Given an array of non negative integers and a number x, find a pair in array whose product is closest to x.

**Examples :**

Input : arr[] = [2, 3, 5, 9] x = 47 Output : {5, 9} Input : arr[] = [2, 3, 5, 9] x = 8 Output : {2, 5}

**Method 1**

A simple solution is to consider every pair and keep track of closest pair (absolute difference between pair product and x is minimum). Finally print the closest pair. Time complexity of this solution is O()

**Method 2 O(n Log n)**

- Sort the array
- Initialize a variable diff as infinite (Diff is used to store the difference between pair and x). We need to find the minimum diff.
- Traverse the array and for each i, do the following :
- Find the lower bound for x/arr[i] in the sub array on right of arr[i], i.e., in sub array arr[i+1..n-1]. Let it be denoted be l.
- Find the upper bound for x/arr[i] in the sub array on right of arr[i], i.e., in sub array arr[i+1..n-1]. Let it be denoted be u.
- If min(abs((arr[i] * l) – x), abs((arr[i] * u) – x)) < diff then update diff and result

**Method 3 O(n for sorted )**

An efficient solution can find the pair in O(n) time. Following is 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]) - x) < diff then update diff and result (b) Else if((arr[l] * arr[r]) < x) then l++ (c) Else r--

Following is the implementation of above algorithm.

## C++

// Simple C++ program to find the pair with // product closest to a given no. #include <bits/stdc++.h> using namespace std; // Prints the pair with product 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 product 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 product, // 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[] = { 2, 3, 5, 9 }, x = 8; int n = sizeof(arr) / sizeof(arr[0]); printClosest(arr, n, x); return 0; }

## Java

// Simple Java program to find // the pair with product closest // to a given no. import java.io.*; class GFG { // Prints the pair with // product 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 product 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 product, // move to smaller values. if (arr[l] * arr[r] > x) r--; // Move to larger values else l++; } System.out.print("The closest pair is "); System.out.print (arr[res_l] + " and " + arr[res_r]); } // Driver Code public static void main (String[] args) { int arr[] = {2, 3, 5, 9}; int x = 8; int n = arr.length; printClosest(arr, n, x); } } // This code is contributed by anuj_67.

## Python3

# Simple Python3 program to find # the pair with product closest # to a given no. import sys # Prints the pair with # product closest to x def printClosest(arr, n, x): # To store indexes # of result pair res_l = 0; res_r = 0; # Initialize left and right # indexes and difference # between pair product and x l = 0; r = n - 1; diff = sys.maxsize; # 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 # product, move to smaller # values. if (arr[l] * arr[r] > x): r = r - 1; # Move to larger values else: l = l + 1; print("The closest pair is", arr[res_l] , "and", arr[res_r]); # Driver Code arr = [2, 3, 5, 9]; x = 8; n = len(arr); printClosest(arr, n, x); # This code is contributed # by rahul

## C#

// Simple C# program to find // the pair with product closest // to a given no. using System; class GFG { // Prints the pair with // product 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 product 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 product, // move to smaller values. if (arr[l] * arr[r] > x) r--; // Move to larger values else l++; } Console.Write("The closest pair is "); Console.Write (arr[res_l] + " and " + arr[res_r]); } // Driver Code public static void Main () { int []arr = {2, 3, 5, 9}; int x = 8; int n = arr.Length; printClosest(arr, n, x); } } // This code is contributed by anuj_67.

## PHP

<?php // Simple PHP program to find // the pair with product closest // to a given no. // Prints the pair with // product 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 product 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] - $x); } // If this pair has more // product, move to smaller // values. if ($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(2, 3, 5, 9); $x = 8; $n = count($arr); printClosest($arr, $n, $x); // This code is contributed by anuj_67. ?>

**Output :**

The closest pair is 2 and 5

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