计算在给定范围内具有重复元素的数组排序所需的最小交换的算法？

def min_swaps_to_sort(arr):
    n = len(arr)
    count = {}  # 统计元素出现次数
    for num in arr:
        if num in count:
            count[num] += 1
        else:
            count[num] = 1
    
    sorted_arr = sorted(arr)  # 排序数组
    positions = {}  # 记录元素初始位置
    for i in range(n):
        if sorted_arr[i] not in positions:
            positions[sorted_arr[i]] = i
    
    swaps = 0  # 最小交换次数
    visited = [False] * n  # 记录元素是否已经被访问过
    for i in range(n):
        if visited[i] or count[arr[i]] == 1:
            continue
        
        cycle_size = 0  # 循环大小
        j = i
        while not visited[j]:
            visited[j] = True
            j = positions[arr[j]]
            cycle_size += 1
        
        swaps += cycle_size - 1
    
    return swaps

# 示例用法
arr = [4, 2, 4, 2, 1, 3, 4, 2]
min_swaps = min_swaps_to_sort(arr)
print("最小交换次数：", min_swaps)