有效的中值计算

Question

我有一个长度为n的数组A。设B是一个包含A的每个第k个元素的数组（我们从不想单独存储 - 这只是为了帮助解释）。我想要找到B的中位数，并且我想将A的元素移动到地板（n/2）'的位置。

我该如何有效地做到这一点？我正试图对std :: nth_element进行一次调用，并将指针传递给A.但是，我需要这个指针来增加k个元素A.我该怎么做？基本上：

A2 = (kFloat *)A; 
std::nth_element(A2, A2 + (n/k)/2, A2 + (n/k)); 
swap(A[ ((n/k)/2)*k ], A[n/2]); // This might be redundant 

其中kFloat将是就像一个浮动的结构，但是当你递增指针它在存储器中移动K *的sizeof（浮点）。

注意：我不需要真正的中位数（当n是偶数时，中间两位的平均值）。

编辑：说我想要什么（不编译，因为不是k为常数）的另一种方式：

std::nth_element((float[k] *)A, ((float[k] *) A)[(n/k)/2], ((float[k] *) A)[n/k]); 

编辑2：我改变algorithm.cc，所以我不想在像Boost这样的库上引入依赖关系。我想仅使用核心C++ 11功能+ std。

Answer 1

对于将来有这个问题的其他人，我修改了algorithm.cc中的一些函数以包含一个stride参数。他们中的很多人都认为_First和_Last跨度很大，所以我不建议打电话给他们。但是，您可以调用下面的函数：

// Same as _Nth_element, but increments pointers by strides of k 
// Takes n, rather than last (needed to avoid confusion about what last should be [see line that computes _Last to see why] 
// _First = pointer to start of the array 
// _Nth = pointer to the position that we want to find the element for (if it were sorted). 
//   This position should be = _First + k*x, for some integer x. That is, it should be a multiple of k. 
// n = Length of array, _First, in primitive type (not length/k). 
// _Pred = comparison operator. Typically use less<>() 
// k = integer specifying the stride. If k = 10, we consider elements 0, 10, 20... only. 
template<class _RanIt, class intType, class _Pr> inline 
void _Nth_element_strided(_RanIt _First, _RanIt _Nth, intType n, _Pr _Pred, intType k); 

调用这个函数，你需要包含这个头：

#ifndef _NTH_ELEMENT_STRIDED_H_ 
#define _NTH_ELEMENT_STRIDED_H_ 

template<class _RanIt, class intType, class _Pr> inline 
void _Median_strided(_RanIt _First, _RanIt _Mid, _RanIt _Last, _Pr _Pred, intType k) { 
    // sort median element to middle 
    if (40 < (_Last - _First)/k) { 
     // median of nine 
     size_t _Step = k * ((_Last - _First + k)/(k*8)); 
     _Med3(_First, _First + _Step, _First + 2 * _Step, _Pred); 
     _Med3(_Mid - _Step, _Mid, _Mid + _Step, _Pred); 
     _Med3(_Last - 2 * _Step, _Last - _Step, _Last, _Pred); 
     _Med3(_First + _Step, _Mid, _Last - _Step, _Pred); 
    } 
    else 
     _Med3(_First, _Mid, _Last, _Pred); 
} 

// Same as _Unguarded_partition, except it increments pointers by k. 
template<class _RanIt, class _Pr, class intType> inline 
pair<_RanIt, _RanIt> _Unguarded_partition_strided(_RanIt _First, _RanIt _Last, _Pr _Pred, intType k) { 
    // partition [_First, _Last), using _Pred 
    _RanIt _Mid = _First + (((_Last - _First)/k)/2)*k; 
    _Median_strided(_First, _Mid, _Last - k, _Pred, k); 
    _RanIt _Pfirst = _Mid; 
    _RanIt _Plast = _Pfirst + k; 

    while (_First < _Pfirst 
     && !_DEBUG_LT_PRED(_Pred, *(_Pfirst - k), *_Pfirst) 
     && !_Pred(*_Pfirst, *(_Pfirst - k))) 
     _Pfirst -= k; 
    while (_Plast < _Last 
     && !_DEBUG_LT_PRED(_Pred, *_Plast, *_Pfirst) 
     && !_Pred(*_Pfirst, *_Plast)) 
     _Plast += k; 

    _RanIt _Gfirst = _Plast; 
    _RanIt _Glast = _Pfirst; 

    for (;;) { 
     // partition 
     for (; _Gfirst < _Last; _Gfirst += k) { 
      if (_DEBUG_LT_PRED(_Pred, *_Pfirst, *_Gfirst)) 
       ; 
      else if (_Pred(*_Gfirst, *_Pfirst)) 
       break; 
      else if (_Plast != _Gfirst) { 
       _STD iter_swap(_Plast, _Gfirst); 
       _Plast += k; 
      } 
      else 
       _Plast += k; 
     } 
     for (; _First < _Glast; _Glast -= k) { 
      if (_DEBUG_LT_PRED(_Pred, *(_Glast - k), *_Pfirst)) 
       ; 
      else if (_Pred(*_Pfirst, *(_Glast - k))) 
       break; 
      else { 
       _Pfirst -= k; 
       if (_Pfirst != _Glast - k) 
        _STD iter_swap(_Pfirst, _Glast - k); 
      } 
     } 

     if (_Glast == _First && _Gfirst == _Last) 
      return (pair<_RanIt, _RanIt>(_Pfirst, _Plast)); 

     if (_Glast == _First) { 
      // no room at bottom, rotate pivot upward 
      if (_Plast != _Gfirst) 
       _STD iter_swap(_Pfirst, _Plast); 
      _Plast += k; 
      _STD iter_swap(_Pfirst, _Gfirst); 
      _Pfirst += k; 
      _Gfirst += k; 
     } 
     else if (_Gfirst == _Last) { 
      // no room at top, rotate pivot downward 
      _Glast -= k; 
      _Pfirst -= k; 
      if (_Glast != _Pfirst) 
       _STD iter_swap(_Glast, _Pfirst); 
      _Plast -= k; 
      _STD iter_swap(_Pfirst, _Plast); 
     } 
     else { 
      _Glast -= k; 
      _STD iter_swap(_Gfirst, _Glast); 
      _Gfirst += k; 
     } 
    } 
} 

