1.数据有序且无重复，查找给定值

/*** @description: 数据有序(小到大)且无重复，查找给定值* @author: michael ming* @date: 2019/4/16 18:54* @modified by: */
#include <iostream>
#define N 10
using namespace std;
int binarySearch_simple(int *arr,size_t n,int num)
{size_t low = 0, high = n-1;while(low <= high){size_t mid = low+(high-low)/2;if(arr[mid]==num)return mid;else if(arr[mid] < num)low = mid+1;elsehigh = mid-1;}return -1;
}
int main()
{cout << "数组打印如下：" << endl;int arr[N] = {1,2,3,4,5,6,7,8,9,10};for(int i = 0; i < N; ++i)cout << arr[i] << " ";cout << "请输入要查找的数，将返回下标，不存在返回-1：";int num;cin >> num;cout << num << " 的下标是：" << binarySearch_simple(arr,N,num) << endl;
}

2.数据有序且有重复，查找第1个给定的值

/*** @description: 查找第一个等于给定值的元素* @author: michael ming* @date: 2019/4/16 19:19* @modified by: */
#include <iostream>
#define N 10
using namespace std;
int binarySearch_simple(int *arr,size_t n,int num)
{size_t low = 0, high = n-1;while(low <= high){size_t mid = low+(high-low)/2;if(arr[mid]==num){if(mid == 0 || arr[mid-1] != num)   //第一个元素，或者前一个元素不等于numreturn mid;else    //否则，要查找的元素在前面high = mid-1;}else if(arr[mid] < num)low = mid+1;elsehigh = mid-1;}return -1;
}
int main()
{cout << "数组打印如下：" << endl;int arr[N] = {1,1,2,2,4,5,6,7,8,9};for(int i = 0; i < N; ++i)cout << arr[i] << " ";cout << "请输入1个数，将返回查找第一个等于给定值的元素的下标，不存在返回-1：";int num;cin >> num;cout << num << " 的下标是：" << binarySearch_simple(arr,N,num) << endl;
}

3.查找最后一个值等于给定值的元素

/*** @description: 查找最后一个值等于给定值的元素* @author: michael ming* @date: 2019/4/16 20:24* @modified by: */
#include <iostream>
#define N 10
using namespace std;
int binarySearch_simple(int *arr,size_t n,int num)
{size_t low = 0, high = n-1;while(low <= high){size_t mid = low+(high-low)/2;if(arr[mid]==num){if(mid == n-1 || arr[mid+1] != num)   //最后一个元素了，或者后面的不等于numreturn mid;else    //否则最后一个元素还在后面low = mid+1;}else if(arr[mid] < num)low = mid+1;elsehigh = mid-1;}return -1;
}
int main()
{cout << "数组打印如下：" << endl;int arr[N] = {1,1,2,2,4,5,6,8,8,9};for(int i = 0; i < N; ++i)cout << arr[i] << " ";cout << "请输入要查找的数，将返回最后一个符合的下标，不存在返回-1：";int num;cin >> num;cout << num << " 的下标是：" << binarySearch_simple(arr,N,num) << endl;
}

4.查找第一个大于等于给定值的元素

/*** @description: 查找第一个大于等于给定值的元素* @author: michael ming* @date: 2019/4/16 20:54* @modified by: */
#include <iostream>
#define N 10
using namespace std;
int binarySearch_simple(int *arr,size_t n,int num)
{size_t low = 0, high = n-1;while(low <= high){size_t mid = low+(high-low)/2;if(arr[mid] >= num) //当找到要求的值时{if(mid == 0 || arr[mid-1] < num)    //判断是第一个元素，或者前面的比我小return mid; //当前满足else    //否则满足要求的还在前面high = mid-1;}else if(arr[mid] < num)low = mid+1;}return -1;
}
int main()
{cout << "数组打印如下：" << endl;int arr[N] = {1,2,2,4,5,6,7,8,9,10};for(int i = 0; i < N; ++i)cout << arr[i] << " ";cout << "请输入一个数，将返回第一个大于等于它的下标，不存在返回-1：";int num;cin >> num;cout << num << " 的下标是：" << binarySearch_simple(arr,N,num) << endl;
}

