1067. Sort with Swap(0,*) (25)

Given any permutation of the numbers {0, 1, 2,..., N-1}, it is easy to sort them in increasing order. But what if Swap(0, *) is the ONLY operation that is allowed to use? For example, to sort {4, 0, 2, 1, 3} we may apply the swap operations in the following way:

Swap(0, 1) => {4, 1, 2, 0, 3}
Swap(0, 3) => {4, 1, 2, 3, 0}
Swap(0, 4) => {0, 1, 2, 3, 4}

Now you are asked to find the minimum number of swaps need to sort the given permutation of the first N nonnegative integers.

Input Specification:

Each input file contains one test case, which gives a positive N (<=10⁵) followed by a permutation sequence of {0, 1, ..., N-1}. All the numbers in a line are separated by a space.

Output Specification:

For each case, simply print in a line the minimum number of swaps need to sort the given permutation.

Sample Input:

10 3 5 7 2 6 4 9 0 8 1

Sample Output:

9

 1 #include <iostream>
 2 #include <set>
 3
 4 using namespace std;
 5
 6 set<int> WrongIndex;
 7 int sequence[100000];
 8
 9 int main()
10 {
11     int n;
12     cin >> n;
13     for (int i = 0; i < n; i++)
14     {
15         int num;
16         cin >> num;
17         sequence[i] = num;
18         if (num != i)
19             WrongIndex.insert(i);
20     }
21     int totalNum = WrongIndex.size();
22     int cycle = 0;
23     while (!WrongIndex.empty())
24     {
25         int initial = *(WrongIndex.begin());
26         int next = sequence[initial];
27         WrongIndex.erase(initial);
28         while (next != initial)
29         {
30             WrongIndex.erase(next);
31             next = sequence[next];
32         }
33         cycle++;
34     }
35     if (totalNum == 0)
36         cout << 0;
37     else if (sequence[0] != 0)
38         cout << totalNum + cycle - 2;
39     else
40         cout << totalNum + cycle;
41 }