# Minimize cost to Swap two given Arrays

Given two arrays A[] and B[] both of size N consisting of distinct elements, the task is to find the minimum cost to swap two given arrays. Cost of swapping two elements A[i] and B[j] is min(A[i], A[j]). The total cost is the cumulative sum of the costs of all swap operations.

Note: Here, the order of elements can differ from the original arrays after swapping.

Examples:

Input: N = 3, A[] = {1, 4, 2}, B[] = {10, 6, 12}
Output:
Explanation:
Following swap operations will give the minimum cost:
swap(A, B): cost = min(A, B) = 1, A[ ] = {12, 4, 2}, B[ ] = {10, 6, 1}
swap(A, B): cost = min(A, B) = 1, A[ ] = {12, 4, 1}, B[ ] = {10, 6, 2}
swap(A, B): cost = min(A, B) = 1, A[ ] = {12, 4, 10}, B[ ] = {1, 6, 2}
swap(A, B): cost = min(A, B) = 1, A[ ] = {12, 1, 10}, B[ ] = {4, 6, 2}
swap(A, B): cost = min(A, B) = 1, A[ ] = {12, 6, 10}, B[ ] = {4, 1, 2}
Therefore, the minimum cost to swap two arrays = 1 + 1 + 1 + 1 + 1 = 5
Input: N = 2, A[] = {9, 12}, B[] = {3, 15}
Output:

Approach:
Follow the steps below to solve the problem:

• Traverse the arrays simultaneously and find the minimum element from them, say K.
• Now, every element with K until the two arrays are swapped. Therefore, the number of swaps required is 2*N – 1.
• Print K * (2 * N – 1) as the answer.

Below is the implementation of the above approach:

 `// C++ program to implement` `// the above appraoch` `#include ` `using` `namespace` `std;`   `// Function to calculate and return the` `// minimum cost required to swap two arrays` `int` `getMinCost(vector<``int``> A, vector<``int``> B,` `               ``int` `N)` `{`   `    ``int` `mini = INT_MAX;` `    ``for` `(``int` `i = 0; i < N; i++) {` `        ``mini = min(mini, min(A[i], B[i]));` `    ``}`   `    ``// Return the total minimum cost` `    ``return` `mini * (2 * N - 1);` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `N = 3;`   `    ``vector<``int``> A = { 1, 4, 2 };` `    ``vector<``int``> B = { 10, 6, 12 };`   `    ``cout << getMinCost(A, B, N);` `    ``return` `0;` `}`

 `// Java program to implement` `// the above appraoch` `class` `GFG{`   `// Function to calculate and return the` `// minimum cost required to swap two arrays` `static` `int` `getMinCost(``int` `[] A, ``int` `[] B,` `                                   ``int` `N)` `{` `    ``int` `mini = Integer.MAX_VALUE;` `    ``for` `(``int` `i = ``0``; i < N; i++)` `    ``{` `        ``mini = Math.min(mini,` `               ``Math.min(A[i], B[i]));` `    ``}`   `    ``// Return the total minimum cost` `    ``return` `mini * (``2` `* N - ``1``);` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    ``int` `N = ``3``;`   `    ``int` `[] A = { ``1``, ``4``, ``2` `};` `    ``int` `[] B = { ``10``, ``6``, ``12` `};`   `    ``System.out.print(getMinCost(A, B, N));` `}` `}`   `// This code is contributed by sapnasingh4991`

 `# Python3 program to implement` `# the above appraoch` `import` `sys`   `# Function to calculate and return the` `# minimum cost required to swap two arrays` `def` `getMinCost(A, B, N):`   `    ``mini ``=` `sys.maxsize ` `    ``for` `i ``in` `range``(N):` `        ``mini ``=` `min``(mini, ``min``(A[i], B[i]))`   `    ``# Return the total minimum cost` `    ``return` `mini ``*` `(``2` `*` `N ``-` `1``)`   `# Driver Code` `N ``=` `3`   `A ``=` `[ ``1``, ``4``, ``2` `]` `B ``=` `[ ``10``, ``6``, ``12` `]`   `print``(getMinCost(A, B, N))`   `# This code is contributed by chitranayal`

 `// C# program to implement` `// the above appraoch` `using` `System;` `class` `GFG{`   `    ``// Function to calculate and return the` `    ``// minimum cost required to swap two arrays` `    ``static` `int` `getMinCost(``int``[] A, ``int``[] B, ``int` `N)` `    ``{` `        ``int` `mini = ``int``.MaxValue;` `        ``for` `(``int` `i = 0; i < N; i++) ` `        ``{` `            ``mini = Math.Min(mini, Math.Min(A[i], B[i]));` `        ``}`   `        ``// Return the total minimum cost` `        ``return` `mini * (2 * N - 1);` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `Main(String[] args)` `    ``{` `        ``int` `N = 3;` `          ``int``[] A = {1, 4, 2};` `        ``int``[] B = {10, 6, 12};` `          ``Console.Write(getMinCost(A, B, N));` `    ``}` `}`   `// This code is contributed by shikhasingrajput`

Output:
```5

```

Time Complexity: O(N)
Auxiliary Space: O(1)

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.

Check out this Author's contributed articles.

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.

Article Tags :
Practice Tags :