Given two arrays * a[]* and

*of equal length*

**b[]***. The task is to pair each element of array*

**n***to an element in array*

**a***, such that sum*

**b***of*

**S****absolute differences of all the pairs is minimum.**

Suppose, two elements

**a[**

**i****]**and

**a[**

**j****]**

**(**

**i****!=**

**j****)**of

*are paired with elements*

**a****b[**

**p****]**and

**b[**

**q****]**of

*respectively,*

**b**then

*should not be equal to*

**p***.*

**q****Examples:**

Input :a[] = {3, 2, 1} b[] = {2, 1, 3}Output :0Explaination :1st pairing: |3 - 2| + |2 - 1| + |1 - 3| = 1 + 1 + 2 = 4 2nd pairing: |3 - 2| + |1 - 1| + |2 - 3| = 1 + 0 + 1 = 2 3rd pairing: |2 - 2| + |3 - 1| + |1 - 3| = 0 + 2 + 2 = 4 4th pairing: |1 - 2| + |2 - 1| + |3 - 3| = 1 + 1 + 0 = 2 5th pairing: |2 - 2| + |1 - 1| + |3 - 3| = 0 + 0 + 0 = 0 6th pairing: |1 - 2| + |3 - 1| + |2 - 3| = 1 + 2 + 1 = 4 Therefore, 5th pairing has minimum sum of absolute difference.Input :n = 4 a[] = {4, 1, 8, 7} b[] = {2, 3, 6, 5}Output :6

The solution to the problem is a simple greedy approach. It consists of **two** steps. **Step 1** : Sort both the arrays in **O (n log n)** time. **Step 2** : Find absolute difference of each pair of **corresponding elements** *(elements at same index)* of both arrays and add the result to the sum * S*. The time complexity of this step is

**O(n)**.

Hence, the overall time complexity of the program is

**O(n log n)**.

## C++

`// C++ program to find minimum sum of absolute` `// differences of two arrays.` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Returns minimum possible pairwise absolute` `// difference of two arrays.` `long` `long` `int` `findMinSum(` `int` `a[], ` `int` `b[], ` `int` `n)` `{` ` ` `// Sort both arrays` ` ` `sort(a, a+n);` ` ` `sort(b, b+n);` ` ` `// Find sum of absolute differences` ` ` `long` `long` `int` `sum= 0 ;` ` ` `for` `(` `int` `i=0; i<n; i++)` ` ` `sum = sum + ` `abs` `(a[i]-b[i]);` ` ` `return` `sum;` `}` `// Driver code` `int` `main()` `{` ` ` `// Both a[] and b[] must be of same size.` ` ` `long` `long` `int` `a[] = {4, 1, 8, 7};` ` ` `long` `long` `int` `b[] = {2, 3, 6, 5};` ` ` `int` `n = ` `sizeof` `(a)/` `sizeof` `(a[0]);` ` ` `printf` `(` `"%lld\n"` `, findMinSum(a, b, n));` ` ` `return` `0;` `}` |

## Java

`// Java program to find minimum sum of` `// absolute differences of two arrays.` `import` `java.util.Arrays;` `class` `MinSum` `{` ` ` `// Returns minimum possible pairwise` ` ` `// absolute difference of two arrays.` ` ` `static` `long` `findMinSum(` `long` `a[], ` `long` `b[], ` `long` `n)` ` ` `{` ` ` `// Sort both arrays` ` ` `Arrays.sort(a);` ` ` `Arrays.sort(b);` ` ` ` ` `// Find sum of absolute differences` ` ` `long` `sum = ` `0` `;` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++)` ` ` `sum = sum + Math.abs(a[i] - b[i]);` ` ` ` ` `return` `sum;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `// Both a[] and b[] must be of same size.` ` ` `long` `a[] = {` `4` `, ` `1` `, ` `8` `, ` `7` `};` ` ` `long` `b[] = {` `2` `, ` `3` `, ` `6` `, ` `5` `};` ` ` `int` `n = a.length;` ` ` `System.out.println(findMinSum(a, b, n));` ` ` `} ` `}` ` ` `// This code is contributed by Raghav Sharma` |

