2.2.19 #

/// <summary>
/// 归并排序类。
/// </summary>
public class MergeSort : BaseSort
{
    public int Counter;

    /// <summary>
    /// 利用归并排序将数组按升序排序。
    /// </summary>
    /// <typeparam name="T">数组元素类型。</typeparam>
    /// <param name="a">待排序的数组。</param>
    public override void Sort<T>(T[] a)
    {
        var aux = new T[a.Length];
        Sort(a, aux, 0, a.Length - 1);
    }

    /// <summary>
    /// 自顶向下地对数组指定范围内进行归并排序，需要辅助数组。
    /// </summary>
    /// <typeparam name="T">需要排序的元素类型。</typeparam>
    /// <param name="a">原数组。</param>
    /// <param name="aux">辅助数组。</param>
    /// <param name="lo">排序范围起点。</param>
    /// <param name="hi">排序范围终点。</param>
    private void Sort<T>(T[] a, T[] aux, int lo, int hi) where T : IComparable<T>
    {
        if (hi <= lo)
            return;
        var mid = lo + (hi - lo) / 2;
        Sort(a, aux, lo, mid);
        Sort(a, aux, mid + 1, hi);
        Merge(a, aux, lo, mid, hi);
    }

    /// <summary>
    /// 将指定范围内的元素归并。
    /// </summary>
    /// <typeparam name="T">数组元素类型。</typeparam>
    /// <param name="a">原数组。</param>
    /// <param name="aux">辅助数组。</param>
    /// <param name="lo">范围起点。</param>
    /// <param name="mid">范围中点。</param>
    /// <param name="hi">范围终点。</param>
    private void Merge<T>(T[] a, T[] aux, int lo, int mid, int hi) where T : IComparable<T>
    {
        for (var k = lo; k <= hi; k++)
        {
            aux[k] = a[k];
        }

        int i = lo, j = mid + 1;
        for (var k = lo; k <= hi; k++)
        {
            if (i > mid)
            {
                a[k] = aux[j];
                j++;
            }
            else if (j > hi)
            {
                a[k] = aux[i];
                i++;
            }
            else if (Less(aux[j], aux[i]))
            {
                a[k] = aux[j];
                Counter += mid - i + 1;    // 统计逆序对数
                j++;
            }
            else
            {
                a[k] = aux[i];
                i++;
            }
        }
    }
}