Binary Searching Algorithm PowerPoint Presentation

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El algoritmo de búsqueda binaria es un método eficiente para encontrar elementos en listas ordenadas, mediante un enfoque de dividir y conquistar. Compara el elemento buscado con el elemento medio y busca en la mitad correspondiente dependiendo del resultado, pudiendo implementarse de manera iterativa o recursiva. Se presentan ejemplos de implementación en C y Java, donde se verifica si el elemento buscado se encuentra en el array y se devuelve su posición.

Software

Binary search is the search technique that works
efficiently on sorted lists. Hence, to search an element
into some list using the binary search technique, we
must ensure that the list is sorted.
Binary search follows the divide and conquer approach
in which the list is divided into two halves, and the item is
compared with the middle element of the list. If the match
is found then, the location of the middle element is
returned. Otherwise, we search into either of the halves
depending upon the result produced through the match.

Binary_Search(a, lower_bound, upper_bound, val) // 'a' is the
given array, 'lower_bound' is the index of the first array element, 'upper_bound' is
the index of the last array element, 'val' is the value to search
Step 1: set beg = lower_bound, end = upper_bound, pos = - 1
Step 2: repeat steps 3 and 4 while beg <=end
Step 3: set mid = (beg + end)/2
Step 4: if a[mid] = val
set pos = mid
print pos
go to step 6
else if a[mid] > val
set end = mid - 1
else
set beg = mid + 1
[end of if]
[end of loop]
Step 5: if pos = -1
print "value is not present in the array"
[end of if]
Step 6: exit

Working of Binary search
There are two methods to implement the binary search
algorithm -
■ Iterative method
■ Recursive method
The recursive method of binary search follows the divide
and conquer approach.
Let the elements of array are -
Let the element to search is, K =
56

To calculate the mid of the array -
mid = (beg + end)/2
So, in the given array -
beg = 0
end = 8
mid = (0 + 8)/2 = 4. So, 4 is the mid of the array.

Now, the element to search is found. So algorithm will return
the index of the element matched.

Binary search in C language
#include <stdio.h>
int binarySearch(int a[], int beg, int end, int val)
{
int mid;
if(end >= beg)
{
mid = (beg + end)/2;
if(a[mid] == val)
{
return mid+1;
}
else if(a[mid] < val)
{
return binarySearch(a, mid+1, end, val);
}
else
{
return binarySearch(a, beg, mid-1, val);
}
}
return -1;
}

int main() {
int a[] = {11, 14, 25, 30, 40, 41, 52, 57, 70};
int val = 40;
int n = sizeof(a) / sizeof(a[0]);
int res = binarySearch(a, 0, n-1, val);
printf("The elements of the array are - ");
for (int i = 0; i < n; i++)
printf("%d ", a[i]);
printf("nElement to be searched is - %d", val);
if (res == -1)
printf("nElement is not present in the array");
else
printf("nElement is present at %d position of array", res);
return 0;
}

Binary search in Java language
class BinarySearch {
static int binarySearch(int a[], int beg, int end, int val)
{
int mid;
if(end >= beg)
{
mid = (beg + end)/2;
if(a[mid] == val)
{
return mid+1;
}
else if(a[mid] < val)
{
return binarySearch(a, mid+1, end, val);
}
else
{
return binarySearch(a, beg, mid-1, val);
}
}
return -1;
}

public static void main(String args[]) {
int a[] = {8, 10, 22, 27, 37, 44, 49, 55, 69};
int val = 37;
int n = a.length;
int res = binarySearch(a, 0, n-1, val);
System.out.print("The elements of the array are: ");
for (int i = 0; i < n; i++)
{
System.out.print(a[i] + " ");
}
System.out.println();
System.out.println("Element to be searched is: " + val);
if (res == -1)
System.out.println("Element is not present in the array");
else
System.out.println("Element is present at " + res + " position of
array");
}
}

Binary Searching Algorithm PowerPoint Presentation

1. Binary search is the search technique that works efficiently on sorted lists. Hence, to search an element into some list using the binary search technique, we must ensure that the list is sorted. Binary search follows the divide and conquer approach in which the list is divided into two halves, and the item is compared with the middle element of the list. If the match is found then, the location of the middle element is returned. Otherwise, we search into either of the halves depending upon the result produced through the match.

2. Binary_Search(a, lower_bound, upper_bound, val) // 'a' is the given array, 'lower_bound' is the index of the first array element, 'upper_bound' is the index of the last array element, 'val' is the value to search Step 1: set beg = lower_bound, end = upper_bound, pos = - 1 Step 2: repeat steps 3 and 4 while beg <=end Step 3: set mid = (beg + end)/2 Step 4: if a[mid] = val set pos = mid print pos go to step 6 else if a[mid] > val set end = mid - 1 else set beg = mid + 1 [end of if] [end of loop] Step 5: if pos = -1 print "value is not present in the array" [end of if] Step 6: exit

3. Working of Binary search There are two methods to implement the binary search algorithm - ■ Iterative method ■ Recursive method The recursive method of binary search follows the divide and conquer approach. Let the elements of array are - Let the element to search is, K = 56

4. To calculate the mid of the array - mid = (beg + end)/2 So, in the given array - beg = 0 end = 8 mid = (0 + 8)/2 = 4. So, 4 is the mid of the array.

5. Now, the element to search is found. So algorithm will return the index of the element matched.

6. Binary search in C language #include <stdio.h> int binarySearch(int a[], int beg, int end, int val) { int mid; if(end >= beg) { mid = (beg + end)/2; if(a[mid] == val) { return mid+1; } else if(a[mid] < val) { return binarySearch(a, mid+1, end, val); } else { return binarySearch(a, beg, mid-1, val); } } return -1; }

7. int main() { int a[] = {11, 14, 25, 30, 40, 41, 52, 57, 70}; int val = 40; int n = sizeof(a) / sizeof(a[0]); int res = binarySearch(a, 0, n-1, val); printf("The elements of the array are - "); for (int i = 0; i < n; i++) printf("%d ", a[i]); printf("nElement to be searched is - %d", val); if (res == -1) printf("nElement is not present in the array"); else printf("nElement is present at %d position of array", res); return 0; }

8. Binary search in Java language class BinarySearch { static int binarySearch(int a[], int beg, int end, int val) { int mid; if(end >= beg) { mid = (beg + end)/2; if(a[mid] == val) { return mid+1; } else if(a[mid] < val) { return binarySearch(a, mid+1, end, val); } else { return binarySearch(a, beg, mid-1, val); } } return -1; }

9. public static void main(String args[]) { int a[] = {8, 10, 22, 27, 37, 44, 49, 55, 69}; int val = 37; int n = a.length; int res = binarySearch(a, 0, n-1, val); System.out.print("The elements of the array are: "); for (int i = 0; i < n; i++) { System.out.print(a[i] + " "); } System.out.println(); System.out.println("Element to be searched is: " + val); if (res == -1) System.out.println("Element is not present in the array"); else System.out.println("Element is present at " + res + " position of array"); } }

Binary Searching Algorithm PowerPoint Presentation

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