1. 冒泡排序 (Bubble Sort)
python
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def bubble_sort(arr):
n = len(arr)
# 遍历数组中的每个元素
for i in range(n):
# 内层循环，从数组的第一个元素到倒数第 i + 1 个元素
for j in range(0, n - i - 1):
# 如果当前元素比下一个元素大，则交换
if arr[j] > arr[j + 1]:
arr[j], arr[j + 1] = arr[j + 1], arr[j]
return arr
2. 选择排序 (Selection Sort)
python
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def selection_sort(arr):
n = len(arr)
# 遍历数组中的每个元素
for i in range(n):
# 假设当前元素是最小值
min_idx = i
# 通过内层循环找到最小值的索引
for j in range(i + 1, n):
if arr[j] < arr[min_idx]:
min_idx = j
# 交换当前元素和找到的最小值
arr[i], arr[min_idx] = arr[min_idx], arr[i]
return arr
3. 插入排序 (Insertion Sort)
python
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def insertion_sort(arr):
# 从第二个元素开始遍历数组
for i in range(1, len(arr)):
key = arr[i]
j = i - 1
# 将当前元素插入到已排序部分的正确位置
while j >= 0 and key < arr[j]:
arr[j + 1] = arr[j]
j -= 1
arr[j + 1] = key
return arr
4. 归并排序 (Merge Sort)
python
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def merge_sort(arr):
if len(arr) > 1:
mid = len(arr) // 2 # 找到数组的中间点
L = arr[:mid] # 将数组分成两部分
R = arr[mid:]
merge_sort(L) # 递归排序左半部分
merge_sort(R) # 递归排序右半部分
i = j = k = 0
# 合并两个已排序的子数组
while i < len(L) and j < len(R):
if L[i] < R[j]:
arr[k] = L[i]
i += 1
else:
arr[k] = R[j]
j += 1
k += 1
# 检查是否还有剩余的元素
while i < len(L):
arr[k] = L[i]
i += 1
k += 1
while j < len(R):
arr[k] = R[j]
j += 1
k += 1
return arr
5. 快速排序 (Quick Sort)
python
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def quick_sort(arr):
if len(arr) <= 1:
return arr
pivot = arr[len(arr) // 2] # 选择数组的中间元素作为基准
left = [x for x in arr if x < pivot] # 所有小于基准的元素
middle = [x for x in arr if x == pivot] # 所有等于基准的元素
right = [x for x in arr if x > pivot] # 所有大于基准的元素
return quick_sort(left) + middle + quick_sort(right)
6. 堆排序 (Heap Sort)
python
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def heapify(arr, n, i):
largest = i # 假设当前节点是最大值
l = 2 * i + 1 # 左子节点
r = 2 * i + 2 # 右子节点
# 如果左子节点存在且大于当前节点
if l < n and arr[i] < arr[l]:
largest = l
# 如果右子节点存在且大于当前最大值
if r < n and arr[largest] < arr[r]:
largest = r
# 如果最大值不是当前节点
if largest != i:
arr[i], arr[largest] = arr[largest], arr[i] # 交换
heapify(arr, n, largest) # 递归堆化受影响的子树
def heap_sort(arr):
n = len(arr)
# 构建最大堆
for i in range(n // 2 - 1, -1, -1):
heapify(arr, n, i)
# 一个个提取元素
for i in range(n - 1, 0, -1):
arr[i], arr[0] = arr[0], arr[i] # 交换
heapify(arr, i, 0)
return arr
7. 希尔排序 (Shell Sort)
python
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def shell_sort(arr):
n = len(arr)
gap = n // 2
while gap > 0:
for i in range(gap, n):
temp = arr[i]
j = i
# 插入排序
while j >= gap and arr[j - gap] > temp:
arr[j] = arr[j - gap]
j -= gap
arr[j] = temp
gap //= 2
return arr
8. 计数排序 (Counting Sort)
python
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def counting_sort(arr):
max_val = max(arr)
m = max_val + 1
count = [0] * m
# 统计每个元素的个数
for a in arr:
count[a] += 1
i = 0
for a in range(m):
for c in range(count[a]):
arr[i] = a
i += 1
return arr
9. 基数排序 (Radix Sort)
python
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def counting_sort_for_radix(arr, exp):
n = len(arr)
output = [0] * n
count = [0] * 10
# 统计每个基数的个数
for i in range(n):
index = arr[i] // exp
count[index % 10] += 1
for i in range(1, 10):
count[i] += count[i - 1]
i = n - 1
while i >= 0:
index = arr[i] // exp
output[count[index % 10] - 1] = arr[i]
count[index % 10] -= 1
i -= 1
for i in range(n):
arr[i] = output[i]
def radix_sort(arr):
max_val = max(arr)
exp = 1
while max_val // exp > 0:
counting_sort_for_radix(arr, exp)
exp *= 10
return arr
10. 桶排序 (Bucket Sort)
python
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def bucket_sort(arr):
if len(arr) == 0:
return arr
bucket = []
slot_num = 10 # 桶的数量
for i in range(slot_num):
bucket.append([])
# 将元素分配到不同的桶中
for j in arr:
index = int(slot_num * j)
bucket[index].append(j)
# 对每个桶中的元素进行排序
for i in range(slot_num):
bucket[i] = insertion_sort(bucket[i])
k = 0
for i in range(slot_num):
for j in range(len(bucket[i])):
arr[k] = bucket[i][j]
k += 1
return arr
11. Tim Sort (Tim Sort)
python
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MIN_MERGE = 32
def calc_min_run(n):
r = 0
while n >= MIN_MERGE:
r |= n & 1
n >>= 1
return n + r
def insertion_sort_for_timsort(arr, left, right):
for i in range(left + 1, right + 1):
temp = arr[i]
j = i - 1
while j >= left and arr[j] > temp:
arr[j + 1] = arr[j]
j -= 1
arr[j + 1] = temp
def merge_for_timsort(arr, l, m, r):
len1, len2 = m - l + 1, r - m
left, right = [], []
for i in range(0, len1):
left.append(arr[l + i])
for i in range(0, len2):
right.append(arr[m + 1 + i])
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