# Permute two arrays such that sum of every pair is greater or equal to K

• Difficulty Level : Easy
• Last Updated : 15 Jul, 2022

Given two arrays of equal size n and an integer k. The task is to permute both arrays such that sum of their corresponding element is greater than or equal to k i.e a[i] + b[i] >= k. The task is print “Yes” if any such permutation exists, otherwise print “No”.

Examples :

```Input : a[] = {2, 1, 3},
b[] = { 7, 8, 9 },
k = 10.
Output : Yes
Permutation  a[] = { 1, 2, 3 } and b[] = { 9, 8, 7 }
satisfied the condition a[i] + b[i] >= K.

Input : a[] = {1, 2, 2, 1},
b[] = { 3, 3, 3, 4 },
k = 5.
Output : No```
Recommended Practice

The idea is to sort one array in ascending order and another array in descending order and if any index does not satisfy the condition a[i] + b[i] >= K then print “No”, else print “Yes”.

If the condition fails on sorted arrays, then there exists no permutation of arrays which can satisfy the inequality. Proof,
Assume asort[] be sorted a[] in ascending order and bsort[] be sorted b[] in descending order.

Let new permutation b[] is created by swapping any two indices i, j of bsort[],

• Case 1: i < j and element at b[i] is now bsort[j].
Now, asort[i] + bsort[j] < K, because bsort[i] > bsort[j] as b[] is sorted in decreasing order and we know asort[i] + bsort[i] < k.
• Case 2: i > j and element at b[i] is now bsort[j].
Now, asort[j] + bsort[i] < k, because asort[i] > asort[j] as a[] is sorted in increasing order and we know asort[i] + bsort[i] < k.

Below is the implementation is this approach:

## C++

 `// C++ program to check whether permutation of two``// arrays satisfy the condition a[i] + b[i] >= k.``#include ``using` `namespace` `std;` `// Check whether any permutation exists which``// satisfy the condition.``bool` `isPossible(``int` `a[], ``int` `b[], ``int` `n, ``int` `k)``{``    ``// Sort the array a[] in decreasing order.``    ``sort(a, a + n);` `    ``// Sort the array b[] in increasing order.``    ``sort(b, b + n, greater<``int``>());` `    ``// Checking condition on each index.``    ``for` `(``int` `i = 0; i < n; i++)``        ``if` `(a[i] + b[i] < k)``            ``return` `false``;` `    ``return` `true``;``}` `// Driven Program``int` `main()``{``    ``int` `a[] = { 2, 1, 3 };``    ``int` `b[] = { 7, 8, 9 };``    ``int` `k = 10;``    ``int` `n = ``sizeof``(a) / ``sizeof``(a);` `    ``isPossible(a, b, n, k) ? cout << ``"Yes"` `: cout << ``"No"``;``    ``return` `0;``}` `// This code is contributed by Aditya Kumar (adityakumar129)`

## C

 `// C program to check whether permutation of two``// arrays satisfy the condition a[i] + b[i] >= k.``#include ``#include ``#include ` `// Compare function for qsort for Increasing Order``int` `cmpfunc1(``const` `void``* a, ``const` `void``* b)``{``    ``return` `(*(``int``*)a - *(``int``*)b);``}` `// Compare function for qsort for decreasing Order``int` `cmpfunc2(``const` `void``* a, ``const` `void``* b)``{``    ``return` `(*(``int``*)b - *(``int``*)a);``}` `// Check whether any permutation exists which``// satisfy the condition.``bool` `isPossible(``int` `a[], ``int` `b[], ``int` `n, ``int` `k)``{``    ``// Sort the array a[] in decreasing order.``    ``qsort``(a, n, ``sizeof``(``int``), cmpfunc1);` `    ``// Sort the array b[] in increasing order.``    ``qsort``(b, n, ``sizeof``(``int``), cmpfunc2);` `    ``// Checking condition on each index.``    ``for` `(``int` `i = 0; i < n; i++)``        ``if` `(a[i] + b[i] < k)``            ``return` `false``;` `    ``return` `true``;``}` `// Driven Program``int` `main()``{``    ``int` `a[] = { 2, 1, 3 };``    ``int` `b[] = { 7, 8, 9 };``    ``int` `k = 10;``    ``int` `n = ``sizeof``(a) / ``sizeof``(a);` `    ``isPossible(a, b, n, k) ? ``printf``(``"Yes"``) : ``printf``(``"No"``);``    ``return` `0;``}` `// This code is contributed by Aditya Kumar (adityakumar129)`

