c++ STL 二分查找(binary search)

二分查找是一种广泛使用的搜索算法，它要求在应用搜索之前对数组进行排序。该算法的主要思想是继续将数组分成两半（分而治之），直到找到元素，或者用尽所有元素。

它通过将数组的中间项与目标进行比较来工作，如果匹配，则返回true；否则，如果中间项大于目标，则在左子数组中执行搜索。

如果中间项小于目标，则在右子数组中执行搜索。

函数原型

binary_search(startaddress, 
              endaddress, valuetofind)

startaddress: 列表起始地址
endaddress: 列表末尾地址
valuetofind: 查找的目标值

基本类型

// CPP program to implement
// Binary Search in
// Standard Template Library (STL)
#include <algorithm>
#include <iostream>

using namespace std;

void show(int a[], int arraysize)
{
	for (int i = 0; i < arraysize; ++i)
		cout << a[i] << ",";
}

int main()
{
	int a[] = { 1, 5, 8, 9, 6, 7, 3, 4, 2, 0 };
	int asize = sizeof(a) / sizeof(a[0]);
	cout << "\nThe array is : \n";
	show(a, asize);

	cout << "\n\nLet's say we want to search for ";
	cout << "\n2 in the array So, we first sort the array";
	sort(a, a + asize);
	cout << "\n\nThe array after sorting is : \n";
	show(a, asize);
	cout << "\n\nNow, we do the binary search";
	if (binary_search(a, a + 10, 2))
		cout << "\nElement found in the array";
	else
		cout << "\nElement not found in the array";

	cout << "\n\nNow, say we want to search for 10";
	if (binary_search(a, a + 10, 10))
		cout << "\nElement found in the array";
	else
		cout << "\nElement not found in the array";

	return 0;
}

输出

The array is : 
1,5,8,9,6,7,3,4,2,0,

Let's say we want to search for 
2 in the array So, we first sort the array

The array after sorting is : 
0,1,2,3,4,5,6,7,8,9,

Now, we do the binary search
Element found in the array

Now, say we want to search for 10
Element not found in the array

自定义类型

二分查找其通过比较加速查找,其核心也是调用的比较函数,所以二分查找和排序一样,自定义类型依赖比较函数的实现

比较函数实现,参考sort

// CPP program to implement
// Binary Search in
// Standard Template Library (STL)
#include <algorithm>
#include <iostream>

using namespace std;

struct MyFav {
    int x;
    int y;
    bool operator<(const MyFav& fav) const {
        return this->x < fav.x;
    }
};

void show(MyFav arr[], int lenth) {
    for(int i=0; i<lenth; i++) {
        cout << arr[i].x << ", " << arr[i].y << endl;
    }
}

int main()
{
	MyFav a[] = {{2, 3}, {5, 1}, {3, 4}, {1, 8}};
	int asize = sizeof(a) / sizeof(a[0]);
	cout << "\nThe array is : \n";
	show(a, asize);

	cout << "\n\nLet's say we want to search for ";
	cout << "\n2 in the array So, we first sort the array";
	sort(a, a + asize);
	cout << "\n\nThe array after sorting is : \n";
	show(a, asize);
	cout << "\n\nNow, we do the binary search";
	if (binary_search(a, a + asize, MyFav{2, 0}))
		cout << "\nElement found in the array";
	else
		cout << "\nElement not found in the array";

	cout << "\n\nNow, say we want to search for 10";
	if (binary_search(a, a + asize, MyFav{10, 0}))
		cout << "\nElement found in the array";
	else
		cout << "\nElement not found in the array";

	return 0;
}

输出

The array is :
2, 3
5, 1
3, 4
1, 8

Let's say we want to search for
2 in the array So, we first sort the array

The array after sorting is :
1, 8
2, 3
3, 4
5, 1

Now, we do the binary search
Element found in the array

Now, say we want to search for 10
Element found in the array