二分查找算法的C++和Python实现

二分查找算法是在有序数组中用到的较为频繁的一种算法,在未接触二分查找算法时,最通用的一种做法是,对数组进行遍历,跟每个元素进行比较,其时间为O(n).但二分查找算法则更优,因为其查找时间为O(lgn),譬如数组{1, 2, 3, 4, 5, 6, 7, 8, 9},查找元素6,用二分查找的算法执行的话,其顺序为:

1. 第一步查找中间元素,即5,由于5<6,则6必然在5之后的数组元素中,那么就在{6, 7, 8, 9}中查找,
2. 寻找{6, 7, 8, 9}的中位数,为7,7>6,则6应该在7左边的数组元素中,那么只剩下6,即找到了。

二分查找算法就是不断将数组进行对半分割,每次拿中间元素和goal进行比较。

C++实现(来自二分查找算法

#include <iostream>
using namespace std;

int binary_search(int *a,int len,int goal);

int main()
{
    const int LEN = 10;
    int a[LEN];
    for (int i = 0;i<LEN;i++)
        a[i] = i*3;
    int target = 5;
    int index = binary_search(a,LEN,target);
    if (index != -1)
        cout<<target<<"在数组中的下标为"<<index<<endl;
    else
        cout<<"不存在"<<target<<endl;

    system("pause");
    return 0;
}

int binary_search(int *a,int len,int goal)
{
    int low = 0;
    int high = len-1;
    while(low<=high)
    {
        int middle = (high -low)/2+low;
        if(a[middle] == goal)
            return middle;
        else if(a[middle]>goal){
            high = middle-1;
            cout<<"high="<<high<<endl;
        }
        else if(a[middle]<goal){
            low = middle+1;
            cout<<"low="<<low<<endl;
        }


    }
    return -1;
}

编译运行结果:

high=3 low=2 high=1 不存在5 请按任意键继续. . .

Python实现

def binary_search(lst,goal):
    l = len(lst)
    left = 0
    right = l-1
    while(left <= right):
        middle = (right - left)/2+left
        print middle
        if lst[middle] == goal:
            return middle
        elif lst[middle]>goal:
            right = middle -1
        elif lst[middle]<goal:
            left = middle +1
    return -1

运行以下实例

length = 10
lst = []
for i in range(length):
    lst.append(i*3)

goal = 21
index = binary_search(lst,goal)
if (index!=-1):
    print 'the index of number %d is %d.'%(goal,index)
else:
    print 'the number %d does not exist.'%(goal)

结果:

4
7
the index of number 21 is 7.
    原文作者:查找算法
    原文地址: https://blog.csdn.net/horseinch/article/details/52006803
    本文转自网络文章,转载此文章仅为分享知识,如有侵权,请联系博主进行删除。
点赞