二分法

二分法使用条件:有序序列

1.查找数组中出现的元素位置

（适用范围:序列不能重复）

#include<iostream>
using namespace std;
#define MAXSIZE 10
int list[MAXSIZE]={1,2,3,4,5,6,7,8,9,10};
int binarysearch(int key)
{
	int left=0;
	int right=MAXSIZE-1;
	while(left<=right)
	{
	 int mid=(left+right)/2;
	 if(list[mid]==key){
	 	return mid;
	}
	 if(key<list[mid])
	 {
	 	right=mid-1;
	 }
	 else
	 {
	 	left=mid+1;
	 }
	}
	return -1;
}

int main()
{
	int key;
	cin>>key;
	int n=binarysearch(key);
	if(n!=-1)
	cout<<"the supscrip is "<<n;
	else 
	cout<<"don't find!";
}

2.查找数组中元素第一次出现的次数

#include<iostream>
using namespace std;
#define MAXSIZE 10
int a[MAXSIZE]={1,2,3,4,5,6,7,7,7,10};

int binsearch_low(int key)
{
    int ans = -1;
    int low = 0,high = MAXSIZE-1;
    while(low <= high){
        int mid = (low + high)/2;
        if(key == a[mid]){
            ans = mid;
            high = mid - 1;
            cout<<"QAQ"<<endl;
        }
        else if(key < a[mid])
            high = mid - 1;
        else
            low = mid + 1;
            cout<<'('<<low<<','<<mid<<','<<high<<')';
    }
    return ans;
}
int main()
{
	int key;
	for(int i=0;i<MAXSIZE;i++)
	{
		cout<<i<<' ';
	}
	cout<<endl;
	for(int i=0;i<MAXSIZE;i++)
	{
		cout<<a[i]<<' ';
	}
	cout<<endl;
		cin>>key;
	int n=binsearch_low(key);
	cout<<endl;
	if(n!=-1)
	cout<<n;
	else 
	cout<<"don't find";
	
	return 0;
 } 

3.查找数组中元素最后一次出现的次数

#include<iostream>
using namespace std;
int list[10]={1,2,3,4,5,6,7,8,9,9};
int research_high(int key)
{
	int low=0;
	int high=10;
	int ans=-1;
	while(low<=high)
	{
		int mid=(low+high)/2;
		if(list[mid]==key)
		{
			ans=mid;
			low=mid+1;
		}
		else if(list[mid]<key)
		{
			low=mid+1;
		 } 
		 else
		 {
		 	high=mid-1;
		 }
		
	}
	return ans;
}
int main()
{
	int key;
	for(int i=0;i<10;i++)
	{
		cout<<i<<' ';
	}
	cout<<endl;
	for(int i=0;i<10;i++)
	{
		cout<<list[i]<<' ';
	}
	cout<<"please input a key!"<<endl;
	cin>>key;
	int n=research_high(key);
	if(n!=-1)
	cout<<n;
	else
	cout<<"NOTHING";
}