📌  相关文章
📜  数据结构-二元搜索

📅  最后修改于: 2020-10-15 01:18:28             🧑  作者: Mango

二元搜寻

二进制搜索是一种在排序列表上有效工作的搜索技术。因此，为了使用二进制搜索技术将元素搜索到某个列表中，我们必须确保对列表进行排序。

二进制搜索遵循分而治之的方法，其中将列表分为两半，并将项目与列表的中间元素进行比较。如果找到匹配项，则返回中间元素的位置，否则，我们将根据通过匹配项产生的结果来搜索这两个部分。

二元搜索算法如下。

BINARY_SEARCH(A，Lower_bound，upper_bound，VAL)

  • 步骤1： [INITIALIZE] SET BEG = lower_bound END = upper_bound，POS =-1
  • 步骤2：在BEG <= END的同时重复步骤3和4
  • 步骤3： SET MID =(BEG + END)/ 2
  • 步骤4：如果A [MID] = VAL SET POS = MID PRINT POS转到步骤6 ELSE如果A [MID]> VAL SET END = MID-1 ELSE SET BEG = MID + 1 [IF的结束] [LOOP结束]
  • 步骤5：如果POS = -1，则打印“阵列中不存在值” [IF结束]
  • 步骤6：退出

复杂

SN Performance Complexity
1 Worst case O(log n)
2 Best case O(1)
3 Average Case O(log n)
4 Worst case space complexity O(1)

例

让我们考虑一个数组arr = {1、5、7、8、13、19、20、23、29}。在数组中找到项目23的位置。

第一步：

BEG = 0 
END = 8ron
MID = 4 
a[mid] = a[4] = 13 < 23, therefore

在第二步：

Beg = mid +1 = 5 
End = 8
mid = 13/2 = 6  
a[mid] = a[6] = 20 < 23, therefore;

第三步：

beg = mid + 1 = 7 
End = 8 
mid = 15/2 = 7
a[mid] = a[7] 
 a[7] = 23 = item; 
therefore, set location = mid; 
The location of the item will be 7.

使用递归的二进制搜索程序

C程序

#include
int binarySearch(int[], int, int, int);
void main ()
{
    int arr[10] = {16, 19, 20, 23, 45, 56, 78, 90, 96, 100};
    int item, location=-1; 
    printf("Enter the item which you want to search ");
    scanf("%d",&item);
    location = binarySearch(arr, 0, 9, item);
    if(location != -1) 
    {
        printf("Item found at location %d",location);
    }
    else
    {
        printf("Item not found");
    }
} 
int binarySearch(int a[], int beg, int end, int item)
{
    int mid;
    if(end >= beg) 
    {    
        mid = (beg + end)/2;
        if(a[mid] == item)
        {
            return mid+1;
        }
        else if(a[mid] < item) 
        {
            return binarySearch(a,mid+1,end,item);
        }
        else 
        {
            return binarySearch(a,beg,mid-1,item);
        }
    
    }
    return -1; 
}

输出：

Enter the item which you want to search 
19 
Item found at location 2

爪哇

import java.util.*;
public class BinarySearch {
public static void main(String[] args) {
    int[] arr = {16, 19, 20, 23, 45, 56, 78, 90, 96, 100};
    int item, location = -1;
    System.out.println("Enter the item which you want to search");
    Scanner sc = new Scanner(System.in);
    item = sc.nextInt();
    location = binarySearch(arr,0,9,item);
    if(location != -1)
    System.out.println("the location of the item is "+location);
    else 
        System.out.println("Item not found");
    }
public static int binarySearch(int[] a, int beg, int end, int item)
{
    int mid;
    if(end >= beg) 
    {    
        mid = (beg + end)/2;
        if(a[mid] == item)
        {
            return mid+1;
        }
        else if(a[mid] < item) 
        {
            return binarySearch(a,mid+1,end,item);
        }
        else 
        {
            return binarySearch(a,beg,mid-1,item);
        }
    
    }
    return -1; 
}
}

输出：

Enter the item which you want to search 
45 
the location of the item is 5

C＃

using System;
                
public class LinearSearch
{
    public static void Main()
    {
    int[] arr = {16, 19, 20, 23, 45, 56, 78, 90, 96, 100};
    int location=-1; 
    Console.WriteLine("Enter the item which you want to search ");
    int item = Convert.ToInt32(Console.ReadLine());
    location = binarySearch(arr, 0, 9, item);
    if(location != -1) 
    {
        Console.WriteLine("Item found at location "+ location);
    }
    else
    {
        Console.WriteLine("Item not found");
    }
} 
public static int binarySearch(int[] a, int beg, int end, int item)
{
    int mid;
    if(end >= beg) 
    {    
        mid = (beg + end)/2;
        if(a[mid] == item)
        {
            return mid+1;
        }
        else if(a[mid] < item) 
        {
            return binarySearch(a,mid+1,end,item);
        }
        else 
        {
            return binarySearch(a,beg,mid-1,item);
        }
    
    }
    return -1; 

    }
}

输出：

Enter the item which you want to search 
20 
Item found at location 3

Python

def binarySearch(arr,beg,end,item):
    if end >= beg:
        mid = int((beg+end)/2)
        if arr[mid] == item :
            return mid+1
        elif arr[mid] < item : 
            return binarySearch(arr,mid+1,end,item)
        else: 
            return binarySearch(arr,beg,mid-1,item)
    return -1
    

arr=[16, 19, 20, 23, 45, 56, 78, 90, 96, 100];
item = int(input("Enter the item which you want to search ?"))
location = -1; 
location = binarySearch(arr,0,9,item);
if location != -1: 
    print("Item found at location %d" %(location))
else: 
    print("Item not found")

输出：

Enter the item which you want to search ? 
96 
Item found at location 9 

Enter the item which you want to search ? 
101 
Item not found

使用迭代的二进制搜索函数

int binarySearch(int a[], int beg, int end, int item)
{
    int mid;
    while(end >= beg) 
    {    
        mid = (beg + end)/2;
        if(a[mid] == item)
        {
            return mid+1;
        }
        else if(a[mid] < item) 
        {
            beg = mid + 1;
        }
        else 
        {
            end = mid - 1; 
        }
    
    }
    return -1; 
}