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1067 Sort with Swap(0, i)

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

#include<cstdio>
#include<algorithm>
using namespace std;

int set[100010];  //数字的位置

int main()
{
  int n;
  scanf_s("%d", &n);
  int temp;
  int left = 0;  //记录除0外不在本位上的数字个数
  for (int i = 0; i < n; i++)
  {
    scanf_s("%d", &temp);
    set[temp] = i;
    if (temp != i&&i)
      left++;
  }
  int ans = 0;  //交换次数
  int k = 1;  //记录除0外最小的不在本位上的数字
  while (left)
  {
    if (set[0])
    {
      swap(set[0], set[set[0]]);
      left--;
      ans++;
    }
    else
    {
      while (k < n)
      {
        if (set[k] != k)
        {
          swap(set[0], set[k]);
          ans++;
          break;
        }
        k++;
      }
    }
  }
  printf("%d", ans);
}

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