// TEMPLATE FUNCTION move_backward 
template<class _BidIt1, class _BidIt2, class intType> inline 
_BidIt2 _Move_backward_strided(_BidIt1 _First, _BidIt1 _Last, _BidIt2 _Dest, intType k) { 
    // move [_First, _Last) backwards to [..., _Dest), arbitrary iterators 
    while (_First != _Last) { 
     _Dest -= k; 
     _Last -= k; 
     *_Dest = _STD move(*_Last); 
    } 
    return (_Dest); 
} 

template<class _BidIt, class _Pr, class intType, class _Ty> inline 
void _Insertion_sort1_strided(_BidIt _First, _BidIt _Last, _Pr _Pred, _Ty *, intType k) { 
    // insertion sort [_First, _Last), using _Pred 
    if (_First != _Last) { 
     for (_BidIt _Next = _First + k; _Next != _Last;) { 
      // order next element 
      _BidIt _Next1 = _Next; 
      _Ty _Val = _Move(*_Next); 

      if (_DEBUG_LT_PRED(_Pred, _Val, *_First)) { 
       // found new earliest element, move to front 
       _Next1 += k; 
       _Move_backward_strided(_First, _Next, _Next1, k); 
       *_First = _Move(_Val); 
      } 
      else { 
       for (_BidIt _First1 = _Next1 - k; _DEBUG_LT_PRED(_Pred, _Val, *_First1);) { 
        *_Next1 = _Move(*_First1); // move hole down 

        _Next1 = _First1; 
        _First1 -= k; 
       } 
       *_Next1 = _Move(_Val); // insert element in hole 
      } 
      _Next += k; 
     } 
    } 
} 

// _Last should point to the last element being considered (the last k'th element), plus k. 
template<class _BidIt, class intType, class _Pr> inline 
void _Insertion_sort_strided(_BidIt _First, _BidIt _Last, _Pr _Pred, intType k) { 
    // insertion sort [_First, _Last), using _Pred 
    _Insertion_sort1_strided(_First,_Last, _Pred, _Val_type(_First), k); 
} 

// Same as _Nth_element, but increments pointers by strides of k 
// Takes n, rather than last (needed to avoid confusion about what last should be [see first line below] 
// _First = pointer to start of the array 
// _Nth = pointer to the position that we want to find the element for (if it were sorted). 
//   This position should be = _First + k*x, for some integer x. That is, it should be a multiple of k. 
// n = Length of array, _First, in primitive type (not length/k). 
// _Pred = comparison operator. Typically use less<>() 
// k = integer specifying the stride. If k = 10, we consider elements 0, 10, 20... only. 
template<class _RanIt, class intType, class _Pr> inline 
void _Nth_element_strided(_RanIt _First, _RanIt _Nth, intType n, _Pr _Pred, intType k) { 

    _RanIt _Last = (n % k == 0 ? _First + n : _First + (n/k + 1)*k); 
    // order Nth element, using _Pred 
    for (; _ISORT_MAX < (_Last - _First)/k;) { 
     // divide and conquer, ordering partition containing Nth 
     pair<_RanIt, _RanIt> _Mid = _Unguarded_partition_strided(_First, _Last, _Pred, k); 

     if (_Mid.second <= _Nth) 
      _First = _Mid.second; 
     else if (_Mid.first <= _Nth) 
      return; // Nth inside fat pivot, done 
     else 
      _Last = _Mid.first; 
    } 

    _Insertion_sort_strided(_First, _Last, _Pred, k); // sort any remainder 
} 

#endif 

使用此功能的一个例子：

for (int counter = 0; true; counter++) { 
     // Test strided methods 
     int n = (rand() % 10000) + 1; 
     int k = (rand() % n) + 1; 
     int * a = new int[n]; 
     int bLen = (n % k == 0 ? n/k : n/k + 1); 
     int * b = new int[bLen]; 
     for (int i = 0; i < n; i++) // Initialize randomly 
      a[i] = rand() % 100; 
     for (int i = 0; i < bLen; i++) 
      b[i] = a[i*k]; 

     int index = rand() % (bLen); // Random index! 
     _Nth_element(b, b + index, b + bLen, less<>()); 
     _Nth_element_strided(a, a + index*k, n, less<>(), k); 

     if (b[index] != a[index*k]) { 
      cout << "Not equal!" << endl; 
      cout << b[index] << '\t' << a[index*k] << endl; 
      getchar(); 
     } 
     else 
      cout << counter << endl; 
    } 

Answer 2

我已经对自定义迭代器实现了一次二进制搜索 - 您可以在https://gist.github.com/IvanVergiliev/6048716处进行检查。这是针对特定问题的，但总体思路是相同的：在您的序列上编写迭代器类并实现所需的运算符（++， - ，+ =）以一次移动k个位置。