Smallest Difference pair of values between two unsorted Arrays

Given two arrays of integers, compute the pair of values (one value in each array) with the smallest (non-negative) difference. Return the difference.

Examples :

Input : A[] = {l, 3, 15, 11, 2}
B[] = {23, 127, 235, 19, 8}
Output : 3
That is, the pair (11, 8)

Input : A[] = {l0, 5, 40}
B[] = {50, 90, 80}
Output : 10
That is, the pair (40, 50)

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

A simple solution is to Brute Force using two loops with Time Complexity O(n2).

A better solution is to sort the arrays. Once the arrays are sorted, we can find the minimum difference by iterating through the arrays using the approach discussed in below post.

Find the closest pair from two sorted arrays

Consider the following two arrays:
A: {l, 2, 11, 15}
B: {4, 12, 19, 23, 127, 235}

1. Suppose a pointer a points to the beginning of A and a pointer b points to the beginning of B. The current difference between a and bis 3. Store this as the min.

2. How can we (potentially) make this difference smaller? Well, the value at bis bigger than the value at a, so moving b will only make the difference larger. Therefore, we want to move a.

3. Now a points to 2 and b (still) points to 4. This difference is 2, so we should update min. Move a, since it is smaller.

4. Now a points to 11 and b points to 4. Move b.

5. Now a points to 11 and b points to 12. Update min to 1. Move b. And so on.

Below is the implementation of the idea.

C++

 // C++ Code to find Smallest  // Difference between two Arrays #include using namespace std;    // function to calculate Small  // result between two arrays int findSmallestDifference(int A[], int B[],                            int m, int n) {     // Sort both arrays using     // sort function     sort(A, A + m);     sort(B, B + n);        int a = 0, b = 0;        // Initialize result as max value     int result = INT_MAX;        // Scan Both Arrays upto      // sizeof of the Arrays     while (a < m && b < n)     {         if (abs(A[a] - B[b]) < result)             result = abs(A[a] - B[b]);            // Move Smaller Value         if (A[a] < B[b])             a++;            else             b++;     }        // return final sma result     return result;  }    // Driver Code int main() {     // Input given array A     int A[] = {1, 2, 11, 5};        // Input given array B     int B[] = {4, 12, 19, 23, 127, 235};           // Calculate size of Both arrays     int m = sizeof(A) / sizeof(A);     int n = sizeof(B) / sizeof(B);        // Call function to print      // smallest result     cout << findSmallestDifference(A, B, m, n);        return 0; }

Java

 // Java Code to find Smallest  // Difference between two Arrays import java.util.*;    class GFG  {            // function to calculate Small      // result between two arrays     static int findSmallestDifference(int A[], int B[],                                       int m, int n)     {         // Sort both arrays          // using sort function         Arrays.sort(A);         Arrays.sort(B);                int a = 0, b = 0;                // Initialize result as max value         int result = Integer.MAX_VALUE;                // Scan Both Arrays upto          // sizeof of the Arrays         while (a < m && b < n)         {             if (Math.abs(A[a] - B[b]) < result)                 result = Math.abs(A[a] - B[b]);                    // Move Smaller Value             if (A[a] < B[b])                 a++;                    else                 b++;         }                    // return final sma result         return result;      }            // Driver Code     public static void main(String[] args)      {         // Input given array A         int A[] = {1, 2, 11, 5};                // Input given array B         int B[] = {4, 12, 19, 23, 127, 235};                       // Calculate size of Both arrays         int m = A.length;         int n = B.length;                // Call function to          // print smallest result         System.out.println(findSmallestDifference                                    (A, B, m, n));                } } // This code is contributed // by Arnav Kr. Mandal.

Python3

 # Python 3 Code to find # Smallest Difference between # two Arrays import sys    # function to calculate # Small result between # two arrays def findSmallestDifference(A, B, m, n):        # Sort both arrays      # using sort function     A.sort()     B.sort()        a = 0     b = 0        # Initialize result as max value     result = sys.maxsize        # Scan Both Arrays upto     # sizeof of the Arrays     while (a < m and b < n):                if (abs(A[a] - B[b]) < result):             result = abs(A[a] - B[b])            # Move Smaller Value         if (A[a] < B[b]):             a += 1            else:             b += 1     # return final sma result     return result     # Driver Code    # Input given array A A = [1, 2, 11, 5]    # Input given array B B = [4, 12, 19, 23, 127, 235]    # Calculate size of Both arrays m = len(A) n = len(B)    # Call function to  # print smallest result print(findSmallestDifference(A, B, m, n))    # This code is contributed by # Smitha Dinesh Semwal

C#

 // C# Code to find Smallest  // Difference between two Arrays using System;    class GFG  {            // function to calculate Small      // result between two arrays     static int findSmallestDifference(int []A, int []B,                                       int m, int n)     {                    // Sort both arrays using         // sort function         Array.Sort(A);         Array.Sort(B);                int a = 0, b = 0;                // Initialize result as max value         int result = int.MaxValue;                // Scan Both Arrays upto          // sizeof of the Arrays         while (a < m && b < n)         {             if (Math.Abs(A[a] - B[b]) < result)                 result = Math.Abs(A[a] - B[b]);                    // Move Smaller Value             if (A[a] < B[b])                 a++;                    else                 b++;         }                    // return final sma result         return result;      }            // Driver Code     public static void Main()      {                    // Input given array A         int []A = {1, 2, 11, 5};                // Input given array B         int []B = {4, 12, 19, 23, 127, 235};                       // Calculate size of Both arrays         int m = A.Length;         int n = B.Length;                // Call function to          // print smallest result         Console.Write(findSmallestDifference                               (A, B, m, n));                } }    // This code is contributed // by nitin mittal.

PHP



Output :

1

This algorithm takes O(m log m + n log n) time to sort and O(m + n) time to find the minimum difference. Therefore, the overall runtime is O(m log m + n log n).

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Improved By : nitin mittal

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