STL算法-数值算法

template <class InputIterator, class T>
T accumulate(InputIterator first, InputIterator last, T init) {
  for ( ; first != last; ++first)
    init = init + *first;
  return init;
}

template <class InputIterator, class T, class BinaryOperation>
T accumulate(InputIterator first, InputIterator last, T init,
             BinaryOperation binary_op) {
  for ( ; first != last; ++first)
    init = binary_op(init, *first);
  return init;
}

template <class InputIterator1, class InputIterator2, class T>
T inner_product(InputIterator1 first1, InputIterator1 last1,
                InputIterator2 first2, T init) {
  for ( ; first1 != last1; ++first1, ++first2)
    init = init + (*first1 * *first2);
  return init;
}

template <class InputIterator1, class InputIterator2, class T,
          class BinaryOperation1, class BinaryOperation2>
T inner_product(InputIterator1 first1, InputIterator1 last1,
                InputIterator2 first2, T init, BinaryOperation1 binary_op1,
                BinaryOperation2 binary_op2) {
  for ( ; first1 != last1; ++first1, ++first2)
    init = binary_op1(init, binary_op2(*first1, *first2));
  return init;
}

template <class InputIterator, class OutputIterator, class T>
OutputIterator __partial_sum(InputIterator first, InputIterator last,
                             OutputIterator result, T*) {
  T value = *first;
  while (++first != last) {
    value = value + *first;
    *++result = value;
  }
  return ++result;
}

template <class InputIterator, class OutputIterator>
OutputIterator partial_sum(InputIterator first, InputIterator last,
                           OutputIterator result) {
  if (first == last) return result;
  *result = *first;
  return __partial_sum(first, last, result, value_type(first));
}

template <class InputIterator, class OutputIterator, class T,
          class BinaryOperation>
OutputIterator __partial_sum(InputIterator first, InputIterator last,
                             OutputIterator result, T*,
                             BinaryOperation binary_op) {
  T value = *first;
  while (++first != last) {
    value = binary_op(value, *first);
    *++result = value;
  }
  return ++result;
}

template <class InputIterator, class OutputIterator, class BinaryOperation>
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);
}

template <class InputIterator, class OutputIterator, class T>
OutputIterator __adjacent_difference(InputIterator first, InputIterator last, 
                                     OutputIterator result, T*) {
  T value = *first;
  while (++first != last) {
    T tmp = *first;
    *++result = tmp - value;
    value = tmp;
  }
  return ++result;
}

template <class InputIterator, class OutputIterator>
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 T, 
          class BinaryOperation>
OutputIterator __adjacent_difference(InputIterator first, InputIterator last, 
                                     OutputIterator result, T*,
                                     BinaryOperation binary_op) {
  T value = *first;
  while (++first != last) {
    T tmp = *first;
    *++result = binary_op(tmp, value);
    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);
}

// Returns x ** n, where n >= 0.  Note that "multiplication"
//  is required to be associative, but not necessarily commutative.
    
template <class T, class Integer, class MonoidOperation>
T power(T x, Integer n, MonoidOperation op) {
  if (n == 0)
    return identity_element(op);
  else {
    while ((n & 1) == 0) {
      n >>= 1;
      x = op(x, x);
    }

    T result = x;
    n >>= 1;
    while (n != 0) {
      x = op(x, x);
      if ((n & 1) != 0)
        result = op(result, x);
      n >>= 1;
    }
    return result;
  }
}

template <class T, class Integer>
inline T power(T x, Integer n) {
  return power(x, n, multiplies<T>());
}


template <class ForwardIterator, class T>
void iota(ForwardIterator first, ForwardIterator last, T value) {
  while (first != last) *first++ = value++;
}