二分查找终极版

来源：互联网发布：北京值得去的地方知乎编辑：程序博客网时间：2024/06/03 21:08

本人最近懒癌发作，博客已经几个月没动了，突然良心发现自己二分理解的不好，万一要去省赛岂不是要收到来自大神的嘲讽？

二分分为四种，严格大于某值的最小值；严格小于某值的最大值；大于等于某值的最小值；小于等于某值的最大值

我们需要关注三个地方：

1.循环的条件 low<high 因为如果两者相等说明找到了

2.改变边界的方法及条件：满足要求条件的时候对应边界=mid 否则mid+1或者-1

3.mid的取整方法：如果的找大于某值的最小值向下取整；小于某值的最大值向上取整

#include<cstdio>#include<cstring>using namespace std;int main(){    int Array[7]={2,4,6,8,10,12,14};    int low=0,high=6,mid=3,target=8;    puts("target:8");    puts("> min");    while(low<high)    {         if (Array[mid] > target)//ok            high = mid;        else            low = mid + 1;        mid = (low + high) / 2;        printf("low=%d,mid=%d,high=%d\n",Array[low],Array[mid],Array[high]);    }    printf("%d\n----------------------\n",Array[mid]);    low=0,high=6,mid=3,target=8;    puts("< max");    while(low<high)    {         int flag=-1;         if (Array[mid] < target)//ok            low = mid;        else            high = mid - 1,flag=1;        mid = (low + high+1) / 2;        printf("flag=%d,low=%d,mid=%d,high=%d\n",flag,Array[low],Array[mid],Array[high]);    }    printf("%d\n----------------------\n",Array[mid]);    low=0,high=6,mid=3,target=8;    puts(">= min");    while(low<high)    {         if (Array[mid] >= target)//ok            high = mid;        else            low = mid + 1;        mid = (low + high) / 2;        printf("low=%d,mid=%d,high=%d\n",Array[low],Array[mid],Array[high]);    }    printf("%d\n----------------------\n",Array[mid]);    low=0,high=6,mid=3,target=8;    puts("<= max");    while(low<high)    {         if (Array[mid] <= target)//ok            low = mid;        else            high = mid - 1;        mid = (low + high+1) / 2;        printf("low=%d,mid=%d,high=%d\n",Array[low],Array[mid],Array[high]);    }    printf("%d\n----------------------\n",Array[mid]);    return 0;}

输出

target:8
> min
low=10,mid=12,high=14
low=10,mid=10,high=12
low=10,mid=10,high=10
10
----------------------
< max
flag=1,low=2,mid=4,high=6
flag=-1,low=4,mid=6,high=6
flag=-1,low=6,mid=6,high=6
6
----------------------
>= min
low=2,mid=4,high=8
low=6,mid=6,high=8
low=8,mid=8,high=8
8
----------------------
<= max
low=8,mid=12,high=14
low=8,mid=10,high=10
low=8,mid=8,high=8
8
----------------------

0 0