Given a sorted array and a number x, find the pair in array whose sum is closest to x

Given a sorted array and a number x, find a pair in an array whose sum is closest to x.

Examples:

Input: arr[] = {10, 22, 28, 29, 30, 40}, x = 54
Output: 22 and 30

Input: arr[] = {1, 3, 4, 7, 10}, x = 15
Output: 4 and 10

A simple solution is to consider every pair and keep track of the closest pair (the absolute difference between pair sum and x is minimum). Finally, print the closest pair. The time complexity of this solution is O(n²)

An efficient solution can find the pair in O(n) time. The idea is similar to method 1 of this post. The following is a detailed algorithm. 

1) Initialize a variable diff as infinite (Diff is used to store the 
   difference between pair and x).  We need to find the minimum diff.
2) Initialize two index variables l and r in the given sorted array.
       (a) Initialize first to the leftmost index:  l = 0
       (b) Initialize second  the rightmost index:  r = n-1
3) Loop while l < r.
       (a) If  abs(arr[l] + arr[r] - sum) < diff  then 
           update diff and result 
       (b) If(arr[l] + arr[r] <  sum )  then l++
       (c) Else r--    

Following is the implementation of the above algorithm.

C++14

// Simple C++ program to find the pair with sum closest to a given no.
#include <bits/stdc++.h>
using namespace std;

// Prints the pair with sum closest to x
void printClosest(int arr[], int n, int x)
{
    int res_l, res_r;  // To store indexes of result pair

    // Initialize left and right indexes and difference between
    // pair sum and x
    int l = 0, r = n-1, diff = INT_MAX;

    // While there are elements between l and r
    while (r > l)
    {
       // Check if this pair is closer than the closest pair so far
       if (abs(arr[l] + arr[r] - x) < diff)
       {
           res_l = l;
           res_r = r;
           diff = abs(arr[l] + arr[r] - x);
       }

       // If this pair has more sum, move to smaller values.
       if (arr[l] + arr[r] > x)
           r--;
       else // Move to larger values
           l++;
    }

    cout <<" The closest pair is " << arr[res_l] << " and " << arr[res_r];
}

// Driver program to test above functions
int main()
{
    int arr[] =  {10, 22, 28, 29, 30, 40}, x = 54;
    int n = sizeof(arr)/sizeof(arr[0]);
    printClosest(arr, n, x);
    return 0;
}
// Code By Mayur Patil

Java

// Java program to find pair with sum closest to x
import java.io.*;
import java.util.*;
import java.lang.Math;

class CloseSum {

    // Prints the pair with sum closest to x
    static void printClosest(int arr[], int n, int x)
    {
        int res_l=0, res_r=0;  // To store indexes of result pair

        // Initialize left and right indexes and difference between
        // pair sum and x
        int l = 0, r = n-1, diff = Integer.MAX_VALUE;

        // While there are elements between l and r
        while (r > l)
        {
            // Check if this pair is closer than the closest pair so far
            if (Math.abs(arr[l] + arr[r] - x) < diff)
            {
               res_l = l;
               res_r = r;
               diff = Math.abs(arr[l] + arr[r] - x);
            }

            // If this pair has more sum, move to smaller values.
            if (arr[l] + arr[r] > x)
               r--;
            else // Move to larger values
               l++;
        }

    System.out.println(" The closest pair is "+arr[res_l]+" and "+ arr[res_r]);
}


    // Driver program to test above function
    public static void main(String[] args)
    {
        int arr[] =  {10, 22, 28, 29, 30, 40}, x = 54;
        int n = arr.length;
        printClosest(arr, n, x);
    }
}
/*This code is contributed by Devesh Agrawal*/

Python3

# Python3 program to find the pair
# with sum
# closest to a given no.

# A sufficiently large value greater
# than any
# element in the input array
MAX_VAL = 1000000000


#Prints the pair with sum closest to x

def printClosest(arr, n, x):

    # To store indexes of result pair
    res_l, res_r = 0, 0

    #Initialize left and right indexes
    # and difference between
    # pair sum and x
    l, r, diff = 0, n-1, MAX_VAL

