数值算法stl_numeric.h
最后更新于：2022-04-01 15:51:18
### 前言
在STL中，算法是独立于特定的数据结构，称为泛型算法。本节介绍的数值算法是在源码SGI STL中的<stl_numeric.h>文件，具体功能详见下面的源码剖析，在源码剖析的时候，针对每个元素都给出了使用例子，这样可以增加对其理解。
### numeric数值算法源码剖析
~~~
#ifndef __SGI_STL_INTERNAL_NUMERIC_H
#define __SGI_STL_INTERNAL_NUMERIC_H
__STL_BEGIN_NAMESPACE
/*
sum (1) :The default operation is to add the elements up;
这个版本的默认操作时累加；
template <class InputIterator, class T>
T accumulate (InputIterator first, InputIterator last, T init);
custom (2): a different operation can be specified as binary_op;
这个版本的操作可以是用户通过binary_op自行指定；指定函数在<stl_function.h>定义，也可自己定义
template <class InputIterator, class T, class BinaryOperation>
T accumulate (InputIterator first, InputIterator last, T init,
BinaryOperation binary_op);
*/
//第一个版本：默认操作是累加
//计算[first,last)区间元素与init的和
//返回一个副本
template <class _InputIterator, class _Tp>
_Tp accumulate(_InputIterator __first, _InputIterator __last, _Tp __init)
{
__STL_REQUIRES(_InputIterator, _InputIterator);
for ( ; __first != __last; ++__first)//遍历指定范围元素
__init = __init + *__first;//将每个元素累加到初始值init上
return __init;
}
//第二个版本：用户可自行指定二元操作函数
template <class _InputIterator, class _Tp, class _BinaryOperation>
_Tp accumulate(_InputIterator __first, _InputIterator __last, _Tp __init,
_BinaryOperation __binary_op)
{
__STL_REQUIRES(_InputIterator, _InputIterator);
for ( ; __first != __last; ++__first)//遍历指定范围元素
__init = __binary_op(__init, *__first);//对每个元素执行二元操作
return __init;
}
//下面举例子：
/*accumulate example:
#include <iostream> // std::cout
#include <functional> // std::minus
#include <numeric> // std::accumulate
int myfunction (int x, int y) {return x+2*y;}
struct myclass {
int operator()(int x, int y) {return x+3*y;}
} myobject;
int main () {
int init = 100;
int numbers[] = {10,20,30};
std::cout << "using default accumulate: ";
std::cout << std::accumulate(numbers,numbers+3,init);
std::cout << '\n';
std::cout << "using functional's minus: ";
std::cout << std::accumulate (numbers, numbers+3, init, std::minus<int>());
std::cout << '\n';
std::cout << "using custom function: ";
std::cout << std::accumulate (numbers, numbers+3, init, myfunction);
std::cout << '\n';
std::cout << "using custom object: ";
std::cout << std::accumulate (numbers, numbers+3, init, myobject);
std::cout << '\n';
return 0;
}
Output:
using default accumulate: 160
using functional's minus: 40
using custom function: 220
using custom object: 280
*/
/*默认操作是把内积(相乘)的值与初始值init相加
用户可以自行指定操作类型
sum/multiply (1)
template <class InputIterator1, class InputIterator2, class T>
T inner_product (InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, T init);
custom (2)
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);
*/
//描述：The two default operations (to add up the result of multiplying the pairs)
//may be overridden by the arguments binary_op1 and binary_op2.
//功能：Returns the result of accumulating init with the inner products of the pairs
//formed by the elements of two ranges starting at first1 and first2.
