Binary Search is an algorithm that helps us find an element in a sorted array in O(log n) time. Its algorithm works on the principle of Divide and Conquer and it works only when the available data is sorted.
Now, when we are using binary search three situation arise:
- If the middle element is the element to be searched, we return the index of the middle element.
- If the middle element is smaller than the element to be searched, we search in the sub-array to the right (Mid to End) in the same way (Get the new middle and check all the three cases again). We search in the right sub-array because the data is sorted, thus all elements before middle element will also be either less than or equal to the middle element.
- If the middle element is greater than the element to be searched, we search in the sub-array to the left(Start to Mid).
This process is continued until either we find the element to be searched or the size of the sub-array reduces to zero.
Example:
There are three ways to perform Binary Search in Scala.
Recursive Approach
In recursive approach, we recursively call for the implemented binary search algorithm with updated values of start and end until either we match the middle element with the element to be searched or the array size reduces to zero. Below is the code for the recursive approach of Binary Search in Scala.
// Scala code for Recursive Binary Search // Creating object object GFG{ // Creating a recursive Binary Search function def RecursiveBinarySearch(arr: Array[Int], Element_to_Search: Int) (low: Int = 0, high: Int = arr.length - 1): Int = { // If element not found if (low > high) return -1 // Getting the middle element var middle = low + (high - low) / 2 // If element found if (arr(middle) == Element_to_Search) return middle // Searching in the left half else if (arr(middle) > Element_to_Search) return RecursiveBinarySearch(arr, Element_to_Search)(low, middle - 1) // Searching in the right half else return RecursiveBinarySearch(arr, Element_to_Search)(middle + 1, high) } // Creating main function def main(args: Array[String]){ // Calling the binary search function and // storing its result in index variable var index = RecursiveBinarySearch(Array(1, 2, 3, 4, 55, 65, 75), 4)(0, 6); // If value not found if(index == -1) print("Not Found") // Else print the index where // the value is found else print("Element found at Index " + index) } } |
Output
Element found at Index 3
Iterative approach
In iterative approach, we run a while loop until we either find the element to be searched or the array size reduces to zero. Below is the code for iterative approach of Binary Search in Scala.
// Scala code for Iterative Binary Search // Creating object object GFG{ // Creating Binary Search function // Accepting the passed array and // element to be searched def IterativeBinarySearch(arr: Array[Int], Element_to_Search: Int): Int ={ // Creating start variable to // point to the first value var low = 0 // Creating end variable to // point to the last value var high = arr.length - 1 // Finding the value in the // array iteratively while (low <= high) { // Getting middle element var middle = low + (high - low) / 2 // If element found in the middle index if (arr(middle) == Element_to_Search) return middle // Searching in the first half else if (arr(middle) > Element_to_Search) high = middle - 1 // Searching in the second half else low = middle + 1 } // If value not found in the // entire array , return -1 -1} // Creating main function def main(args: Array[String]) { // Calling the binary search function and // storing its result in index variable var index = IterativeBinarySearch(Array(1, 2, 3, 4, 55, 65, 75), 65); // If value not found if(index == -1) print("Not Found") // Else print the index where // the value is found else print("Element found at Index " + index) } } |
<Output
Element found at Index 5
Pattern Matching And Functional Programming Approach
In this, we first match the middle element with the element to be searched. If the element is present, we return the index of it. Otherwise, we keep calling the created function with the updated parameters. Below is the code for the approach:
// Scala code for Iterative Binary Search // Creating object object GFG{ // Using the functional programming approach def FunctionalBinarySearch(arr: Array[Int], Element_to_Search: Int): Int ={ def BinarySearch(arr: Array[Int], Element_to_Search: Int, low: Int, high: Int): Int = { // If element not found if (low > high) return -1 // Getting middle index var middle = low + (high - low) / 2 // Pattern matching arr match { // If element found , return the index case(arr:Array[Int]) if (arr(middle) == Element_to_Search) => middle // Call the function for the second half case(arr:Array[Int]) if (arr(middle) < Element_to_Search) => BinarySearch(arr, Element_to_Search, middle + 1, high) // Call the function for the first half case(arr:Array[Int]) if (arr(middle) > Element_to_Search) => BinarySearch(arr, Element_to_Search, low, middle - 1) } } // Calling the Binary Search function BinarySearch(arr, Element_to_Search, 0, arr.length - 1) } // Creating main function def main(args: Array[String]){ // Calling the binary search function and // storing its result in index variable var index = FunctionalBinarySearch(Array(1, 2, 3, 4, 55, 65, 75), 44); // If value not found if(index == -1) print("Element not found") // Else print the index where // the value is found else print("Element found at Index " + index) } } |
Output
Element not found
