几种形式下的二分搜索

操作对象：

      给定一个不减序列  int incre[9]={1,2,2,2,2,4,6,6,8};

      给定一个不增序列 int decre[9]={8,6,6,4,2,2,2,2,1};

第一种：int binary_search(int *a,int x,int y,intv);     在[x,y)区间中查找满足a[i]=v的i的值，若不存在,则返回-1;其中a[]为不减序列

int Binary_Search(int *a,int x,int y,int v)   //[x,y){    int m;    while(x<y){        m=(x+y)/2;        if(a[m]==v) return m;        else if(a[m]<v)  x=m+1;        else    y=m;    }    return -1;}

第二种：int binary_search_decre(int *a,int x,int y,int v);在[x,y]区间中查找满足a[i]=v的i的值，若不存在,则返回-1;其中a[]为不增序列int Binary_Search_decre(int *a,int x,int y,int v) //[x,y){    int m;    while(x<y){        m=(x+y)/2;        if(a[m]==v) return m;        else if(a[m]<v) y=m;        else  x=m+1;    }    return -1;}

第三种:int lower_bound(int *a,int x,int y,int v);在[x,y)中查找满足a[i]>=v最小的i的值;其中a[i]为单调不减int lower_Bound(int *a,int x,int y,int v)   //[x,y){    int m;    while(x<y){        m=(x+y)/2;        if(a[m]>=v) y=m;        else    x=m+1;    }    return x;}测试结果，和C++标准库中lower_bound()用法的结果比较 

第三种：lower_bound_decre(int *a,int x,int y,int v);在[x,y)区间中查找a[i]<=v的最小i的值;其中a[]为单调不增int lower_bound_decre(int *a,int x,int y,int v){    int m;    while(x<y){        m=(x+y)/2;        if(a[m]<=v) y=m;        else    x=m+1;    }    return x;}

第四种：int upper_bound(int *a,int x,int y,int v);在[x,y)区间中查找满足a[i]>v的最小的i的值;其中a[]为单调不减int upper_Bound(int *a,int x,int y,int v){    int m;    while(x<y){        m=(x+y)/2;        if(a[m]<=v) x=m+1;        else    y=m;    }    return x;}

测试结果以及与C++标准库中upper_bound()的比较

第五种:int upper_bound_decre(int *a,int x,int y,int v);在[x,y)区间中查找a[i]<v的最小的i的值;其中i为单调不增int upper_bound_decre(int *a,int x,int y,int v){    int m;    while(x<y){        m=(x+y)/2;        if(a[m]>=v) x=m+1;        else    y=m;    }    return x;}

