# Minimum swaps to make two arrays identical

Given two arrays which have same values but in different order, we need to make second array same as first array using minimum number of swaps.
Examples:

Input  : arrA[] = {3, 6, 4, 8},
arrB[] = {4, 6, 8, 3}
Output : 2
we can make arrB to same as arrA in 2 swaps
which are shown below,
swap 4 with 8,   arrB = {8, 6, 4, 3}
swap 8 with 3,   arrB = {3, 6, 4, 8}

This problem can be solved by modifying the array B. We save the index of array A elements in array B i.e. if ith element of array A is at jth position in array B, then we will make arrB[i] = j
For above given example, modified array B will be, arrB = {3, 1, 0, 2}. This modified array represents distribution of array A element in array B and our goal is to sort this modified array in minimum number of swaps because after sorting only array B element will be aligned with array A elements.

So we count these swaps in modified array and that will be our final answer.
Please see below code for better understanding.

// C++ program to make an array same to another
// using minimum number of swap
#include <bits/stdc++.h>
using namespace std;
// Function returns the minimum number of swaps
// required to sort the array
int minSwapsToSort(int arr[], int n)
{
// Create an array of pairs where first
// element is array element and second element
// is position of first element
pair<int, int> arrPos[n];
for (int i = 0; i < n; i++)
{
arrPos[i].first = arr[i];
arrPos[i].second = i;
}
// Sort the array by array element values to
// get right position of every element as second
// element of pair.
sort(arrPos, arrPos + n);
// To keep track of visited elements. Initialize
// all elements as not visited or false.
vector<bool> vis(n, false);
// Initialize result
int ans = 0;
// Traverse array elements
for (int i = 0; i < n; i++)
{
// already swapped and corrected or
// already present at correct pos
if (vis[i] || arrPos[i].second == i)
continue;
// find out the number of  node in
// this cycle and add in ans
int cycle_size = 0;
int j = i;
while (!vis[j])
{
vis[j] = 1;
// move to next node
j = arrPos[j].second;
cycle_size++;
}
ans += (cycle_size - 1);
}
// Return result
return ans;
}
// method returns minimum number of swap to make
// array B same as array A
int minSwapToMakeArraySame(int a[], int b[], int n)
{
// map to store position of elements in array B
// we basically store element to index mapping.
map<int, int> mp;
for (int i = 0; i < n; i++)
mp[b[i]] = i;
// now we're storing position of array A elements
// in array B.
for (int i = 0; i < n; i++)
b[i] = mp[a[i]];
/* We can uncomment this section to print modified
b array
for (int i = 0; i < N; i++)
cout << b[i] << " ";
cout << endl; */
// returing minimum swap for sorting in modified
// array B as final answer
return minSwapsToSort(b, n);
}
//  Driver code to test above methods
int main()
{
int a[] = {3, 6, 4, 8};
int b[] = {4, 6, 8, 3};
int n = sizeof(a) / sizeof(int);
cout << minSwapToMakeArraySame(a, b, n);
return 0;
}

Output:

2

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source and credits.
source and credits: http://www.geeksforgeeks.org
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