STL源码剖析之数值算法<numeric.h>

一、accumulate

作用：初始化init，对区间[first，last）的迭代器i执行init += *i或init = binaryop（init，*i）。 

template <class _InputIterator, class _Tp>//版本1，用来计算init和[first，last)区间元素的总和
_Tp accumulate(_InputIterator __first, _InputIterator __last, _Tp __init)
{
  for ( ; __first != __last; ++__first)
    __init = __init + *__first;
  return __init;
}

template <class _InputIterator, class _Tp, class _BinaryOperation>//版本2，对迭代器中每一个元素时执行二元操作
_Tp accumulate(_InputIterator __first, _InputIterator __last, _Tp __init,
               _BinaryOperation __binary_op)
{
  for ( ; __first != __last; ++__first)
    __init = __binary_op(__init, *__first);
  return __init;
}

二、inner_product

作用：初始化init，对区间[first1，last1）和[first2，first2+（last1-first1））的两个迭代器i和j执行init += *i**j或init = binaryop1（init，binaryop1（*i，*j））。 

template <class _InputIterator1, class _InputIterator2, class _Tp>//版本1，两个迭代器元素的内积
_Tp inner_product(_InputIterator1 __first1, _InputIterator1 __last1,
                  _InputIterator2 __first2, _Tp __init)
{
  for ( ; __first1 != __last1; ++__first1, ++__first2)
    __init = __init + (*__first1 * *__first2);
  return __init;
}

template <class _InputIterator1, class _InputIterator2, class _Tp,
          class _BinaryOperation1, class _BinaryOperation2>  //版本2，两个迭代器的二元操作，提供operator+和operator*
_Tp inner_product(_InputIterator1 __first1, _InputIterator1 __last1,
                  _InputIterator2 __first2, _Tp __init, 
                  _BinaryOperation1 __binary_op1,
                  _BinaryOperation2 __binary_op2)
{
  for ( ; __first1 != __last1; ++__first1, ++__first2)
    __init = __binary_op1(__init, __binary_op2(*__first1, *__first2));
  return __init;
}

三、partial_num

作用：局部计算总和，*first赋值给*result，*first+*（first+1）赋值给*（result+1），依次类推，直至first==last。原始序列为[1,2,3,4,5],执行后得到[1,3,6,10,15]。

template <class _InputIterator, class _OutputIterator, class _Tp>
_OutputIterator 
__partial_sum(_InputIterator __first, _InputIterator __last,
              _OutputIterator __result, _Tp*)
{
  _Tp __value = *__first;
  while (++__first != __last) {
    __value = __value + *__first;
    *++__result = __value;//记录每次两个元素相加的值
  }
  return ++__result;
}
template <class _InputIterator, class _OutputIterator>//版本1
_OutputIterator 
partial_sum(_InputIterator __first, _InputIterator __last,
            _OutputIterator __result)
{
  if (__first == __last) return __result;//没有元素返回空
  *__result = *__first;//*first赋值给result第一个元素
  return __partial_sum(__first, __last, __result, __VALUE_TYPE(__first));//result从第二个元素开始记录两两相加的结果
}

template <class _InputIterator, class _OutputIterator, class _Tp,
          class _BinaryOperation>
_OutputIterator 
__partial_sum(_InputIterator __first, _InputIterator __last, 
              _OutputIterator __result, _Tp*, _BinaryOperation __binary_op)
{
  _Tp __value = *__first;
  while (++__first != __last) {
    __value = __binary_op(__value, *__first);//两两元素执行二元操作
    *++__result = __value;
  }
  return ++__result;
}

template <class _InputIterator, class _OutputIterator, class _BinaryOperation>//版本2
_OutputIterator 
partial_sum(_InputIterator __first, _InputIterator __last,
            _OutputIterator __result, _BinaryOperation __binary_op)
{
  if (__first == __last) return __result;
  *__result = *__first;
  return __partial_sum(__first, __last, __result, __VALUE_TYPE(__first), 
                       __binary_op);
}

四、adjacent_difference

作用：计算相邻元素的差。原始序列为[1,2,3,4,5],执行partial_num后得到[1,3,6,10,15],再执行adjacent_difference后得到[1,2,3,4,5]。

template <class _InputIterator, class _OutputIterator, class _Tp>
_OutputIterator 
__adjacent_difference(_InputIterator __first, _InputIterator __last,
                      _OutputIterator __result, _Tp*)
{
  _Tp __value = *__first;
  while (++__first != __last) {
    _Tp __tmp = *__first;
    *++__result = __tmp - __value;//计算相邻元素的差额
    __value = __tmp;
  }
  return ++__result;
}

template <class _InputIterator, class _OutputIterator>//版本1
_OutputIterator
adjacent_difference(_InputIterator __first,
                    _InputIterator __last, _OutputIterator __result)
{
  if (__first == __last) return __result;
  *__result = *__first;
  return __adjacent_difference(__first, __last, __result,
                               __VALUE_TYPE(__first));
}

template <class _InputIterator, class _OutputIterator, class _Tp, 
          class _BinaryOperation>
_OutputIterator
__adjacent_difference(_InputIterator __first, _InputIterator __last, 
                      _OutputIterator __result, _Tp*,
                      _BinaryOperation __binary_op) {
  _Tp __value = *__first;
  while (++__first != __last) {
    _Tp __tmp = *__first;
    *++__result = __binary_op(__tmp, __value);//相邻元素的二元操作
    __value = __tmp;
  }
  return ++__result;
}

template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
_OutputIterator 
adjacent_difference(_InputIterator __first, _InputIterator __last,
                    _OutputIterator __result, _BinaryOperation __binary_op)
{
  if (__first == __last) return __result;
  *__result = *__first;
  return __adjacent_difference(__first, __last, __result,
                               __VALUE_TYPE(__first),
                               __binary_op);
}

五、power（SGI专属，不在STL之列）

作用：指定元素的n次方

template <class _Tp, class _Integer>
inline _Tp __power(_Tp __x, _Integer __n)
{
  return __power(__x, __n, multiplies<_Tp>());//指定操作为乘法，则为乘幂
}
template <class _Tp, class _Integer, class _MonoidOperation>//幂次方
inline _Tp power(_Tp __x, _Integer __n, _MonoidOperation __opr)
{
  return __power(__x, __n, __opr);
}

template <class _Tp, class _Integer>
inline _Tp power(_Tp __x, _Integer __n)
{
  return __power(__x, __n);
}

六、itoa（SGI专属，不在STL之列）

作用：设定某个区间内容

template <class _ForwardIter, class _Tp>
void 
iota(_ForwardIter __first, _ForwardIter __last, _Tp __value)
{
  while (__first != __last)
    *__first++ = __value++;
}