排列操作（Permutation operations）

一、is_permutation

1、原型：

template< class ForwardIt1, class ForwardIt2 >
bool is_permutation( ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2 );template< class ForwardIt1, class ForwardIt2, class BinaryPredicate >
bool is_permutation( ForwardIt1 first1, ForwardIt1 last1,ForwardIt2 first2, BinaryPredicate p );

2、说明：

判读序列1是否是序列2的一种排列方式

3、官方demo

#include <algorithm>
#include <vector>
#include <iostream>
int main()
{std::vector<int> v1{1,2,3,4,5};std::vector<int> v2{3,5,4,1,2};std::cout << "3,5,4,1,2 is a permutation of 1,2,3,4,5? "<< std::boolalpha<< std::is_permutation(v1.begin(), v1.end(), v2.begin()) << '\n';std::vector<int> v3{3,5,4,1,1};std::cout << "3,5,4,1,1 is a permutation of 1,2,3,4,5? "<< std::boolalpha<< std::is_permutation(v1.begin(), v1.end(), v3.begin()) << '\n';
}

Output:

3,5,4,1,2 is a permutation of 1,2,3,4,5? true
3,5,4,1,1 is a permutation of 1,2,3,4,5? false

二、next_permutation

1、原型：

template< class BidirIt >
bool next_permutation( BidirIt first, BidirIt last );template< class BidirIt, class Compare >
bool next_permutation( BidirIt first, BidirIt last, Compare comp );

2、说明：

按字典顺序生成下一个序列，如果有返回true；如果没有，生成第一个排列序列（std::sort(first, last)），并返回false。

3、官方demo

#include <algorithm>
#include <string>
#include <iostream>int main()
{std::string s = "aba";std::sort(s.begin(), s.end());do {std::cout << s << '\n';} while(std::next_permutation(s.begin(), s.end()));
}

Output:

aab
aba
baa

三、prev_permutation

1、原型：

template< class BidirIt >
bool prev_permutation( BidirIt first, BidirIt last);template< class BidirIt, class Compare >
bool prev_permutation( BidirIt first, BidirIt last, Compare comp);

2、说明：

按字典顺序生成上一个序列，如果有返回true；如果没有，生成第一个排列序列（std::sort(first, last)），并返回false。

3、官方demo

打印abc的六种排列顺序

#include <algorithm>
#include <string>
#include <iostream>
#include <functional>
int main()
{std::string s="abc";std::sort(s.begin(), s.end(), std::greater<char>());do {std::cout << s << ' ';} while(std::prev_permutation(s.begin(), s.end()));std::cout << '\n';
}

Output:

cba cab bca bac acb abc

数值操作（Numeric operations）

一、iota

1、原型：

template< class ForwardIt, class T >
void iota( ForwardIt first, ForwardIt last, T value );

2、说明：

以递增的值填充[first, last)范围

3、官方demo

#include <algorithm>
#include <iostream>
#include <list>
#include <numeric>
#include <random>
#include <vector>int main()
{std::list<int> l(10);std::iota(l.begin(), l.end(), -4);	//以递增的值填充到链表l中std::vector<std::list<int>::iterator> v(l.size());std::iota(v.begin(), v.end(), l.begin());std::shuffle(v.begin(), v.end(), std::mt19937{std::random_device{}()});	//std::shuffle不能操作std::list，因此使用vectorstd::cout << "Contents of the list: ";for(auto n: l) std::cout << n << ' ';std::cout << '\n';std::cout << "Contents of the list, shuffled: ";for(auto i: v) std::cout << *i << ' ';std::cout << '\n';
}

Possible output:

Contents of the list: -4 -3 -2 -1 0 1 2 3 4 5
Contents of the list, shuffled: 0 -1 3 4 -4 1 -2 -3 2 5

二、accumulate

1、原型：

template< class InputIt, class T >
T accumulate( InputIt first, InputIt last, T init );template< class InputIt, class T, class BinaryOperation >
T accumulate( InputIt first, InputIt last, T init, BinaryOperation op );

