package class45;

import java.util.HashMap;
import java.util.HashSet;

public class Problem_0403_FrogJump {

	public static boolean canCross(int[] stones) {
		HashSet<Integer> set = new HashSet<>();
		for (int num : stones) {
			set.add(num);
		}
		HashMap<Integer, HashMap<Integer, Boolean>> dp = new HashMap<>();
		return jump(1, 1, stones[stones.length - 1], set, dp);
	}

	public static boolean jump(int cur, int pre, int end, HashSet<Integer> set,
			HashMap<Integer, HashMap<Integer, Boolean>> dp) {
		if (cur == end) {
			return true;
		}
		if (!set.contains(cur)) {
			return false;
		}
		if (dp.containsKey(cur) && dp.get(cur).containsKey(pre)) {
			return dp.get(cur).get(pre);
		}
		boolean ans = (pre > 1 && jump(cur + pre - 1, pre - 1, end, set, dp)) 
				|| jump(cur + pre, pre, end, set, dp)
				|| jump(cur + pre + 1, pre + 1, end, set, dp);
		if (!dp.containsKey(cur)) {
			dp.put(cur, new HashMap<>());
		}
		if (!dp.get(cur).containsKey(pre)) {
			dp.get(cur).put(pre, ans);
		}
		return ans;
	}

}