数据结构排序算法---八大排序复杂度及代码实现

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稳定性：相同的数据排序后，相对位置是否发生改变

一、冒泡排序

时间复杂度：O(N^2)
空间复杂度：O(1)
稳定性：稳定

代码实现

void Swap(int* a, int* b)
{int tmp;tmp = *a;*a = *b;*b = tmp;
}
void BubbleSort(int* a, int n)
{for (int j = 0; j < n; j++){int exchange = 0;for (size_t i = 1; i < n-j; i++)if (a[i - 1] > a[i]){Swap(&a[i - 1], &a[i]);exchange = 1;}if (exchange == 0){break;}}
}

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二、直接插入排序

时间复杂度：O(N^2)
空间复杂度：O(1)
稳定性：稳定

代码实现

void InsertSort(int* a, int n)
{for (int i = 0; i < n; i++){int end = i;int tmp = a[end + 1];while (end>=0){if (tmp < a[end])a[end + 1] = a[end];elsebreak;--end;}a[end + 1] = tmp;} 
}

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三、希尔排序

时间复杂度：O(N^1.3)
空间复杂度：O(1)
稳定性：不稳定

代码实现

void ShellSort(int* a, int 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;}elsebreak;}a[end + gap] = tmp;}}
}

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四、选择排序

时间复杂度：O(N^2)
空间复杂度：O(1)
稳定性：不稳定

代码实现

void SelectSort(int* a, int n)
{int begin = 0;int end = n - 1;while (begin < end){int max = begin, min = begin;for (int i = begin+1; i <= end; i++){if (a[i] > a[max])max = i;if (a[i] < a[min])min = i;}Swap(&a[begin], &a[min]);if (max == begin)max = min;Swap(&a[end], &a[max]);--end;++begin;}
}

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五、堆排序

时间复杂度：O(N*logN)
空间复杂度：O(1)
稳定性：不稳定

代码实现

void AdjustDown(int* a, int n, int parent)
{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;}}
}void HeapSort(int* a, int n)
{for (int i = (n - 1 - 1) / 2; i >= 0; i--){AdjustDown(a, n, i);}int end = n - 1;while (end > 0){Swap(&a[0], &a[end]);AdjustDown(a, end, 0);--end;}
}

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六、快速排序

时间复杂度：O(N*logN)
空间复杂度：O(logN)
稳定性：不稳定

代码实现

//三数取中
int GetMidi(int* a, int left, int right)
{int midi = (left + right) / 2;if (a[left] < a[midi]){if (a[midi] < a[right])return midi;else if (a[right] < a[left])return left;elsereturn right;}else{if (a[left] < a[right])return left;else if (a[right] < a[midi])return midi;elsereturn right;}
}
//hoare
int PartSort1(int* a, int left,int right)
{int keyP = left;//GetMidi(a,left,right);while (left < right){while (a[right] >= a[keyP] && left < right)--right;while (a[left] <= a[keyP] && left < right)++left;Swap(&a[left], &a[right]);}Swap(&a[keyP], &a[left]);return left;
}
//挖坑法
int PartSort2(int* a, int left, int right)
{int midi = GetMidi(a, left, right);Swap(&a[left], &a[midi]);int keyP = a[left];//int keyP = left;int hole = left;while (left < right){while (a[right] >= keyP && left < right)--right;a[hole] = a[right];hole = right;while (a[left] <= keyP && left < right)++left;a[hole] = a[left];hole = left;}a[hole] = keyP;return hole;
}
//前后指针
int PartSort3(int* a, int left, int right)
{int prev = left;int cur = prev + 1;int keyP = left;while (cur <= right){if (a[cur] < a[keyP] && ++prev != cur){Swap(&a[prev], &a[cur]);}cur++;}Swap(&a[prev], &a[keyP]);return prev;
}void QuickSort(int* a, int begin, int end)
{if (begin >= end)return;int key = PartSort1(a, begin, end);QuickSort(a, begin, key - 1);QuickSort(a, key + 1, end);
}void QuickSort1(int* a, int begin, int end)
{if (begin >= end)return;//小区间优化,小区间不在递归分割排序，降低递归次数if ((end - begin + 1) > 10){int key = PartSort1(a, begin, end);QuickSort1(a, begin, key - 1);QuickSort1(a, key + 1, end);}else{InsertSort(a + begin, end - begin + 1);}
}void QuickSortNonR(int* a, int begin, int end)//非递归
{Stack st;StackInit(&st);StackPush(&st, end);StackPush(&st, begin);while (!StackEmpty(&st)){int left = StackTop(&st);StackPop(&st);int right = StackTop(&st);StackPop(&st);int key = PartSort3(a, left, right);if (key + 1 < right){StackPush(&st, right);StackPush(&st, key + 1);}if (begin < key - 1){StackPush(&st, key - 1);StackPush(&st, begin);}}StackDestory(&st);
}

其中包含了，三数取中（基准值），快排的三种实现方法（hoare，挖坑法，前后指针）及非递归方法

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七、归并排序

时间复杂度：O(N*logN)
空间复杂度：O(N)
稳定性：稳定

代码实现

void PartMergeSort(int* a, int* tmp, int begin, int end)
{if (end <= begin)return;int mid = (begin + end) / 2;PartMergeSort(a, tmp, begin, mid);PartMergeSort(a, tmp, mid + 1, end);int begin1 = begin, end1 = mid;int begin2 = mid + 1, end2 = end;int count = begin;while (begin1 <= end1 && begin2 <= end2){if (a[begin1] < a[begin2])tmp[count++] = a[begin1++];elsetmp[count++] = a[begin2++];}while (begin1 <= end1){tmp[count++] = a[begin1++];}while (begin2 <= end2){tmp[count++] = a[begin2++];}memcpy(a + begin, tmp + begin, (end - begin + 1) * sizeof(int));
}void MergeSort(int* a, int n)
{int* tmp = malloc(sizeof(int) * n);if (tmp == NULL){perror("malloc fail");exit(-1);}PartMergeSort(a, tmp, 0, n - 1);free(tmp);
}void MergeSortNonR(int* a, int n)
{int* tmp = malloc(sizeof(int) * n);if (tmp == NULL){perror("malloc fail");exit(-1);}int gap = 1;while (gap < n){for (int i = 0; i < n; i += 2 * gap){int begin1 = i, end1 = i + gap - 1;int begin2 = i + gap, end2 = i + 2 * gap - 1;int count = i;if (begin2 >= n)break;if (end2 >= n)end2 = n - 1;while (begin1 <= end1 && begin2 <= end2){if (a[begin1] < a[begin2])tmp[count++] = a[begin1++];elsetmp[count++] = a[begin2++];}while (begin1 <= end1){tmp[count++] = a[begin1++];}while (begin2 <= end2){tmp[count++] = a[begin2++];}memcpy(a + i, tmp + i, (end2-i+1) * sizeof(int));}	gap *= 2;}
}

其中包含了递归及非递归实现方法

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八、计数排序

时间复杂度：O(N+range)
空间复杂度：O(range)

代码实现

void CountSort(int* a, int n)
{int min = a[0], max = a[0];for (size_t i = 0; i < n; i++){if (a[i] < min)min = a[i];if (a[i] > max)max = a[i];}int range = max - min + 1;int* count = (int*)malloc(sizeof(int) * range);printf("\nrange:%d\n", range);if (count == NULL){perror("malloc fail");return;}memset(count, 0, sizeof(int) * range);// 统计数据出现次数for (int i = 0; i < n; i++){count[a[i] - min]++;}// 排序int j = 0;for (int i = 0; i < range; i++){while (count[i]--){a[j++] = i + min;}}
}