5.查找最后一个小于等于给定值的元素

/*** @description: 查找最后一个小于等于给定值的元素* @author: michael ming* @date: 2019/4/16 23:09* @modified by: */
#include <iostream>
#define N 10
using namespace std;
int binarySearch_simple(int *arr,size_t n,int num)
{size_t low = 0, high = n-1;while(low <= high){size_t mid = low+(high-low)/2;if(arr[mid] > num)high = mid-1;else if(arr[mid] <= num){if(mid == n-1 || arr[mid+1] > num)  //最后一个元素，或者后面的比它大了return mid; //它是最后一个小于等于的elselow = mid+1;    //否则后面还有满足的，下限往上加}}return -1;
}
int main()
{cout << "数组打印如下：" << endl;int arr[N] = {1,2,2,4,5,6,7,10,10,10};for(int i = 0; i < N; ++i)cout << arr[i] << " ";cout << "请输入一个数，返回最后一个小于等于给定值的元素的下标，不存在返回-1：";int num;cin >> num;cout << num << " 的下标是：" << binarySearch_simple(arr,N,num) << endl;
}

6.查找IP归属（利用上面#5代码）

/*** @description: 查找ip地址归属，找到最后一个区间开始地址<=ip的* @author: michael ming* @date: 2019/4/16 23:38* @modified by: */
#include <iostream>
#include "binarySearch_findLastLessNum.cpp"
int main()
{int start[5] = {101,201,301,401,501};   //假设为ip起始地址（A,B,C,D,E）int end[5] =    {200,300,400,500,600};  //对应ip终止地址size_t ip;while(1){std::cout << "请输入要查询的ip: ";std::cin >> ip;int index = binarySearch_simple(start,5,ip);    //在ip区间头里查找最后一个<=我的if(index != -1 && ip <= end[index])switch(index){case 0:std::cout << "ip in city A"<< std::endl;break;case 1:std::cout << "ip in city B"<< std::endl;break;case 2:std::cout << "ip in city C"<< std::endl;break;case 3:std::cout << "ip in city D"<< std::endl;break;case 4:std::cout << "ip in city E"<< std::endl;break;}elsestd::cout << "ip not found!" << std::endl;}
}

7.循环有序数组，查找给定值

例如：4,5,6,7,1,2,3
循环数组性质：以数组中间点为分区，数组分成一个有序数组和一个循环有序数组。

如果首元素 arr[low] < arr[mid]，左半部分：有序，右半部分：循环有序；
如果首元素 arr[low] > arr[mid]，右半部分：有序，左半部分：循环有序；
判断查找的数是否在有序的半边范围内，更新上下限
时间复杂度为 O(logN)。

/*** @description: 循环有序数组，查找给定值* @author: michael ming* @date: 2019/4/17 0:25* @modified by: */
#include <iostream>
#define N 10
int circular_Arr_BS(int *arr, size_t n, int num)
{size_t low = 0, high = n-1;while(low <= high){size_t mid = low+(high-low)/2;if(arr[mid] == num)return mid;if(arr[mid] < arr[low]) //转折点在左边,右边有序{if(arr[mid] <= num && num <= arr[high]) //数据在右边low = mid+1;elsehigh = mid-1;}else    //转折点在右边，左边有序{if(arr[low] <= num && num < arr[mid])   //数据在左边high = mid-1;elselow = mid+1;}}return -1;
}
int main()
{int arr[N] = {4,5,6,7,8,9,10,1,2,3};size_t mid = (N-1)/2;int num;std::cin >> num;std::cout << circular_Arr_BS(arr,N,num);return 0;
}