# 二進位制（二分查詢）搜尋

``````BINARY_SEARCH(A, lower_bound, upper_bound, VAL)

END = upper_bound, POS = - 1

SET POS = MID
PRINT POS

ELSE IF A[MID] > VAL
SET END = MID - 1
ELSE
SET BEG = MID + 1
[END OF IF]
[END OF LOOP]

PRINT "VALUE IS NOT PRESENT IN THE ARRAY"
[END OF IF]

``````

1 最壞情況 O(log n)
2 最好情況 O(1)
3 平均情況 O(log n)
4 最壞情況空間複雜性 O(1)

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

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

``````beg = mid + 1 = 7
End = 8
mid = 15/2 = 7
a[mid] = a[7]
a[7] = 23 = item;

``````

``````#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
{
}
}
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;
}
``````

``````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
}
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;
}
}
``````

``````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 ");
location = binarySearch(arr, 0, 9, item);
if(location != -1)
{
Console.WriteLine("Item found at location "+ location);
}
else
{
}
}
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;

}
}
``````

``````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:
``````

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

Enter the item which you want to search ?
101
``````

``````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;
}
``````