python逆序对计数问题

逆序对计数问题是指在一个序列中，找出所有满足条件ai > aj (i < j)的数对(ai, aj)，并统计数对的个数。下面是一个Python实现的例子：

def merge_sort(arr):
    if len(arr) <= 1:
        return arr, 0
    mid = len(arr) // 2
    left, count_left = merge_sort(arr[:mid])
    right, count_right = merge_sort(arr[mid:])
    merged, count_merge = merge(left, right)
    return merged, count_left + count_right + count_merge

def merge(left, right):
    merged = []
    count = 0
    i, j = 0, 0
    while i < len(left) and j < len(right):
        if left[i] <= right[j]:
            merged.append(left[i])
            i += 1
        else:
            merged.append(right[j])
            count += len(left) - i
            j += 1
    merged.extend(left[i:])
    merged.extend(right[j:])
    return merged, count

# 示例
arr = [7, 5, 6, 4]
sorted_arr, count = merge_sort(arr)
print("逆序对个数：", count)  # 输出：5

这个例子使用了归并排序的思想来解决逆序对计数问题。归并排序的时间复杂度为O(nlogn)，因此该算法的时间复杂度也是O(nlogn)。