    # While there are elements between l and r
    while r > l:
        # Check if this pair is closer than the
        # closest pair so far
        if abs(arr[l] + arr[r] - x) < diff:
            res_l = l
            res_r = r
            diff = abs(arr[l] + arr[r] - x)

        if arr[l] + arr[r] > x:
        # If this pair has more sum, move to
        # smaller values.
            r -= 1
        else:
        # Move to larger values
            l += 1

    print('The closest pair is {} and {}'
         .format(arr[res_l], arr[res_r]))


# Driver code to test above
if __name__ == "__main__":
    arr = [10, 22, 28, 29, 30, 40]
    n = len(arr)
    x=54
    printClosest(arr, n, x)

# This code is contributed by Tuhin Patra

C#

// C# program to find pair with sum closest to x
using System;

class GFG {

    // Prints the pair with sum closest to x
    static void printClosest(int []arr, int n, int x)
    {

        // To store indexes of result pair
        int res_l = 0, res_r = 0;

        // Initialize left and right indexes and
        // difference between pair sum and x
        int l = 0, r = n-1, diff = int.MaxValue;

        // While there are elements between l and r
        while (r > l)
        {

            // Check if this pair is closer than the
            // closest pair so far
            if (Math.Abs(arr[l] + arr[r] - x) < diff)
            {
                res_l = l;
                res_r = r;
                diff = Math.Abs(arr[l] + arr[r] - x);
            }

            // If this pair has more sum, move to
            // smaller values.
            if (arr[l] + arr[r] > x)
            r--;
            else // Move to larger values
            l++;
        }

        Console.Write(" The closest pair is " +
                 arr[res_l] + " and " + arr[res_r]);
    }

    // Driver program to test above function
    public static void Main()
    {
        int []arr = {10, 22, 28, 29, 30, 40};
        int x = 54;
        int n = arr.Length;

        printClosest(arr, n, x);
    }
}

// This code is contributed by nitin mittal.

PHP

<?php
// Simple PHP program to find the
// pair with sum closest to a
// given no.

// Prints the pair with
// sum closest to x
function printClosest($arr, $n, $x)
{

    // To store indexes
    // of result pair
    $res_l;
    $res_r;

    // Initialize left and right
    // indexes and difference between
    // pair sum and x
    $l = 0;
    $r = $n - 1;
    $diff = PHP_INT_MAX;

    // While there are elements
    // between l and r
    while ($r > $l)
    {

        // Check if this pair is closer
        // than the closest pair so far
        if (abs($arr[$l] + $arr[$r] - $x) <
                                      $diff)
        {
            $res_l = $l;
            $res_r = $r;
            $diff = abs($arr[$l] + $arr[$r] - $x);
        }

        // If this pair has more sum,
        // move to smaller values.
        if ($arr[$l] + $arr[$r] > $x)
            $r--;

        // Move to larger values
        else
            $l++;
    }

    echo " The closest pair is "
         , $arr[$res_l] ," and "
         , $arr[$res_r];
}

    // Driver Code
    $arr = array(10, 22, 28, 29, 30, 40);
    $x = 54;
    $n = count($arr);
    printClosest($arr, $n, $x);

// This code is contributed by anuj_67.
?>

Javascript

<script>

// JavaScript program to find pair
// with sum closest to x


    // Prints the pair with sum closest to x
    function printClosest(arr,n,x)
    {
    // To store indexes of result pair
        let res_l=0, res_r=0;

        // Initialize left and right indexes
        // and difference between
        // pair sum and x
        let l = 0, r = n-1, diff = Number.MAX_VALUE;

        // While there are elements
        // between l and r
        while (r > l)
        {
            // Check if this pair is closer
            // than the closest pair so far
            if (Math.abs(arr[l] +
                arr[r] - x) < diff)
            {
            res_l = l;
            res_r = r;
            diff = Math.abs(arr[l] + arr[r] - x);
            }

            // If this pair has more sum,
            // move to smaller values.
            if (arr[l] + arr[r] > x)
            r--;
            else // Move to larger values
            l++;
        }

    document.write(
    " The closest pair is "+arr[res_l]+" and "+ arr[res_r]
    );
}


    // Driver program to test above function

        let arr = [10, 22, 28, 29, 30, 40], x = 54;
        let n = arr.length;
        printClosest(arr, n, x);



// This code is contributed by sravan kumar

</script>

Output

 The closest pair is 22 and 30

Time Complexity: O(n), where n is the length of an Array.
Auxiliary Space: O(1)