C/C++标准库之numeric

Posted 2022-02-08 非晚非晚

<numeric>是C++标准程序库中的一个头文件，定义了C++ STL标准中的基础性的数值算法，函数并不多，一共5个，偶有接触，这里一并介绍一下，免得每次网上翻阅查找。

这五个函数分别为：accumulate；adjacent_difference；inner_product；partial_sum；iota。

文章目录

• 1. accumulate
• 2. adjacent_difference
• 3. inner_product
• 4. partial_sum
• 5. iota

1. accumulate

功能：以init为初值，对迭代器给出的值序列做累加，返回累加结果值

• 函数模板

//模板一：默认累加
template <class InputIterator, class T>
   T accumulate (InputIterator first, InputIterator last, T init);

//模板二：自定义操作--binary_op
   template <class InputIterator, class T, class BinaryOperation>
   T accumulate (InputIterator first, InputIterator last, T init,
                 BinaryOperation binary_op);

• 应用举例

#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);//init + numbers = 100 + 10 + 20 + 30 = 160
	std::cout << '\\n';

	std::cout << "using functional's minus: ";
	std::cout << std::accumulate(numbers, numbers + 3, init, std::minus<int>());//init - numbers = 100 - 10 - 20 - 30 = 40
	std::cout << '\\n';

	std::cout << "using custom function: ";
	std::cout << std::accumulate(numbers, numbers + 3, init, myfunction);//init (myfunction) numbers
	std::cout << '\\n';

	std::cout << "using custom object: ";
	std::cout << std::accumulate(numbers, numbers + 3, init, myobject);//init (myobject) numbers
	std::cout << '\\n';

	return 0;

输出：

using default accumulate: 160
using functional's minus: 40
using custom function: 220
using custom object: 280

2. adjacent_difference

功能：对输入序列，计算相邻两项的差值(后一个减前一个元素)，写入到输出序列(result)中。

• 函数模板

//模板一：默认形式，相邻差值写入至result中
template <class InputIterator, class OutputIterator>
   OutputIterator adjacent_difference (InputIterator first, InputIterator last,
                                       OutputIterator result);

//模板二：自定义操作--binary_op
template <class InputIterator, class OutputIterator, class BinaryOperation>
   OutputIterator adjacent_difference ( InputIterator first, InputIterator last,
                                        OutputIterator result, BinaryOperation binary_op );

• 应用举例

#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);//后面减前面的：1 1 1 2 4 2 1
	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::multiplies<int>()：表示乘法
	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);//自定义方法
	std::cout << "using custom function: ";
	for (int i = 0; i < 7; i++)
		std::cout << result[i] << ' ';
	std::cout << '\\n';
	return 0;

输出：

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 

3. inner_product

功能：计算两个输入序列的内积。

• 函数模板

//模板一：默认模板
template <class InputIterator1, class InputIterator2, class T>
   T inner_product (InputIterator1 first1, InputIterator1 last1,
                    InputIterator2 first2, T init);

//模板二：自定义操作--binary_op1 binary_op2
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);

• 应用举例

#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 = 100;
	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);//init = init + (*first1)*(*first2) ==》100 + 10*1 + 20*2 + 30*3
	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;

输出：

using default inner_product: 240
using functional operations: 70
using custom functions: 34

4. partial_sum

功能：计算局部累加和(每次都加上前面的所有元素)，计算结果放入result中。

//模板一：默认计算计算局部累加和
template <class InputIterator, class OutputIterator>
   OutputIterator partial_sum (InputIterator first, InputIterator last,
                               OutputIterator result);

//模板二：自定义操作--binary_op
template <class InputIterator, class OutputIterator, class BinaryOperation>
   OutputIterator partial_sum (InputIterator first, InputIterator last,
                               OutputIterator result, BinaryOperation binary_op);

• 应用举例

#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);//每次加入前面所有的元素放入result中
	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>());//每次乘以前面的元素
	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);//自定义操作myop
	std::cout << "using custom function: ";
	for (int i = 0; i < 5; i++)
		std::cout << result[i] << ' ';
	std::cout << '\\n';
	return 0;

输出：

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 

5. iota

功能：向序列中写入以val为初值的连续值序列。

• 函数模板

template <class ForwardIterator, class T>
  void iota (ForwardIterator first, ForwardIterator last, T val);

• 应用举例

#include <iostream> // std::cout
#include <numeric>	// std::iota

int main()

	int numbers[10];

	std::iota(numbers, numbers + 10, 100);//以100为初值

	for (int &i : numbers)
		std::cout << ' ' << i;

	std::cout << '\\n';

	return 0;

输出：

 100 101 102 103 104 105 106 107 108 109

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参考：http://www.cplusplus.com/reference/numeric/