十大排序算法精解与实战
堆排序的实现
堆排序基于二叉堆数据结构，通常使用数组实现。构建最大堆或最小堆后，通过反复提取堆顶元素完成排序。
构建最大堆的调整过程：
def heapify(arr, n, i):
largest = i
left = 2 * i + 1
right = 2 * i + 2
if left < n and arr[left] > arr[largest]:
largest = left
if right < n and arr[right] > arr[largest]:
largest = right
if largest != i:
arr[i], arr[largest] = arr[largest], arr[i]
heapify(arr, n, largest)
完整的堆排序算法：
def heap_sort(arr):
n = len(arr)
for i in range(n//2 - 1, -1, -1):
heapify(arr, n, i)
for i in range(n-1, 0, -1):
arr[0], arr[i] = arr[i], arr[0]
heapify(arr, i, 0)
计数排序的实现
计数排序适用于整数数据且范围不大的场景。统计每个元素出现次数后计算前缀和，确定元素最终位置。
实现步骤：
def counting_sort(arr):
max_val = max(arr)
count = [0] * (max_val + 1)
for num in arr:
count[num] += 1
for i in range(1, len(count)):
count[i] += count[i-1]
output = [0] * len(arr)
for num in reversed(arr):
output[count[num]-1] = num
count[num] -= 1
return output
桶排序的实现
桶排序将数据分到有限数量的桶中，每个桶单独排序后合并。适用于均匀分布的数据。
典型实现：
def bucket_sort(arr, bucket_size=5):
min_val, max_val = min(arr), max(arr)
bucket_count = (max_val - min_val) // bucket_size + 1
buckets = [[] for _ in range(bucket_count)]
for num in arr:
buckets[(num - min_val) // bucket_size].append(num)
return [num for bucket in buckets for num in sorted(bucket)]
基数排序的实现
基数排序按数字的每位进行排序，从最低位到最高位依次处理。需要稳定的子排序算法（通常用计数排序）。
LSD（最低位优先）实现：
def radix_sort(arr):
max_digits = len(str(max(arr)))
for digit in range(max_digits):
buckets = [[] for _ in range(10)]
for num in arr:
digit_val = (num // 10**digit) % 10
buckets[digit_val].append(num)
arr = [num for bucket in buckets for num in bucket]
return arr
性能对比与适用场景
堆排序时间复杂度稳定为O(n log n)，适合需要保证最坏情况性能的场景。计数排序在数据范围较小时效率可达O(n+k)。桶排序在数据分布均匀时性能优异。基数排序对数字位数固定的数据表现良好，时间复杂度为O(nk)。
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