Find the common base path of a list of file paths

BasePath.java

//package ;

import java.nio.file.Path;
import java.nio.file.Paths;
import java.util.List;

/**
 * @see  <a href="https://www.geeksforgeeks.org/longest-common-prefix-using-binary-search/">Longest
 *              Common Prefix using Binary Search</a>
 */
public class BasePath {

    private List<Path> list = new java.util.ArrayList<>();

    private int minLength = Integer.MAX_VALUE;

    public void add(String first, String... more) {
        add(Paths.get(first, more));
    }

    public void add(Path path) {
        list.add(path);
        if (path.getNameCount() < minLength) {
            minLength = path.getNameCount();
        }
    }

    public String find() {
        if (list.isEmpty()) {
            return "";
        }

        Path[] paths = list.toArray(new Path[list.size()]);
        int low = minLength, high = paths.length - 1;
        while (low <= high) {
            int mid = low + (high - low) / 2;
            if (startWith(paths, low, mid)) {
                low = mid + 1;
            } else {
                high = mid - 1;
            }
        }
        return (low == 0) ? "" : paths[0].subpath(0, low).toString();
    }

    private static boolean startWith(Path[] paths, int start, int end) {
        Path prefix = paths[0];
        for (int i = 1, n = paths.length; i < n; i++) {
            Path str = paths[i];
            for (int j = start; j <= end; j++) {
                if (!str.getName(j).equals(prefix.getName(j))) {
                    return false;
                }
            }
        }
        return true; 
    }

    public void clear() {
        list.clear();
        minLength = Integer.MAX_VALUE;
    }

}