Optimal sort

#include <bits/stdc++.h>

using namespace std;

#define debug(x) cerr << #x << ": " << x << endl;
#define ll long long
#define ull unsigned long long
#define vi vector<int>

int nb_swaps(vi& a) {
    int n = a.size();
    int swaps = 0;
    for (int i = 0; i < n-1; i++) {
        int min = a[i], idmin = i;

        for (int j = i+1; j < n; j++) {
            if (a[j] < min) {
                min = a[j];
                idmin = j;
            }
        }

        if (idmin != i) {
            swap(a[idmin], a[i]);
            swaps++;
        }
    }
    return swaps;
}

int minSwapsToSort(vector<int>& arr) {
    int n = arr.size();
    vector<pair<int, int>> arrPos(n);

    // Store array elements with their original positions
    for (int i = 0; i < n; i++) {
        arrPos[i] = {arr[i], i};
    }

    // Sort the array by values
    sort(arrPos.begin(), arrPos.end());

    vector<bool> visited(n, false);
    int swaps = 0;

    // Calculate the minimum number of swaps
    for (int i = 0; i < n; i++) {
        // Already visited or already in correct position
        if (visited[i] || arrPos[i].second == i)
            continue;

        // Find cycle size
        int cycleSize = 0;
        int j = i;
        while (!visited[j]) {
            visited[j] = true;
            j = arrPos[j].second;
            cycleSize++;
        }

        if (cycleSize > 1)
            swaps += (cycleSize - 1);
    }

    return swaps;
}


int main() {
    int n; cin >> n;

    vi a (n);
    int k;
    for (int i = 0; i < n; i++)
    {
        cin >> k;
        a[i] = k;
    }

    // sort(a.begin(), a.end());
    // vector<bool> visited (n);

    // int swaps = 0;
    // for (int i = 0; i < n; i++)
    // {
    //     if (i != a[i].second) {
    //         swaps++;
    //     }

    //     if (visited[a[i].second] == false && i == a[a[i].second].second) {
    //         swaps--;
    //     }

    //     visited[i] = true;
    // }
    
    // cout << swaps << endl;

    cout << minSwapsToSort(a) << endl;

    return 0;
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED

Test 22

Verdict: ACCEPTED

Test 23

Verdict: ACCEPTED

Test 24

Verdict: ACCEPTED

Test 25

Verdict: ACCEPTED

Test 26

Verdict: ACCEPTED

Test 27

Verdict: ACCEPTED

Test 28

Verdict: ACCEPTED

Test 29

Verdict: ACCEPTED

Test 30

Verdict: ACCEPTED

Test 31

Verdict: ACCEPTED

Test 32

Verdict: ACCEPTED

Test 33

Verdict: ACCEPTED

Test 34

Verdict: ACCEPTED

Test 35

Verdict: ACCEPTED

Test 36

Verdict: ACCEPTED

Test 37

Verdict: ACCEPTED

Test 38

Verdict: ACCEPTED

Test 39

Verdict: ACCEPTED

Test 40

Verdict: ACCEPTED

Test 41

Verdict: ACCEPTED

Test 42

Verdict: ACCEPTED

Test 43

Verdict: ACCEPTED

Test 44

Verdict: ACCEPTED

Test 45

Verdict: ACCEPTED

Test 46

Verdict: ACCEPTED

Test 47

Verdict: ACCEPTED

Test 48

Verdict: ACCEPTED

Test 49

Verdict: ACCEPTED

Test 50

Verdict: ACCEPTED

Test 51

Verdict: ACCEPTED

Test 52

Verdict: ACCEPTED

Test 53

Verdict: ACCEPTED

Test 54

Verdict: ACCEPTED

Test 55

Verdict: ACCEPTED

Test 56

Verdict: ACCEPTED

Test 57

Verdict: ACCEPTED

Test 58

Verdict: ACCEPTED

Test 59

Verdict: ACCEPTED

Test 60

Verdict: ACCEPTED

Test 61

Verdict: ACCEPTED

Test 62

Verdict: ACCEPTED

Test 63

Verdict: ACCEPTED

Test 64

Verdict: ACCEPTED

Test 65

Verdict: ACCEPTED

Test 66

Verdict: ACCEPTED

Test 67

Verdict: ACCEPTED

Test 68

Verdict: ACCEPTED

Test 69

Verdict: ACCEPTED

Test 70

Verdict: ACCEPTED