(Analysis by Nick Wu)

In this problem, we're given a list of $N$ integers, with the guarantee that removing exactly one of them can result in a sorted array.

Because removing one of them can result in a sorted array, if we consider the elements that are not in the right order, those must form a sequence that is almost sorted, except that either the minimum element is in the rightmost slot or the maximum element is in the leftmost slot. Consequently, if there are $K$ elements that are out of order, it will take $K-1$ swaps to fix them, since every swap except for the last one can only fix the location of one such element.

import java.io.*;
import java.util.*;
public class outofplace {
public static void main(String[] args) throws IOException {
PrintWriter pw = new PrintWriter(new BufferedWriter(new FileWriter("outofplace.out")));

int[] height = new int[n];
int[] sorted = new int[n];
for(int i = 0; i < n; i++) {
sorted[i] = height[i];
}
Arrays.sort(sorted);
int swaps = -1;
for(int a = 0; a < n; a++) {
if(sorted[a] != height[a]) {
swaps++;
}
}
swaps = Math.max(0, swaps);
pw.println(swaps);
pw.close();
}

}