Given two arrays A[] and B[] of same size n. We need to first permute any of arrays such that the sum of product of pairs( 1 element from each) is minimum. That is ** SUM ( Ai*Bi) for all i** is minimum. We also need to count number of de-arrangements present in original array as compared to permuted array.

Examples:

Input : A[] = {4, 3, 2}, B[] = {7, 12, 5} Output : 3 Explanation : A[] = {4, 3, 2} and B[] = {5, 7, 12} results in minimum product sum. B[] = {7, 12, 5} is 3-position different from new B[]. Input : A[] = {4, 3, 2}, B[] = { 1, 2, 3} Output : 0 Explanation : A[] = {4, 3, 2} and B[] = {1, 2, 3} results in minimum product sum. B[] = {1, 2, 3} is exactly same as new one.

Idea behind finding the minimum sum of product from two array is to sort both array one in increasing and other in decreasing manner. These type of arrays will always produce minimum sum of pair product. Sorting both array will give the pair value i.e. which element from A is paired to which element from B[]. After that count the de-arrangement from original arrays.

** Algorithm :**

- make a copy of both array.
- sort copy_A[] in increasing, copy_B[] in decreasing order.
- Iterate for all Ai, find Ai in copy_A[] as copy_A[j] and

check whether copy_B[j] == B[i] or not. Increment count if not equal. - Return Count Value. That will be our answer.

`// CPP program to count de-arrangements for ` `// minimum product. ` `#include<bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// function for finding de-arrangement ` `int` `findDearrange (` `int` `A[], ` `int` `B[], ` `int` `n) ` `{ ` ` ` `// create copy of array ` ` ` `vector <` `int` `> copy_A (A, A+n); ` ` ` `vector <` `int` `> copy_B (B, B+n); ` ` ` ` ` `// sort array in inc & dec way ` ` ` `sort(copy_A.begin(), copy_A.end()); ` ` ` `sort(copy_B.begin(), copy_B.end(),greater<` `int` `>()); ` ` ` ` ` `// count no. of de arrangements ` ` ` `int` `count = 0; ` ` ` `for` `(` `int` `i=0; i<n;i++) ` ` ` `{ ` ` ` `vector<` `int` `>::iterator itA; ` ` ` ` ` `// find position of A[i] in sorted array ` ` ` `itA = lower_bound(copy_A.begin(), ` ` ` `copy_A.end(), A[i]); ` ` ` ` ` `// check whether B[i] is same as required or not ` ` ` `if` `(B[i] != copy_B[itA-copy_A.begin()]) ` ` ` `count++; ` ` ` `} ` ` ` ` ` `// return count ` ` ` `return` `count; ` `} ` ` ` `// driver function ` `int` `main() ` `{ ` ` ` `int` `A[] = {1, 2, 3, 4}; ` ` ` `int` `B[] = {6, 3, 4, 5}; ` ` ` `int` `n = ` `sizeof` `(A) /` `sizeof` `(A[0]);; ` ` ` `cout << findDearrange(A,B,n); ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

Output:

2

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready.

## Recommended Posts:

- Minimum sum of product of two arrays
- Minimum sum of two elements from two arrays such that indexes are not same
- Minimize the sum of product of two arrays with permutations allowed
- Split the given array into K sub-arrays such that maximum sum of all sub arrays is minimum
- Maximum OR sum of sub-arrays of two different arrays
- Find sub-arrays from given two arrays such that they have equal sum
- Count of possible arrays from prefix-sum and suffix-sum arrays
- Find Maximum dot product of two arrays with insertion of 0's
- Maximum product from array such that frequency sum of all repeating elements in product is less than or equal to 2 * k
- Maximize product of array by replacing array elements with its sum or product with element from another array
- Minimum sum of absolute difference of pairs of two arrays
- Minimum total sum from the given two arrays
- Generate all possible sorted arrays from alternate elements of two given sorted arrays
- Sum of product of all elements of sub-arrays of size k
- Find Sum of pair from two arrays with maximum sum
- Maximum Product Subarray | Added negative product case
- Smallest pair of indices with product of subarray co-prime with product of the subarray on the left or right
- Minimum flips in two binary arrays so that their XOR is equal to another array
- Making elements of two arrays same with minimum increment/decrement
- Minimum changes required to make two arrays identical

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.