//版本一：使用默认操作
template <class _InputIterator1, class _InputIterator2, class _Tp>
_Tp inner_product(_InputIterator1 __first1, _InputIterator1 __last1,
_InputIterator2 __first2, _Tp __init)
{
__STL_REQUIRES(_InputIterator2, _InputIterator);
__STL_REQUIRES(_InputIterator2, _InputIterator);
//以第一个序列的元素个数为据，将两个序列都走一遍
for ( ; __first1 != __last1; ++__first1, ++__first2)、
__init = __init + (*__first1 * *__first2);//执行两个序列的内积与初始值init相加
return __init;
}
//版本二：用户可自行指定二元操作函数
template <class _InputIterator1, class _InputIterator2, class _Tp,
class _BinaryOperation1, class _BinaryOperation2>
_Tp inner_product(_InputIterator1 __first1, _InputIterator1 __last1,
_InputIterator2 __first2, _Tp __init,
_BinaryOperation1 __binary_op1,
_BinaryOperation2 __binary_op2)
{
__STL_REQUIRES(_InputIterator2, _InputIterator);
__STL_REQUIRES(_InputIterator2, _InputIterator);
//以第一个序列的元素个数为据，将两个序列都走一遍
for ( ; __first1 != __last1; ++__first1, ++__first2)
//首先指定__binary_op2操作，再指定__binary_op1操作
__init = __binary_op1(__init, __binary_op2(*__first1, *__first2));
return __init;
}
//下面举例子：
/*inner_product example:
#include <iostream> // std::cout
#include <functional> // std::minus, std::divides
#include <numeric> // std::inner_product
int myaccumulator (int x, int y) {return x-y;}
int myproduct (int x, int y) {return x+y;}
int main () {
int init = 10;
int series1[] = {10,20,30};
int series2[] = {1,2,3};
std::cout << "using default inner_product: ";
std::cout << std::inner_product(series1,series1+3,series2,init);
std::cout << '\n';
std::cout << "using functional operations: ";
std::cout << std::inner_product(series1,series1+3,series2,init,
std::minus<int>(),std::divides<int>());
std::cout << '\n';
std::cout << "using custom functions: ";
std::cout << std::inner_product(series1,series1+3,series2,init,
myaccumulator,myproduct);
std::cout << '\n';
return 0;
}
Output:
using default inner_product: 150
using functional operations: -20
using custom functions: -56
*/
//局部求和
/*功能与描述：
Assigns to every element in the range starting at result the partial sum of
the corresponding elements in the range [first,last).
If x represents an element in [first,last) and y represents an element in result, the ys can be calculated as:
y0 = x0
y1 = x0 + x1
y2 = x0 + x1 + x2
y3 = x0 + x1 + x2 + x3
y4 = x0 + x1 + x2 + x3 + x4
... ... ...
*/
/*版本一：默认操作是：The default operation is to add the elements up;
sum (1)
template <class InputIterator, class OutputIterator>
OutputIterator partial_sum (InputIterator first, InputIterator last,
OutputIterator result);
版本二：用户可以自行指定二元操作：operation can be specified as binary_op instead.
custom (2)
template <class InputIterator, class OutputIterator, class BinaryOperation>
OutputIterator partial_sum (InputIterator first, InputIterator last,
OutputIterator result, BinaryOperation binary_op);
*/
//版本一：默认操作函数
template <class _InputIterator, class _OutputIterator, class _Tp>
_OutputIterator
__partial_sum(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _Tp*)
{
_Tp __value = *__first;
while (++__first != __last) {//遍历区间元素
__value = __value + *__first;//区间前n个元素的总和
*++__result = __value;//把元素赋给输出端
}
return ++__result;
}
template <class _InputIterator, class _OutputIterator>
_OutputIterator
partial_sum(_InputIterator __first, _InputIterator __last,
_OutputIterator __result)
{
__STL_REQUIRES(_InputIterator, _InputIterator);
__STL_REQUIRES(_OutputIterator, _OutputIterator);
if (__first == __last) return __result;//若为空
*__result = *__first;//初始值
//调用上面的函数，萃取出first的类型方便上面函数使用
