二分法搜索算法实现详解

本文概述

• BINARY_SEARCH（A, Lower_bound, upper_bound, VAL）
• 复杂
• 使用递归的二进制搜索程序
• 使用迭代的二进制搜索功能

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

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<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; 
}

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

蟒蛇

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功能

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; 
}