There are two approches to Code Binary Search :
At first let us see the Iterative approach :
package main
import "fmt"
func search(arr []int, number int) int {
left := 0
right := len(arr)-1
for left <= right {
midPoint := int((left + right) / 2)
if (number == arr[midPoint]) {
return midPoint
}
if (number < arr[midPoint]) {
right = midPoint-1
} else {
left = midPoint+1
}
}
return -1
}
func main() {
arr := []int{ 5, 8, 20, 28, 44, 66, 81, 92, 99 }
num := 5 // Number to be searched.
fmt.Println("The Array elements are : ")
for _, val := range arr {
fmt.Println(val)
}
index := search(arr, num)
if(index == -1) {
fmt.Println("Element is not present in the array")
} else {
fmt.Println("The element", num, "is present at index",index)
}
}
The above code is quite simple.
We will be searching for the number 5.
num := 5 // Number to be searched.
From the array,
arr := []int{ 5, 8, 20, 28, 44, 66, 81, 92, 99 }Now, we will call the search(...) method. Where the Binary Search logic resides.
func search(arr []int, number int) int {
left := 0
right := len(arr)-1
for left <= right {
midPoint := int((left + right) / 2)
if (number == arr[midPoint]) {
return midPoint
}
if (number < arr[midPoint]) {
right = midPoint-1
} else {
left = midPoint+1
}
}
return -1
}So, initially we are assigning the value of the variable left with 0 and right with arr.length-1 (i.e. 8).
left := 0 right := len(arr)-1
Next, we run a while loop that only stops when left and right variables have crossed each other or we find the element.
In simple words it only stops when left variable is greater than right.
for left <= right {
midPoint := int((left + right) / 2)
if (number == arr[midPoint]) {
return midPoint
}
if (number < arr[midPoint]) {
right = midPoint-1
} else {
left = midPoint+1
}
}We calculate the midpoint.
midPoint := int((left + right) / 2)
i.e. 4(As we take 4 only from 4.5).
Then we check, if the number to be searched (i.e. 5) is equal to arr[midpoint] or not?
if (number == arr[midPoint]) {
return midPoint
}In this case, the number to be searched i.e. 5 is not equal to arr[midpoint] i.e. 44.
So, we go to the next if statement. Where we check if the number to be searched is less than arr[midpoint] or not?
if (number < arr[midPoint]) {
right = midPoint-1
}In this case the number to be searched i.e. 5 is less than arr[midpoint] i.e. 44.
So, we make the right variable point to a position, just before the midpoint was pointing to.
And discard the right part along with the midpoint.
right = midPoint-1
And the while loop repeats again.
Calculating the midpoint.
And the same process repeats until we find the element.
Now, we find the element.
if (number == arr[midPoint]) {
return midPoint
}And the loop ends returning midpoint.
And we get the index, where the element 5 resides.
index := search(arr, num)
Finally, we print the index, where the element 5 is present.
fmt.Println("The element", num, "is present at index",index)And, what if the element we are searching is not present in the array?
Say, we are trying to search for the element 4, which is not in the array.
In that case left and right crosses each other and index is returned as -1.
return -1
And we print the below statement.
if(index == -1) {
fmt.Println("Element is not present in the array")
}Next, let us look at the recursive approach.
Recursion is a process, where a method calls itself. There are some recursive algorithms that are a little tough to understand.
But, trust me, the Recursive approach of Binary Search is very easy to understand.
package main
import "fmt"
func search(arr [] int, left int, right int, number int) int {
if (left <= right) {
midPoint := int((left + right) / 2)
if (number == arr[midPoint]) {
return midPoint
}
if (number < arr[midPoint]) {
return search(arr, left, midPoint-1, number)
} else {
return search(arr, midPoint+1, right, number)
}
}
return -1;
}
func main() {
arr := []int{ 5, 8, 20, 28, 44, 66, 81, 92, 99 }
len := len(arr)-1
num := 5 // Number to be searched.
fmt.Println("The Array elements are : ")
for _, val := range arr {
fmt.Println(val)
}
index := search(arr, 0, len , num)
if(index == -1) {
fmt.Println("Element is not present in the array")
} else {
fmt.Println("The element", num, "is present at index",index)
}
}
The above recursive code is almost same as the Iterative approach, with a mild difference.
Let us just understand the difference.
Below is the only piece of code that is different from the Iterative code.
if (number < arr[midPoint]) {
return search(arr, left, midPoint-1, number)
} else {
return search(arr, midPoint+1, right, number)
}Let us take the iterative piece and compare it.
if (number < arr[midPoint]) {
right = midPoint-1
} else {
left = midPoint+1
}In the iterative piece we have made
right = midpoint-1
If the number to be searched is less than the midpoint.
We have exactly done the same thing in recursive approach as well.
if (number < arr[midPoint]) {
return search(arr, left, midPoint-1, number)
}If the number to be searched is less than the midpoint. We make a recursive call to the method :
Which means, the func search(arr []int, left int, right int, number int) int method is called again with the new value of right as midPoint-1.
Which is exactly same as the Iterative piece.
right = midpoint-1;
Similarly, in the else part of Recursive code, we have,
else {
return search(arr, midPoint+1, right, number)
}
Which is exactly same as the Iterative piece.
left = midPoint+1
We have claimed that the running time for Binary search is O(log n).
How do we calculate log n ?
There are 9 elements in the above array. For a clean and easy calculation let us consider the above array has 8 elements.
We know 8 can also be represented as (2)3 .
Now, we can say,
And,
Now since, we have considered the above array has 8 elements. Which has a running time of log 3.
Let's prove it:
So, Binary Search ran 3 times. And thats all we had to prove.
Running time of Binary Search : O(log n)