return __partial_sum(__first, __last, __result, __VALUE_TYPE(__first));
}
//版本二：用户指定二元操作函数
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) {//遍历区间元素
__value = __binary_op(__value, *__first);//区间前n个元素的__binary_op
*++__result = __value;//把元素赋给输出端
}
return ++__result;
}
template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
_OutputIterator
partial_sum(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _BinaryOperation __binary_op)
{
__STL_REQUIRES(_InputIterator, _InputIterator);
__STL_REQUIRES(_OutputIterator, _OutputIterator);
if (__first == __last) return __result;
*__result = *__first;
//调用上面的函数，萃取出first的类型方便上面函数使用
return __partial_sum(__first, __last, __result, __VALUE_TYPE(__first),
__binary_op);
}
//下面举例：
/*partial_sum example:
#include <iostream> // std::cout
#include <functional> // std::multiplies
#include <numeric> // std::partial_sum
int myop (int x, int y) {return x+y+1;}
int main () {
int val[] = {1,2,3,4,5};
int result[5];
std::partial_sum (val, val+5, result);
std::cout << "using default partial_sum: ";
for (int i=0; i<5; i++) std::cout << result[i] << ' ';
std::cout << '\n';
std::partial_sum (val, val+5, result, std::multiplies<int>());
std::cout << "using functional operation multiplies: ";
for (int i=0; i<5; i++) std::cout << result[i] << ' ';
std::cout << '\n';
std::partial_sum (val, val+5, result, myop);
std::cout << "using custom function: ";
for (int i=0; i<5; i++) std::cout << result[i] << ' ';
std::cout << '\n';
return 0;
}
Output:
using default partial_sum: 1 3 6 10 15
using functional operation multiplies: 1 2 6 24 120
using custom function: 1 4 8 13 19
*/
/*功能与描述：
Assigns to every element in the range starting at result the difference
between its corresponding element in the range [first,last)
and the one preceding it (except for *result, which is assigned *first).
If x represents an element in [first,last) and y represents an element in result, the ys can be calculated as:
y0 = x0
y1 = x1 - x0
y2 = x2 - x1
y3 = x3 - x2
y4 = x4 - x3
... ... ...
The default operation is to calculate the difference, but some other operation can be specified as binary_op instead.
*/
/*
difference (1)
template <class InputIterator, class OutputIterator>
OutputIterator adjacent_difference (InputIterator first, InputIterator last,
OutputIterator result);
custom (2)
template <class InputIterator, class OutputIterator, class BinaryOperation>
OutputIterator adjacent_difference ( InputIterator first, InputIterator last,
OutputIterator result, BinaryOperation binary_op );
*/
//版本一：默认操作函数
template <class _InputIterator, class _OutputIterator, class _Tp>
_OutputIterator
__adjacent_difference(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _Tp*)
{
_Tp __value = *__first;
while (++__first != __last) {//遍历区间
_Tp __tmp = *__first;//初始化tmp
*++__result = __tmp - __value;//计算相邻两元素的差额(后-前)，并赋给输出端
__value = __tmp;//更新当前值
}
return ++__result;
}
template <class _InputIterator, class _OutputIterator>
_OutputIterator
adjacent_difference(_InputIterator __first,
_InputIterator __last, _OutputIterator __result)
{
__STL_REQUIRES(_InputIterator, _InputIterator);
__STL_REQUIRES(_OutputIterator, _OutputIterator);
if (__first == __last) return __result;//若为空直接返回
*__result = *__first;//初始值
//调用上面的函数__adjacent_difference()
return __adjacent_difference(__first, __last, __result,
__VALUE_TYPE(__first));
}
//版本二：可指定操作函数
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) {//遍历区间
_Tp __tmp = *__first;//初始化tmp
*++__result = __binary_op(__tmp, __value);//计算相邻两元素的操作，并赋给输出端
