algorithm算法库学习之——堆操作，最小/最大操作，比较操作，排列操作

algorithm此头文件是算法库的一部分。本篇介绍堆操作，最小/最大操作，比较操作，排列操作。

接口API

堆操作
is_heap	检查给定范围是否为一个最大堆 (函数模板)
is_heap_until (C++11)	查找能成为最大堆的最大子范围 (函数模板)
make_heap	从一个元素范围创建出一个最大堆 (函数模板)
push_heap	将一个元素加入到一个最大堆 (函数模板)
pop_heap	从最大堆中移除最大元素 (函数模板)
sort_heap	将一个最大堆变成一个按升序排序的元素范围 (函数模板)
最小/最大操作
max	返回各给定值中的较大者 (函数模板)
max_element	返回范围内的最大元素 (函数模板)
min	返回各给定值中的较小者 (函数模板)
min_element	返回范围内的最小元素 (函数模板)
minmax (C++11)	返回两个元素的较小和较大者 (函数模板)
minmax_element (C++11)	返回范围内的最小元素和最大元素 (函数模板)
比较操作
equal	确定两个元素集合是否是相同的 (函数模板)
lexicographical_compare	当一个范围按字典顺序小于另一个范围时，返回 true (函数模板)
排列操作
is_permutation (C++11)	判断一个序列是否为另一个序列的排列 (函数模板)
next_permutation	产生某个元素范围的按字典顺序的下一个较大的排列 (函数模板)
prev_permutation	产生某个元素范围的按字典顺序的下一个较小的排列 (函数模板)

