二分查找&上下界查找【二分】对二分的初步理解

二分查找的复杂度为O（log N）

#include <iostream>
#include <algorithm>
using namespace std;
const int inf = 0x3f3f3f3f;
int BS(int a[],int size,int s)	//非递归写法,s为需要查找的数
{
	int l=0;
	int r=size-1;
	while(l <= r) {
		int mid = l+(r-l)/2;
		if(a[mid] == s)
			return mid;
		else if(a[mid] > s)
			r = mid-1;
		else
			l = mid+1;
	}
	return -1;
}
int BSS(int a[],int l,int r,int s)	//递归写法
{
	if(l > r)
		return -1;
	int mid = l+(r-l)/2;
	if(a[mid] == s)
		return mid;
	else if(a[mid] > s)
		BSS(a,l,mid-1,s);
	else
		BSS(a,mid+1,r,s);
}
int LB(int a[],int size,int s)
{
	int MAX = -1;
	int l = 0;
	int r = size-1;
	while(l <= r) { 
		int mid = l+(r-l)/2;
		if(a[mid] >= s)
			r = mid-1;
		else {
			MAX = mid;
			l = mid+1;
		}
	}
	return MAX;
}
int UB(int a[],int size,int s)
{
	int l = 0;
	int r = size-1;
	int MIN = inf;
	while( l <= r) {
		int mid = l+(r-l)/2;
		if(a[mid] <= s)
			l = mid+1;
		else {
			MIN = mid;
			r = mid-1;
		}
	}
	return MIN;
} 
int main()
{
	int a[10] = {8,5,6,9,2,10,5,2,4,6};
	sort(a,a+10);
	for(int i=0;i<10;i++)
		cout << a[i] << " " ;
	cout << endl;
	cout << BS(a,10,2) <<endl;		//二分查找非递归写法
	cout << BSS(a,0,9,2) << endl;	// 二分查找递归写法
	cout << binary_search(a,a+10,2) << endl;		// 库函数
	cout << LB(a,10,5) << endl;   // 最大下非递归
	cout << lower_bound(a,a+10,5)-a << endl;		// 返回[ ) 返回的是左边那个数小于s的 s地址 （嘴笨）
	cout << UB(a,10,5) << endl;
	cout << upper_bound(a,a+10,5)-a << endl;  // 返回第一个大于s的数的地址 
	 
}