以下是使用Java编写的算法，用于计算小美从出发地到目的地的最短距离：

import java.util.Scanner;

public class ShortestDistance {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        
        // 输入站的数量
        int n = scanner.nextInt();
        
        // 输入站之间的距离
        int[] distances = new int[n];
        for (int i = 0; i < n; i++) {
            distances[i] = scanner.nextInt();
        }
        
        // 输入出发地和目的地
        int x = scanner.nextInt();
        int y = scanner.nextInt();
        
        // 计算最短距离
        int shortestDistance = calculateShortestDistance(n, distances, x, y);
        
        // 输出最短距离
        System.out.println(shortestDistance);
    }
    
    private static int calculateShortestDistance(int n, int[] distances, int x, int y) {
        int totalDistance = 0;
        
        // 计算从出发地到目的地的顺时针距离
        if (x < y) {
            for (int i = x - 1; i < y - 1; i++) {
                totalDistance += distances[i];
            }
        } else {
            for (int i = x - 1; i < n - 1; i++) {
                totalDistance += distances[i];
            }
            for (int i = 0; i < y - 1; i++) {
                totalDistance += distances[i];
            }
        }
        
        // 计算从目的地到出发地的逆时针距离
        int reverseDistance = 0;
        if (x > y) {
            for (int i = y - 1; i < x - 1; i++) {
                reverseDistance += distances[i];
            }
        } else {
            for (int i = y - 1; i < n - 1; i++) {
                reverseDistance += distances[i];
            }
            for (int i = 0; i < x - 1; i++) {
                reverseDistance += distances[i];
            }
        }
        
        // 取最短距离
        return Math.min(totalDistance, reverseDistance);
    }
}

请注意，此算法假设输入的站编号从1开始。