完整的代码：

/**   author:liuwen*/#include <iostream>#include <cstring>#include <cstdio>#include <string>#include <algorithm>using namespace std;int incre[9]={1,2,2,2,2,4,6,6,8};int decre[9]={8,6,6,4,2,2,2,2,1};int Binary_Search(int *a,int x,int y,int v)   //[x,y){    int m;    while(x<y){        m=(x+y)/2;        if(a[m]==v) return m;        else if(a[m]<v)  x=m+1;        else    y=m;    }    return -1;}int Binary_Search_decre(int *a,int x,int y,int v) //[x,y){    int m;    while(x<y){        m=(x+y)/2;        if(a[m]==v) return m;        else if(a[m]<v) y=m;        else  x=m+1;    }    return -1;}int lower_Bound(int *a,int x,int y,int v)   //[x,y){    int m;    while(x<y){        m=(x+y)/2;        if(a[m]>=v) y=m;        else    x=m+1;    }    return x;}//[x,y) 在一个单调不增的序列decre[]中,查找decre[]满足decre[i]<=v 条件的最小的iint lower_bound_decre(int *a,int x,int y,int v){    int m;    while(x<y){        m=(x+y)/2;        if(a[m]<=v) y=m;        else    x=m+1;    }    return x;}int upper_Bound(int *a,int x,int y,int v){    int m;    while(x<y){        m=(x+y)/2;        if(a[m]<=v) x=m+1;        else    y=m;    }    return x;}//[x,y) 在一个单调不增的序列decre[]中,查找decre[]满足decre[i]<v 条件的最小的iint upper_bound_decre(int *a,int x,int y,int v){    int m;    while(x<y){        m=(x+y)/2;        if(a[m]>=v) x=m+1;        else    y=m;    }    return x;}int main(){    freopen("in.txt","r",stdin);    cout<<"三种二分搜索(binary_search, lower_bound, upper_bound"<<endl;    cout<<"不减序列  incre[9]={1,2,2,2,2,4,6,6,8} "<<endl;    cout<<"不增序列  decre[9]={8,6,6,4,2,2,2,2,1} "<<endl<<endl;                ///**************测试1: binary_search    cout<<"**********测试1: binary_search**********"<<endl;    cout<<"不减序列  incre[9]={1,2,2,2,2,4,6,6,8} "<<endl;    cout<<"Binary_Search(incre,0,7,2)    "<<Binary_Search(incre,0,7,2)<<endl;    cout<<"Binary_Search(incre,0,7,4)    "<<Binary_Search(incre,0,7,4)<<endl;    cout<<"Binary_Search(incre,0,7,1)    "<<Binary_Search(incre,0,7,1)<<endl;    cout<<"Binary_Search(incre,0,7,10)   "<<Binary_Search(incre,0,7,10)<<endl;    cout<<"不增序列  decre[9]={8,6,6,4,2,2,2,2,1} "<<endl;    cout<<"Binary_Search_decre(decre,0,7,2)    "<<Binary_Search_decre(decre,0,7,2)<<endl;    cout<<"Binary_Search_decre(decre,0,7,4)    "<<Binary_Search_decre(decre,0,7,4)<<endl;    cout<<"Binary_Search_decre(decre,0,7,1)    "<<Binary_Search_decre(decre,0,7,1)<<endl;    cout<<"Binary_Search_decre(decre,0,7,10)   "<<Binary_Search_decre(decre,0,7,10)<<endl<<endl;                ///**************测试2: lower_bound    cout<<"**********测试2: lower_bound**********"<<endl;    cout<<"不减序列  incre[9]={1,2,2,2,2,4,6,6,8} "<<endl;    cout<<"lower_Bound(incre,0,9,2)    "<<lower_Bound(incre,0,9,2)<<endl;    cout<<"lower_Bound(incre,0,9,6)    "<<lower_Bound(incre,0,9,6)<<endl;    cout<<"lower_Bound(incre,0,9,4)    "<<lower_Bound(incre,0,9,4)<<endl;    cout<<"lower_Bound(incre,0,9,5)    "<<lower_Bound(incre,0,9,5)<<endl;    cout<<"lower_Bound(incre,0,9,8)    "<<lower_Bound(incre,0,9,8)<<endl;    cout<<"lower_Bound(incre,0,9,10)   "<<lower_Bound(incre,0,9,10)<<endl;    cout<<"跟C++标准库里面的 lower_bound()比较"<<endl;    cout<<"lower_bound(incre,incre+9,2)-incre    "<<lower_bound(incre,incre+9,2)-incre<<endl;    cout<<"lower_bound(incre,incre+9,6)-incre    "<<lower_bound(incre,incre+9,6)-incre<<endl;    