算法导论归并排序那块的一道思考题：
1.merge的时候统计逆序数的个数。
#include < iostream >
using   namespace  std;
 int  a[ 1000 ];
 int  cnt;
 int  merge( int  a[], int  p, int  q, int  z)
{   
     int  l[ 1000 ],r[ 1000 ];
    l[ 0 ] = q - p + 1 ;
    r[ 0 ] = z - q;
    l[l[ 0 ] + 1 ] = 0x7fffffff ;
    r[r[ 0 ] + 1 ] = 0x7fffffff ;
     int  i,j,k;
     for (i = 1 ;i <= l[ 0 ];i ++ )
    {
        l[i] = a[p + i - 1 ];
    }
     for (j = 1 ;j <= r[ 0 ];j ++ )
    {
        r[j] = a[q + j];
    }
    i = 1 ;
    j = 1 ;
     for (k = p;k <= z;k ++ )
    {   
         if (l[i] <= r[j])
            a[k] = l[i ++ ];
         else
        {   
            a[k] = r[j ++ ];
            cnt += (l[ 0 ] - i + 1 );
        }
    }
     return   0 ;
}
 int  mergesort( int  a[], int  p, int  q)
{
     if (p >= q)
         return   0 ;
     else  
    {
         int  mid = (p + q) >> 1 ;
        mergesort(a,p,mid);
        mergesort(a,mid + 1 ,q);
        merge(a,p,mid,q);
    }
     return   0 ;
}

 int  main()
{   
     int  n;
     int  i;
    printf( " 输入待排序的数字个数：\n " ); 
    scanf( " %d " , & n);
    printf( " 输入待排序数组:\n " );
     for ( int  i = 1 ;i <= n;i ++ )
        scanf( " %d " , & a[i]);
    printf( " 待排序数组：\n " );
     for (i = 1 ;i <= n;i ++ )
    {
        printf( " %d  " ,a[i]);
    }
    printf( " \n " );
    mergesort(a, 1 ,n);
    printf( " 已排序数组：\n " );
     for (i = 1 ;i <= n;i ++ )
    {
        printf( " %d  " ,a[i]);
    }
    printf( " \n逆序数为： " );
    printf( " %d\n " ,cnt);
    system( " pause " );
     return   0 ;
}
2.离散化，扫描原始数列，若已插入某数字，设某数字离散化的位置为t，则t的cnt+1，维护树状数组。每次cnt+1之前之前算一下sum[n]-sum[t](n为离散化后数组中元素的个数)，然后插入。
//PKU 2299
#include < iostream >
#include < algorithm >
#define  N 500010
using   namespace  std;
 int  c[N];
 int  a[N];
 int  b[N];
 int  n;
 int  num = 1 ;
 int  lowbit( int  t)
{
     return  t & (t ^ (t - 1 ));
}
 int  getsum( int  t)
{
     int  sum = 0 ;
     for ( int  i = t;i > 0 ;i -= lowbit(i))
        sum += c[i];
     return  sum;
}
 void  update( int  t)
{
     for ( int  i = t;i <= num;i += lowbit(i))
        c[i] ++ ;
}
 int  search( int  i)
{
     int  mid,l = 1 ,r = num;
     while (l <= r)
    {
        mid = (l + r) / 2 ;
         if (a[mid] == i)
             return  mid;
         else   if (a[mid] > i)
            r = mid - 1 ;
         else  l = mid + 1 ;
    }
}
 int  main()
{
     while (scanf( " %d " , & n) != EOF && n)
    {
         for ( int  i = 1 ;i <= n;i ++ )
        {
            scanf( " %d " , & a[i]);
            b[i] = a[i];
        }
        num = 1 ;
        sort(a + 1 ,a + 1 + n);
         for ( int  i = 2 ;i <= n;i ++ )
        {
             if (a[i] != a[i - 1 ])
                a[ ++ num] = a[i];
        }
        memset(c, 0 , sizeof (c));
         long   long  sum = 0 ;
        update(search(b[ 1 ]));
         for ( int  i = 2 ;i <= n;i ++ )
        {
             int  t = search(b[i]);
            sum += getsum(num) - getsum(t);
            update(t);
        }
        printf( " %lld\n " ,sum);
    }
    
}