## Java

 `// Java program to check whether``// permutation of two arrays satisfy``// the condition a[i] + b[i] >= k.``import` `java.util.*;` `class` `GFG``{``// Check whether any permutation``// exists which satisfy the condition.``static` `boolean` `isPossible(Integer a[], ``int` `b[],``                                  ``int` `n, ``int` `k)``{``    ``// Sort the array a[] in decreasing order.``    ``Arrays.sort(a, Collections.reverseOrder());` `    ``// Sort the array b[] in increasing order.``    ``Arrays.sort(b);` `    ``// Checking condition on each index.``    ``for` `(``int` `i = ``0``; i < n; i++)``    ``if` `(a[i] + b[i] < k)``        ``return` `false``;` `    ``return` `true``;``}` `// Driver code``public` `static` `void` `main(String[] args) {``    ``Integer a[] = {``2``, ``1``, ``3``};``    ``int` `b[] = {``7``, ``8``, ``9``};``    ``int` `k = ``10``;``    ``int` `n = a.length;` `    ``if` `(isPossible(a, b, n, k))``    ``System.out.print(``"Yes"``);``    ``else``    ``System.out.print(``"No"``);``}``}` `// This code is contributed by Anant Agarwal.`

## Python3

 `# Python program to check``# whether permutation of two``# arrays satisfy the condition``# a[i] + b[i] >= k.` `# Check whether any``# permutation exists which``# satisfy the condition.``def` `isPossible(a,b,n,k):` `    ``# Sort the array a[]``    ``# in decreasing order.``    ``a.sort(reverse``=``True``)`` ` `    ``# Sort the array b[]``    ``# in increasing order.``    ``b.sort()`` ` `    ``# Checking condition``    ``# on each index.``    ``for` `i ``in` `range``(n):``        ``if` `(a[i] ``+` `b[i] < k):``            ``return` `False`` ` `    ``return` `True`  `# Driver code` `a ``=` `[ ``2``, ``1``, ``3``]``b ``=` `[``7``, ``8``, ``9``]``k ``=` `10``n ``=``len``(a)`` ` `if``(isPossible(a, b, n, k)):``    ``print``(``"Yes"``)``else``:``    ``print``(``"No"``)` `# This code is contributed``# by Anant Agarwal.`

## C#

 `// C# program to check whether``// permutation of two arrays satisfy``// the condition a[i] + b[i] >= k.``using` `System;` `class` `GFG``{``// Check whether any permutation``// exists which satisfy the condition.``static` `bool` `isPossible(``int` `[]a, ``int` `[]b,``                       ``int` `n, ``int` `k)``{``    ``// Sort the array a[]``    ``// in decreasing order.``    ``Array.Sort(a);` `    ``// Sort the array b[]``    ``// in increasing order.``    ``Array.Reverse(b);` `    ``// Checking condition on each index.``    ``for` `(``int` `i = 0; i < n; i++)``    ``if` `(a[i] + b[i] < k)``        ``return` `false``;` `    ``return` `true``;``}` `// Driver code``public` `static` `void` `Main()``{``    ``int` `[]a = {2, 1, 3};``    ``int` `[]b = {7, 8, 9};``    ``int` `k = 10;``    ``int` `n = a.Length;` `    ``if` `(isPossible(a, b, n, k))``    ``Console.WriteLine(``"Yes"``);``    ``else``    ``Console.WriteLine(``"No"``);``}``}` `// This code is contributed by anuj_67.`

## PHP

 `= k.` `// Check whether any permutation``// exists which satisfy the condition.``function` `isPossible( ``\$a``, ``\$b``, ``\$n``, ``\$k``)``{``    ` `    ``// Sort the array a[] in``    ``// decreasing order.``    ``sort(``\$a``);` `    ``// Sort the array b[] in``    ``// increasing order.``    ``rsort(``\$b``);` `    ``// Checking condition on each``    ``// index.``    ``for` `( ``\$i` `= 0; ``\$i` `< ``\$n``; ``\$i``++)``        ``if` `(``\$a``[``\$i``] + ``\$b``[``\$i``] < ``\$k``)``            ``return` `false;` `    ``return` `true;``}` `// Driven Program``    ``\$a` `= ``array``( 2, 1, 3 );``    ``\$b` `= ``array``( 7, 8, 9 );``    ``\$k` `= 10;``    ``\$n` `= ``count``(``\$a``);` `    ``if``(isPossible(``\$a``, ``\$b``, ``\$n``, ``\$k``))``        ``echo` `"Yes"` `;``    ``else``        ``echo` `"No"``;` `// This code is contributed by``// anuj_67.``?>`

## Javascript

 ``

Output

`Yes`

Time Complexity: O(n log n).

This article is contributed by Anuj Chauhan. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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