cout<<"lower_bound(incre,incre+9,4)-incre    "<<lower_bound(incre,incre+9,4)-incre<<endl;    cout<<"lower_bound(incre,incre+9,5)-incre    "<<lower_bound(incre,incre+9,5)-incre<<endl;    cout<<"lower_bound(incre,incre+9,8)-incre    "<<lower_bound(incre,incre+9,8)-incre<<endl;    cout<<"lower_bound(incre,incre+9,10)-incre   "<<lower_bound(incre,incre+9,10)-incre<<endl<<endl;            ///**************测试2: lower_bound_decre    cout<<"测试lower_bound_decre(decre,0,9,v)\n"        <<"在一个单调不增的序列decre[]中,查找decre[]满足decre[i]<=v 条件的最小的i"<<endl;    cout<<"不增序列  decre[9]={8,6,6,4,2,2,2,2,1} "<<endl;    cout<<"lower_bound_decre(decre,0,9,2)    "<<lower_bound_decre(decre,0,9,2)<<endl;    cout<<"lower_bound_decre(decre,0,9,8)    "<<lower_bound_decre(decre,0,9,8)<<endl;    cout<<"lower_bound_decre(decre,0,9,6)    "<<lower_bound_decre(decre,0,9,6)<<endl;    cout<<"lower_bound_decre(decre,0,9,4)    "<<lower_bound_decre(decre,0,9,4)<<endl;    cout<<"lower_bound_decre(decre,0,9,10)   "<<lower_bound_decre(decre,0,9,10)<<endl;    cout<<"lower_bound_decre(decre,0,9,0)    "<<lower_bound_decre(decre,0,9,0)<<endl;    cout<<"lower_bound_decre(decre,0,9,-1)   "<<lower_bound_decre(decre,0,9,-1)<<endl<<endl;            ///**************测试3: upper_bound    cout<<"**********测试3: upper_bound**********"<<endl;    cout<<"不减序列  incre[9]={1,2,2,2,2,4,6,6,8} "<<endl;    cout<<"upper_Bound(incre,0,9,2)    "<<upper_Bound(incre,0,9,2)<<endl;    cout<<"upper_Bound(incre,0,9,1)    "<<upper_Bound(incre,0,9,1)<<endl;    cout<<"upper_Bound(incre,0,9,4)    "<<upper_Bound(incre,0,9,4)<<endl;    cout<<"upper_Bound(incre,0,9,6)    "<<upper_Bound(incre,0,9,6)<<endl;    cout<<"upper_Bound(incre,0,9,8)    "<<upper_Bound(incre,0,9,8)<<endl;    cout<<"upper_Bound(incre,0,9,10)   "<<upper_Bound(incre,0,9,10)<<endl;    cout<<"与C++标准库中upper_bound()的比较"<<endl;    cout<<"upper_bound(incre,incre+9,2)-incre    "<<upper_bound(incre,incre+9,2)-incre<<endl;    cout<<"upper_bound(incre,incre+9,1)-incre    "<<upper_bound(incre,incre+9,1)-incre<<endl;    cout<<"upper_bound(incre,incre+9,4)-incre    "<<upper_bound(incre,incre+9,4)-incre<<endl;    cout<<"upper_bound(incre,incre+9,6)-incre    "<<upper_bound(incre,incre+9,6)-incre<<endl;    cout<<"upper_bound(incre,incre+9,8)-incre    "<<upper_bound(incre,incre+9,8)-incre<<endl;    cout<<"upper_bound(incre,incre+9,10)-incre   "<<upper_bound(incre,incre+9,10)-incre<<endl<<endl;            ///**************测试4: upper_bound_decre    cout<<"**********测试4: upper_bound_decre**********\n"        <<"在一个单调不增的序列decre[]中,查找decre[]满足decre[i]<v 条件的最小的i"<<endl;    cout<<"不增序列  decre[9]={8,6,6,4,2,2,2,2,1} "<<endl;    cout<<"upper_bound_decre(decre,0,9,2)    "<<upper_bound_decre(decre,0,9,2)<<endl;    cout<<"upper_bound_decre(decre,0,9,4)    "<<upper_bound_decre(decre,0,9,4)<<endl;    cout<<"upper_bound_decre(decre,0,9,6)    "<<upper_bound_decre(decre,0,9,6)<<endl;    cout<<"upper_bound_decre(decre,0,9,8)    "<<upper_bound_decre(decre,0,9,8)<<endl;    cout<<"upper_bound_decre(decre,0,9,1)    "<<upper_bound_decre(decre,0,9,1)<<endl;    cout<<"upper_bound_decre(decre,0,9,10)   "<<upper_bound_decre(decre,0,9,10)<<endl;    cout<<"upper_bound_decre(decre,0,9,-1)   "<<upper_bound_decre(decre,0,9,-1)<<endl;    return 0;}