First strictly greater element in a sorted array in Java

Given a sorted array and a target value, find the first element that is strictly greater than given element.

Examples: 

Input : arr[] = {1, 2, 3, 5, 8, 12} 
        Target = 5
Output : 4 (Index of 8)

Input : {1, 2, 3, 5, 8, 12} 
        Target = 8
Output : 5 (Index of 12)

Input : {1, 2, 3, 5, 8, 12} 
        Target = 15
Output : -1

A simple solution is to linearly traverse the given array and find the first element that is strictly greater. If no such element exists, then return -1.

An efficient solution is to use Binary Search. In a general binary search, we are looking for a value that appears in the array. Sometimes, however, we need to find the first element which is either greater than a target.

To see that this algorithm is correct, consider each comparison being made. If we find an element that's no greater than the target element, then it and everything below it can't possibly match, so there's no need to search that region. We can thus search for the right half. If we find an element that is larger than the element in question, then anything after it must also be larger, so they can't be the first element that's bigger and so we don't need to search them. The middle element is thus the last possible place it could be.

Note that on each iteration we drop off at least half the remaining elements from consideration. If the top branch executes, then the elements in the range [low, (low + high) / 2] are all discarded, causing us to lose floor((low + high) / 2) - low + 1 >= (low + high) / 2 - low = (high - low) / 2 elements.

If the bottom branch executes, then the elements in the range [(low + high) / 2 + 1, high] are all discarded. This loses us high - floor(low + high) / 2 + 1 >= high - (low + high) / 2 = (high - low) / 2 elements.

Consequently, we'll end up finding the first element greater than the target in O(lg n) iterations of this process. 

Implementation:

// C++ program to find first element that
// is strictly greater than given target.
#include <iostream>
using namespace std;

int next(int arr[], int target, int end)
{
    int start = 0;

    int ans = -1;
    while (start <= end)
    {
        int mid = (start + end) / 2;

        // Move to right side if target is
        // greater.
        if (arr[mid] <= target)
            start = mid + 1;

        // Move left side.
        else
        {
            ans = mid;
            end = mid - 1;
        }
    }

    return ans;
}

// Driver code
int main()
{
    int arr[] = {1, 2, 3, 5, 8, 12};
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << next(arr, 8, n-1);
    return 0;
}

// This code is contributed by sanjeev2552

// Java program to find first element that 
// is strictly greater than given target. 
  
class GfG { 
    private static int next(int[] arr, int target) 
    { 
        int start = 0, end = arr.length - 1; 
  
        int ans = -1; 
        while (start <= end) { 
            int mid = (start + end) / 2; 
  
            // Move to right side if target is 
            // greater. 
            if (arr[mid] <= target) { 
                start = mid + 1; 
            } 
  
            // Move left side. 
            else { 
                ans = mid; 
                end = mid - 1; 
            } 
        } 
        return ans; 
    } 
  
    // Driver code 
    public static void main(String[] args) 
    { 
        int[] arr = { 1, 2, 3, 5, 8, 12 }; 
        System.out.println(next(arr, 8)); 
    } 
} 

# Python program to find first element that
# is strictly greater than given target.

def next(arr, target):
    start = 0;
    end = len(arr) - 1;

    ans = -1;
    while (start <= end):
        mid = (start + end) // 2;

        # Move to right side if target is
        # greater.
        if (arr[mid] <= target):
            start = mid + 1;

        # Move left side.
        else:
            ans = mid;
            end = mid - 1;

    return ans;

# Driver code
if __name__ == '__main__':
    arr = [1, 2, 3, 5, 8, 12];
    print(next(arr, 8));

# This code is contributed by 29AjayKumar

// C# program to find first element that
// is strictly greater than given target.
using System;

class GfG
{
    private static int next(int[] arr, int target)
    {
        int start = 0, end = arr.Length - 1;

        int ans = -1;
        while (start <= end) 
        {
            int mid = (start + end) / 2;

            // Move to right side if target is
            // greater.
            if (arr[mid] <= target) 
            {
                start = mid + 1;
            }

            // Move left side.
            else 
            {
                ans = mid;
                end = mid - 1;
            }
        }
        return ans;
    }

    // Driver code
    public static void Main()
    {
        int[] arr = { 1, 2, 3, 5, 8, 12 };
        Console.WriteLine(next(arr, 8));
    }
}

// This code is contributed by Code_Mech

<?php
// PHP program to find first element that 
// is strictly greater than given target. 
function next0($arr, $target) 
{ 
    $start = 0; $end = sizeof($arr) - 1; 

    $ans = -1; 
    while ($start <= $end)
    { 
        $mid = (int)(($start + $end) / 2); 

        // Move to right side if target is 
        // greater. 
        if ($arr[$mid] <= $target) 
        { 
            $start = $mid + 1; 
        } 

        // Move left side. 
        else 
        { 
            $ans = $mid; 
            $end = $mid - 1; 
        } 
    } 
    return $ans; 
}

// Driver code 
{ 
    $arr = array( 1, 2, 3, 5, 8, 12 ); 
    echo(next0($arr, 8)); 
} 

// This code  is contributed by Code_Mech
?>

<script>

// Javascript program to find first element that
// is strictly greater than given target.
function next(arr, target)
{
    let start = 0, end = arr.length - 1;
    let ans = -1;
    
    while (start <= end) 
    {
        let mid = parseInt((start + end) / 2, 10);

        // Move to right side if target is
        // greater.
        if (arr[mid] <= target) 
        {
            start = mid + 1;
        }

        // Move left side.
        else 
        {
            ans = mid;
            end = mid - 1;
        }
    }
    return ans;
}

// Driver code
let arr = [ 1, 2, 3, 5, 8, 12 ];
document.write(next(arr, 8));

// This code is contributed by decode2207

</script>

5

Time Complexity: O(log(n))
Auxiliary Space: O(1)