (end-begin > 20)
{
int keyi = PartSort3(a, begin, end);
//[begin, keyi-1] meeti [keyi+1, end]
QuickSort(a, begin, keyi - 1);
QuickSort(a, keyi + 1, end);
}
else
{
InsertSort(a + begin, end - begin + 1);
}
}
// 快速排序 非遞回實作
//最大的問題->遞回深度太深,程式本身沒問題,但是堆疊空間不夠,導致堆疊溢位
//只能改成非遞回,改成非遞回有兩種方式:
//1.直接改回圈->斐波那契數列求解
//2.樹遍歷非遞回和快排非遞回等等,只能用Stack存盤資料模擬遞回程序
#include "Stack.h"
void QuickSortNonR(int* a, int begin, int end)
{
Stack st;
StackInit(&st);
StackPush(&st, begin);
StackPush(&st, end);
while (!StackEmpty(&st))
{
int left, right;
right = StackTop(&st);
StackPop(&st);
left = StackTop(&st);
StackPop(&st);
int keyi = PartSort1(a, left, right);
if (left < keyi - 1)
{
StackPush(&st, left);
StackPush(&st, keyi - 1);
}
if (keyi+1 < right)
{
StackPush(&st, keyi+1);
StackPush(&st, right);
}
}
StackDestory(&st);
}
void _Merge(int* a, int* tmp, int begin1, int end1, int begin2, int end2)
{
int i = begin1;
int j = begin1;
while (begin1 <= end1 && begin2 <= end2)
{
if (a[begin1] < a[begin2])
tmp[i++] = a[begin1++];
else
tmp[i++] = a[begin2++];
}
while (begin1 <= end1)
tmp[i++] = a[begin1++];
while (begin2 <= end2)
tmp[i++] = a[begin2++];
//歸并完成后,拷回原陣列
for (; j <= end2; j++)
{
a[j] = tmp[j];
}
}
void _MergeSort(int* a, int left, int right, int* tmp)
{
if (left >= right)
return;
int mid = (left + right) >> 1;
// [left, mid][mid+1,right]
_MergeSort(a, left, mid, tmp);
_MergeSort(a, mid + 1, right, tmp);
int begin1 = left, end1 = mid;
int begin2 = mid + 1, end2 = right;
//兩段有序子區間歸并到tmp,并拷貝回去
_Merge(a, tmp, left, mid, mid + 1, right);
}
// 歸并排序遞回實作
// 時間復雜度:O(N*logN)
// 空間復雜度:O(N)
void MergeSort(int* a, int n)
{
int* tmp = (int*)malloc(sizeof(int) * n);
if (tmp == NULL)
{
printf("malloc fail\n");
exit(-1);
}
_MergeSort(a, 0, n - 1, tmp);
free(tmp);
}
// 歸并排序非遞回實作
void MergeSortNonR(int* a, int n)
{
int* tmp = (int*)malloc(sizeof(int) * n);
if (tmp == NULL)
{
printf("malloc fail\n");
exit(-1);
}
int gap = 1;
while (gap < n)
{
for (int i = 0; i < n; i += 2 * gap)
{
//[i,i+gap-1][i+gap, i+2*gap-1]
int begin1 = i, end1 = i + gap - 1, begin2 = i + gap, end2 = i + 2 * gap - 1;
//如果第二個小區間不存在,結束本次回圈
if (begin2 >= n)
break;
//如果第二個小區間存在,但是不夠gap個,結束位置越界了,修正
if (end2 >= n)
end2 = n - 1;
_Merge(a, tmp, begin1, end1, begin2, end2);
}
gap *= 2;
}
free(tmp);
}
//計數排序
//時間復雜度:O(N+range)
//空間復雜度:O(range)
//只適合,一組資料,資料的范圍比較集中,那么效率很高,局限性也在這里
//并且只適合整數,如果是浮點數、字串等等就不行了
void CountSort(int* a, int n)
{
int max = a[0], min = a[0];
for (int i = 0; i < n; i++)
{
if (a[i] > max)
max = a[i];
if (a[i] < min)
min = a[i];
}
int range = max - min + 1;
int* count = malloc(sizeof(int) * range);
memset(count, 0, sizeof(int)*range);
for (int i = 0; i < n; i++)
{
count[a[i] - min]++;
}
int i = 0;
for (int j = 0; j < range; j++)
{
while (count[j]--)
{
a[i++] = j + min;
}
}
free(count);
}
Stack.c
#include "Stack.h"
void StackInit(Stack* pst)
{
assert(pst);
pst->a = (STDataType*)malloc(sizeof(STDataType) * 4);
pst->top = 0;
pst->capacity = 4;
}
void StackDestory(Stack* pst)
{
assert(pst);
free(pst->a);
pst->a = NULL;
pst->capacity = pst->top = 0;
}
//性質就決定在堆疊頂出入資料
void StackPush(Stack* pst, STDataType x)
{
assert(pst);
if (pst->top == pst->capacity)
{
STDataType* tmp = (STDataType*)realloc(pst->a, sizeof(STDataType)*pst->capacity * 2);
if (tmp == NULL)
{
printf("realloc fail");
exit(-1);
}
pst->a = tmp;
pst->capacity *= 2;
}
pst->a[pst->top] = x;
pst->top++;
}
void StackPop(Stack* pst)
{
assert(pst);
assert(!StackEmpty(pst));
pst->top--;
}
STDataType StackTop(Stack* pst)
{
assert(pst);
assert(!StackEmpty(pst));
return pst->a[pst->top - 1];
}
bool StackEmpty(Stack* pst)
{
assert(pst);
return pst->top == 0;
}
int StackSize(Stack* pst)
{
assert(pst);
return pst->top;
}
Sort.h
#define _CRT_SECURE_NO_WARNINGS 1
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <string.h>
// 排序實作的介面
//
void PrintArray(int* a, int n);
// 插入排序
void InsertSort(int* a, int n);
// 希爾排序
void ShellSort(int* a, int n);
// 選擇排序
void SelectSort(int* a, int n);
// 堆排序
void AdjustDwon(int* a, int n, int root);
void HeapSort(int* a, int n);
// 冒泡排序
void BubbleSort(int* a, int n);
// 快速排序遞回實作
// 快速排序hoare版本
int PartSort1(int* a, int left, int right);
// 快速排序挖坑法
int PartSort2(int* a, int left, int right);
// 快速排序前后指標法
int PartSort3(int* a, int left, int right);
void QuickSort(int* a, int begin, int end);
// 快速排序 非遞回實作
void QuickSortNonR(int* a, int begin, int end);
// 歸并排序遞回實作
void MergeSort(int* a, int n);
// 歸并排序非遞回實作
void MergeSortNonR(int* a, int n);
//計數排序
void CountSort(int* a, int n);
Stack.h
#pragma once
#define _CRT_SECURE_NO_WARNINGS 1
#include <stdbool.h>
#include <assert.h>
#include <stdio.h>
#include <malloc.h>
#include <stdlib.h>
typedef int STDataType;
//typedef char STDataType;
struct Stack
{
STDataType* a;
int top; //堆疊頂
int capacity; //容量
};
//typedef struct Stack ST;
typedef struct Stack Stack;
void StackInit(Stack* pst);
void StackDestory(Stack* pst);
//性質就決定在堆疊頂出入資料
void StackPush(Stack* pst, STDataType x);
void StackPop(Stack* pst);
STDataType StackTop(Stack* pst);
bool StackEmpty(Stack* pst);
int StackSize(Stack* pst);
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