2、说明：

计算序列的累积值（连续加、连续乘等）

3、官方demo

#include <iostream>
#include <vector>
#include <numeric>
#include <string>
#include <functional>int main()
{std::vector<int> v{1, 2, 3, 4, 5, 6, 7, 8, 9, 10};int sum = std::accumulate(v.begin(), v.end(), 0);	// 加int product = std::accumulate(v.begin(), v.end(), 1, std::multiplies<int>());	// 乘auto dash_fold = [](std::string a, int b) {	// 连接操作return std::move(a) + '-' + std::to_string(b);};std::string s = std::accumulate(std::next(v.begin()), v.end(),	// std::next是为了从第二个值开始，在前面加“-”std::to_string(v[0]), // 从第一个元素开始dash_fold);// 使用反向迭代器右折叠std::string rs = std::accumulate(std::next(v.rbegin()), v.rend(),std::to_string(v.back()), // 从最后一个元素开始dash_fold);std::cout << "sum: " << sum << '\n'<< "product: " << product << '\n'<< "dash-separated string: " << s << '\n'<< "dash-separated string (right-folded): " << rs << '\n';
}

Output:

sum: 55
product: 3628800
dash-separated string: 1-2-3-4-5-6-7-8-9-10
dash-separated string (right-folded): 10-9-8-7-6-5-4-3-2-1

三、inner_product

1、原型：

template< class InputIt1, class InputIt2, class T >
T inner_product( InputIt1 first1, InputIt1 last1,InputIt2 first2, T init );template<class InputIt1, class InputIt2, class T,class BinaryOperation1, class BinaryOperation2>
T inner_product( InputIt1 first1, InputIt1 last1,InputIt2 first2, T init,BinaryOperation1 op1,BinaryOperation2 op2 );

2、说明：

计算两个序列的内积：即序列1和序列2的顺序对应的元素乘积之和

3、官方demo

#include <numeric>
#include <iostream>
#include <vector>
#include <functional>
int main()
{std::vector<int> a{0, 1, 2, 3, 4};std::vector<int> b{5, 4, 2, 3, 1};int r1 = std::inner_product(a.begin(), a.end(), b.begin(), 0);std::cout << "Inner product of a and b: " << r1 << '\n';int r2 = std::inner_product(a.begin(), a.end(), b.begin(), 0,std::plus<>(), std::equal_to<>());std::cout << "Number of pairwise matches between a and b: " <<  r2 << '\n';
}

Output:

Inner product of a and b: 21
Number of pairwise matches between a and b: 2	//成对匹配的数量

四、adjacent_difference

1、原型：

template< class InputIt, class OutputIt >
OutputIt adjacent_difference( InputIt first, InputIt last, OutputIt d_first );template< class InputIt, class OutputIt, class BinaryOperation >
OutputIt adjacent_difference( InputIt first, InputIt last,OutputIt d_first, BinaryOperation op );

2、说明：

计算相邻元素之间的差值。

3、官方demo

#include <numeric>
#include <vector>
#include <array>
#include <iostream>
#include <functional>
#include <iterator>int main()
{std::vector v {2, 4, 6, 8, 10, 12, 14, 16, 18, 20};std::adjacent_difference(v.begin(), v.end(), v.begin());for (auto n : v)std::cout << n << ' ';std::cout << '\n';// 斐波纳契数列 std::array<int, 10> a {1};adjacent_difference(begin(a), std::prev(end(a)), std::next(begin(a)), std::plus<> {});copy(begin(a), end(a), std::ostream_iterator<int> {std::cout, " "});
}

Output:

2 2 2 2 2 2 2 2 2 2
1 1 2 3 5 8 13 21 34 55

五、partial_sum

1、原型：

template< class InputIt, class OutputIt >
OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first );template< class InputIt, class OutputIt, class BinaryOperation >
OutputIt partial_sum( InputIt first, InputIt last, OutputIt d_first, BinaryOperation op );

2、说明：

以如下形式计算，并将结果保存在d_first开始的目标区域：

	*(d_first)   = *first;*(d_first+1) = *first + *(first+1);*(d_first+2) = *first + *(first+1) + *(first+2);

3、官方demo

#include <numeric>
#include <vector>
#include <iostream>
#include <iterator>
#include <functional>int main()
{std::vector<int> v = {2, 2, 2, 2, 2, 2, 2, 2, 2, 2}; // or std::vector<int>v(10, 2);std::cout << "The first 10 even numbers are: ";std::partial_sum(v.begin(), v.end(), std::ostream_iterator<int>(std::cout, " "));std::cout << '\n';std::partial_sum(v.begin(), v.end(), v.begin(), std::multiplies<int>());std::cout << "The first 10 powers of 2 are: ";for (auto n : v) {std::cout << n << " ";}std::cout << '\n';
}

Output:

The first 10 even numbers are: 2 4 6 8 10 12 14 16 18 20 
The first 10 powers of 2 are: 2 4 8 16 32 64 128 256 512 1024