<p>A frog is crossing a river. The river is divided into some number of units, and at each unit, there may or may not exist a stone. The frog can jump on a stone, but it must not jump into the water.</p>

<p>Given a list of <code>stones</code>&nbsp;positions (in units) in sorted <strong>ascending order</strong>, determine if the frog can cross the river by landing on the last stone. Initially, the frog is on the first stone and assumes the first jump must be <code>1</code> unit.</p>

<p>If the frog&#39;s last jump was <code>k</code> units, its next jump must be either <code>k - 1</code>, <code>k</code>, or <code>k + 1</code> units. The frog can only jump in the forward direction.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> stones = [0,1,3,5,6,8,12,17]
<strong>Output:</strong> true
<strong>Explanation:</strong> The frog can jump to the last stone by jumping 1 unit to the 2nd stone, then 2 units to the 3rd stone, then 2 units to the 4th stone, then 3 units to the 6th stone, 4 units to the 7th stone, and 5 units to the 8th stone.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> stones = [0,1,2,3,4,8,9,11]
<strong>Output:</strong> false
<strong>Explanation:</strong> There is no way to jump to the last stone as the gap between the 5th and 6th stone is too large.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= stones.length &lt;= 2000</code></li>
	<li><code>0 &lt;= stones[i] &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>stones[0] == 0</code></li>
	<li><code>stones</code>&nbsp;is sorted in a strictly increasing order.</li>
</ul>

class Solution:
    def canCross(self, stones: list[int]) -> bool:
        # Dictionary to store the set of possible jumps that can reach each stone
        dp = {}
        
        # Initial state: first stone can be reached with a jump of 1
        dp[stones[0]] = {0}
        
        for stone in stones:
            if stone not in dp:
                continue
            for jump in dp[stone]:
                for next_jump in (jump - 1, jump, jump + 1):
                    if next_jump > 0:
                        next_stone = stone + next_jump
                        if next_stone in dp:
                            dp[next_stone].add(next_jump)
                        else:
                            dp[next_stone] = {next_jump}
        
        # The last stone must be in the dp dictionary
        return stones[-1] in dp

# Example usage
solution = Solution()
print(solution.canCross([0,1,3,5,6,8,12,17]))  # Output: true
print(solution.canCross([0,1,2,3,4,8,9,11]))   # Output: false

19123