__value = __tmp;//更新当前值
}
return ++__result;
}
template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
_OutputIterator
adjacent_difference(_InputIterator __first, _InputIterator __last,
_OutputIterator __result, _BinaryOperation __binary_op)
{
__STL_REQUIRES(_InputIterator, _InputIterator);
__STL_REQUIRES(_OutputIterator, _OutputIterator);
if (__first == __last) return __result;//若为空直接返回
*__result = *__first;//初始值
//调用上面的函数__adjacent_difference()
return __adjacent_difference(__first, __last, __result,
__VALUE_TYPE(__first),
__binary_op);
}
//下面举例子：
/*adjacent_difference example:
#include <iostream> // std::cout
#include <functional> // std::multiplies
#include <numeric> // std::adjacent_difference
int myop (int x, int y) {return x+y;}
int main () {
int val[] = {1,2,3,5,9,11,12};
int result[7];
std::adjacent_difference (val, val+7, result);
std::cout << "using default adjacent_difference: ";
for (int i=0; i<7; i++) std::cout << result[i] << ' ';
std::cout << '\n';
std::adjacent_difference (val, val+7, result, std::multiplies<int>());
std::cout << "using functional operation multiplies: ";
for (int i=0; i<7; i++) std::cout << result[i] << ' ';
std::cout << '\n';
std::adjacent_difference (val, val+7, result, myop);
std::cout << "using custom function: ";
for (int i=0; i<7; i++) std::cout << result[i] << ' ';
std::cout << '\n';
return 0;
}
output:
using default adjacent_difference: 1 1 1 2 4 2 1
using functional operation multiplies: 1 2 6 15 45 99 132
using custom function: 1 3 5 8 14 20 23
*/
// Returns __x **__n, where __n >= 0. _Note that "multiplication"
// is required to be associative, but not necessarily commutative.
//power为SGI专属，并不在STL标准之列，它用来计算某数的n幂次方。
// 版本一，幂次方。如果指定为乘法运算，则当n >= 0 时传回 x^n。
// 注意，"multiplication" 必须满足结合律（associative），
// 但不需满足交换律（commutative）。
template <class _Tp, class _Integer, class _MonoidOperation>
_Tp __power(_Tp __x, _Integer __n, _MonoidOperation __opr)
{
if (__n == 0)
return identity_element(__opr);
else {
while ((__n & 1) == 0) {
__n >>= 1;
__x = __opr(__x, __x);
}
_Tp __result = __x;
__n >>= 1;
while (__n != 0) {
__x = __opr(__x, __x);
if ((__n & 1) != 0)
__result = __opr(__result, __x);
__n >>= 1;
}
return __result;
}
}
//版本二：以 multiplies<_Tp>()操作调用版本一
template <class _Tp, class _Integer>
inline _Tp __power(_Tp __x, _Integer __n)
{
return __power(__x, __n, multiplies<_Tp>());
}
// Alias for the internal name __power. Note that power is an extension,
// not part of the C++ standard.
//对上面函数的封装
template <class _Tp, class _Integer, class _MonoidOperation>
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);
}
// iota is not part of the C++ standard. It is an extension.
//C++11已经把这个列为STL的标准
//设定某个区间的内容，使其每个元素从指定值value开始，呈现递增
//在 [first,last) 范围内內填入value, value+1, value+2...
template <class _ForwardIter, class _Tp>
void
iota(_ForwardIter __first, _ForwardIter __last, _Tp __value)
{
__STL_REQUIRES(_ForwardIter, _Mutable_ForwardIterator);
__STL_CONVERTIBLE(_Tp, typename iterator_traits<_ForwardIter>::value_type);
while (__first != __last)
*__first++ = __value++;
}
//举例子：
/*iota example
#include <iostream> // std::cout
#include <numeric> // std::iota
int main () {
int numbers[10];
std::iota (numbers,numbers+10,100);
std::cout << "numbers:";
for (int& i:numbers) std::cout << ' ' << i;
std::cout << '\n';
return 0;
}
output:
numbers: 100 101 102 103 104 105 106 107 108 109
*/
__STL_END_NAMESPACE
#endif /* __SGI_STL_INTERNAL_NUMERIC_H */
// Local Variables:
// mode:C++
// End:
~~~
参考资料：
《STL源码剖析》侯捷