## Python3

`# Python3 program to find minimum sum` `# of absolute differences of two arrays.` `def` `findMinSum(a, b, n):` ` ` `# Sort both arrays` ` ` `a.sort()` ` ` `b.sort()` ` ` `# Find sum of absolute differences` ` ` `sum` `=` `0` ` ` ` ` `for` `i ` `in` `range` `(n):` ` ` `sum` `=` `sum` `+` `abs` `(a[i] ` `-` `b[i])` ` ` `return` `sum` `# Driver program` ` ` `# Both a[] and b[] must be of same size.` `a ` `=` `[` `4` `, ` `1` `, ` `8` `, ` `7` `]` `b ` `=` `[` `2` `, ` `3` `, ` `6` `, ` `5` `]` `n ` `=` `len` `(a)` `print` `(findMinSum(a, b, n))` `# This code is contributed by Anant Agarwal.` |

## C#

`// C# program to find minimum sum of` `// absolute differences of two arrays.` `using` `System;` `class` `MinSum {` ` ` ` ` `// Returns minimum possible pairwise` ` ` `// absolute difference of two arrays.` ` ` `static` `long` `findMinSum(` `long` `[]a, ` `long` `[]b,` ` ` `long` `n)` ` ` `{` ` ` ` ` `// Sort both arrays` ` ` `Array.Sort(a);` ` ` `Array.Sort(b);` ` ` ` ` `// Find sum of absolute differences` ` ` `long` `sum = 0 ;` ` ` `for` `(` `int` `i = 0; i < n; i++)` ` ` `sum = sum + Math.Abs(a[i] - b[i]);` ` ` ` ` `return` `sum;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `Main(String[] args)` ` ` `{` ` ` `// Both a[] and b[] must be of same size.` ` ` `long` `[]a = {4, 1, 8, 7};` ` ` `long` `[]b = {2, 3, 6, 5};` ` ` `int` `n = a.Length;` ` ` `Console.Write(findMinSum(a, b, n));` ` ` `}` `}` `// This code is contributed by parashar...` |

## PHP

`<?php` `// PHP program to find minimum sum` `// of absolute differences of two` `// arrays.` `// Returns minimum possible pairwise` `// absolute difference of two arrays.` `function` `findMinSum(` `$a` `, ` `$b` `, ` `$n` `)` `{` ` ` ` ` `// Sort both arrays` ` ` `sort(` `$a` `);` ` ` `sort(` `$a` `, ` `$n` `);` ` ` `sort(` `$b` `);` ` ` `sort(` `$b` `, ` `$n` `);` ` ` `// Find sum of absolute` ` ` `// differences` ` ` `$sum` `= 0 ;` ` ` `for` `(` `$i` `= 0; ` `$i` `< ` `$n` `; ` `$i` `++)` ` ` `$sum` `= ` `$sum` `+ ` `abs` `(` `$a` `[` `$i` `] -` ` ` `$b` `[` `$i` `]);` ` ` `return` `$sum` `;` `}` ` ` `// Driver Code` ` ` `// Both a[] and b[] must` ` ` `// be of same size.` ` ` `$a` `= ` `array` `(4, 1, 8, 7);` ` ` `$b` `= ` `array` `(2, 3, 6, 5);` ` ` `$n` `= sizeof(` `$a` `);` ` ` `echo` `(findMinSum(` `$a` `, ` `$b` `, ` `$n` `));` `// This code is contributed by nitin mittal.` `?>` |

## Javascript

`<script>` `// JavaScript program for the above approach` `// Function to return the minimum number` `// Returns minimum possible pairwise` `// absolute difference of two arrays.` ` ` `function` `findMinSum(a, b, n)` ` ` `{` ` ` `// Sort both arrays` ` ` `a.sort();` ` ` `b.sort();` ` ` ` ` `// Find sum of absolute differences` ` ` `let sum = 0 ;` ` ` `for` `(let i = 0; i < n; i++)` ` ` `sum = sum + Math.abs(a[i] - b[i]);` ` ` ` ` `return` `sum;` ` ` `}` ` ` `// Driver Code` ` ` `// Both a[] and b[] must be of same size.` ` ` `let a = [4, 1, 8, 7];` ` ` `let b = [2, 3, 6, 5];` ` ` `let n = a.length;` ` ` `document.write(findMinSum(a, b, n));` `// This code is contributed by code_hunt.` `</script>` |

**Output : **

6

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