示例代码：

#include <algorithm>
#include <functional>
#include <iostream>
#include <iterator>
#include <utility>      // std::pair
#include <vector>
#include <array>
#include <cctype>       // std::tolower
#include <string>
#include <ctime>        // std::time
#include <cstdlib>      // std::rand, std::srand
#include <random>       // std::default_random_engine
#include <chrono>       // std::chrono::system_clock#include <iomanip>bool myfn(int i, int j) { return i < j; }struct myclass {bool operator() (int i, int j) { return i < j; }
} myobj;bool is_palindrome(const std::string& s)
{return std::equal(s.cbegin(), s.cbegin() + s.size() / 2, s.crbegin());
}void test_equal(const std::string& s)
{std::cout << std::quoted(s)<< (is_palindrome(s) ? " 是" : " 不是")<< "回文\n";
}// a case-insensitive comparison function:
bool mycomp(char c1, char c2)
{return std::tolower(c1) < std::tolower(c2);
}template<typename Os, typename V>
Os& operator<<(Os& os, const V& v)
{os << "{ ";for (const auto& e : v)os << e << ' ';return os << '}';
}int main()
{// make_heap example 从一个元素范围创建出一个最大堆 int myints[] = { 10,20,30,5,15 };std::vector<int> v(myints, myints + 5);std::make_heap(v.begin(), v.end());std::cout << "initial max heap   : " << v.front() << '\n';// pop_heap example 从最大堆中移除最大元素std::pop_heap(v.begin(), v.end()); v.pop_back();std::cout << "max heap after pop : " << v.front() << '\n';// push_heap example 将一个元素加入到一个最大堆 v.push_back(99); std::push_heap(v.begin(), v.end());std::cout << "max heap after push: " << v.front() << '\n';// sort_heap example 将一个最大堆变成一个按升序排序的元素范围std::sort_heap(v.begin(), v.end());std::cout << "final sorted range :";for (unsigned i = 0; i < v.size(); i++)std::cout << ' ' << v[i];std::cout << '\n';// is_heap example 检查给定范围是否为一个最大堆 std::vector<int> foo{ 9,5,2,6,4,1,3,8,7 };if (!std::is_heap(foo.begin(), foo.end()))std::make_heap(foo.begin(), foo.end());std::cout << "Popping out elements:";while (!foo.empty()) {std::pop_heap(foo.begin(), foo.end());   // moves largest element to backstd::cout << ' ' << foo.back();         // prints backfoo.pop_back();                         // pops element out of container}std::cout << '\n';// is_heap_until example 查找能成为最大堆的最大子范围std::vector<int> foo2{ 2,6,9,3,8,4,5,1,7 };std::sort(foo2.begin(), foo2.end());std::reverse(foo2.begin(), foo2.end());auto last = std::is_heap_until(foo2.begin(), foo2.end());std::cout << "The " << (last - foo2.begin()) << " first elements are a valid heap:";for (auto it = foo2.begin(); it != last; ++it)std::cout << ' ' << *it;std::cout << '\n';// min example 返回各给定值中的较小者std::cout << "min(1,2)==" << std::min(1, 2) << '\t';std::cout << "min(2,1)==" << std::min(2, 1) << '\t';std::cout << "min('a','z')==" << std::min('a', 'z') << '\t';std::cout << "min(3.14,2.72)==" << std::min(3.14, 2.72) << '\n';// max example 返回各给定值中的较大者 std::cout << "max(1,2)==" << std::max(1, 2) << '\t';std::cout << "max(2,1)==" << std::max(2, 1) << '\t';std::cout << "max('a','z')==" << std::max('a', 'z') << '\t';std::cout << "max(3.14,2.73)==" << std::max(3.14, 2.73) << '\n';// minmax example 返回两个元素的较小和较大者 auto result = std::minmax({ 1,2,3,4,5 });std::cout << "minmax({1,2,3,4,5}): ";std::cout << result.first << ' ' << result.second << '\n';// min_element example 返回范围内的最小元素 // max_element example 返回范围内的最大元素 int myints2[] = { 3,7,2,5,6,4,9 };// using default comparison:std::cout << "The smallest element is " << *std::min_element(myints2, myints2 + 7) << '\n';std::cout << "The largest element is " << *std::max_element(myints2, myints2 + 7) << '\n';// using function myfn as comp:std::cout << "The smallest element is " << *std::min_element(myints2, myints2 + 7, myfn) << '\n';std::cout << "The largest element is " << *std::max_element(myints2, myints2 + 7, myfn) << '\n';// using object myobj as comp:std::cout << "The smallest element is " << *std::min_element(myints2, myints2 + 7, myobj) << '\n';std::cout << "The largest element is " << *std::max_element(myints2, myints2 + 7, myobj) << '\n';// minmax_element example 返回范围内的最小元素和最大元素 std::array<int, 7> foo3{ 3,7,2,9,5,8,6 };auto result3 = std::minmax_element(foo3.begin(), foo3.end());// print result:std::cout << "min is " << *result3.first;std::cout << ", at position " << (result3.first - foo3.begin()) << '\n';std::cout << "max is " << *result3.second;std::cout << ", at position " << (result3.second - foo3.begin()) << '\n';// equal example 确定两个元素集合是否是相同的 test_equal("radar");test_equal("hello");// lexicographical_compare example 当一个范围按字典顺序小于另一个范围时，返回 truechar foo5[] = "Apple";char bar5[] = "apartment";std::cout << std::boolalpha;std::cout << "Comparing foo and bar lexicographically (foo<bar):\n";std::cout << "Using default comparison (operator<): ";std::cout << std::lexicographical_compare(foo5, foo5 + 5, bar5, bar5 + 9);std::cout << '\n';std::cout << "Using mycomp as comparison object: ";std::cout << std::lexicographical_compare(foo5, foo5 + 5, bar5, bar5 + 9, mycomp);std::cout << '\n';// is_permutation example 判断一个序列是否为另一个序列的排列 static auto v1 = { 1, 2, 3, 4, 5 };static auto v2 = { 3, 5, 4, 1, 2 };static auto v3 = { 3, 5, 4, 1, 1 };std::cout << v2 << " 是 " << v1 << " 的排列：" << std::boolalpha<< std::is_permutation(v1.begin(), v1.end(), v2.begin()) << '\n'<< v3 << " 是 " << v1 << " 的排列：" << std::boolalpha<< std::is_permutation(v1.begin(), v1.end(), v3.begin()) << '\n';// next_permutation example 产生某个元素范围的按字典顺序的下一个较大的排列 int myints6[] = { 1,2,3 };std::sort(myints6, myints6 + 3);std::cout << "The 3! possible permutations with 3 elements:\n";do {std::cout << myints6[0] << ' ' << myints6[1] << ' ' << myints6[2] << '\n';} while (std::next_permutation(myints6, myints6 + 3));std::cout << "After loop: " << myints6[0] << ' ' << myints6[1] << ' ' << myints6[2] << '\n';// prev_permutation example 产生某个元素范围的按字典顺序的下一个较小的排列 int myints7[] = { 1,2,3 };std::sort(myints7, myints7 + 3);std::reverse(myints7, myints7 + 3);std::cout << "The 3! possible permutations with 3 elements:\n";do {std::cout << myints7[0] << ' ' << myints7[1] << ' ' << myints7[2] << '\n';} while (std::prev_permutation(myints7, myints7 + 3));std::cout << "After loop: " << myints7[0] << ' ' << myints7[1] << ' ' << myints7[2] << '\n';std::cout << "hello world\n";return 0;
}

运行结果：