二進位制（二分查詢）搜尋

二進位制搜尋是一種在排序列表上有效工作的搜尋技術。 因此，要使用二進位制搜尋技術來搜尋某個列表中的元素，需要確保對列表是一個已排好順序。

二進位制搜尋遵循分而治之的方法，其中，列表被分成兩半，並且專案與列表的中間元素進行比較。 如果找到匹配，則返回中間元素的位置，否則根據匹配產生的結果搜尋到兩半中的任何一個。

二進位制搜尋演算法如下。

BINARY_SEARCH(A, lower_bound, upper_bound, VAL)
第1步: [INITIALIZE] SET BEG = lower_bound
    END = upper_bound, POS = - 1
第2步: Repeat Steps 3 and 4 while BEG <=END
第3步: SET MID = (BEG + END)/2
第4步: IF A[MID] = VAL
    SET POS = MID
    PRINT POS
轉到第6步
    ELSE IF A[MID] > VAL
    SET END = MID - 1
    ELSE
    SET BEG = MID + 1
    [END OF IF]
    [END OF LOOP]
第5步: IF POS = -1
    PRINT "VALUE IS NOT PRESENT IN THE ARRAY"
    [END OF IF]
第6步: EXIT

複雜度

範例

考慮有一個陣列arr = {1,5,7,8,13,19,20,23,29}，要在陣列中查詢專案：23的位置。

第1步：

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

第2步：

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

第3步：

beg = mid + 1 = 7   
End = 8   
mid = 15/2 = 7  
a[mid] = a[7]   
 a[7] = 23 = item;   
那麼, 設定 location = mid;   
專案的位置為： 7

演算法可參考以下圖解 -

使用遞迴的二進位制搜尋程式

使用C語言實現 -

#include<stdio.h>  
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;   
}

執行上面範例程式碼，得到以下結果：

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

Java語言實現二進位制查詢 -

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;   
 }  
}

執行上面範例程式碼，得到以下結果 -

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

C#語言實現範例程式碼 -

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;   

    }  
}

執行上面範例程式碼，得到以下結果 -

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

Python語言實現程式碼 -

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")

執行上面範例程式碼，得到以下結果 -

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

使用疊代的二進位制搜尋函式實現 -

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;   
}