<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:
        stone_map = {stones[i] : i for i in range(len(stones))}
        dp = {(0,0): 1}
        for i in range(len(stones)):
            for j in range(i + 1):
                prev_step = stones[i] - stones[j]
                if (i, prev_step) in dp:
                    for next_step in range(prev_step - 1, prev_step + 2):
                        next_possible_stone = next_step + stones[i]

                        if next_possible_stone in stone_map:
                            dp[(stone_map[next_possible_stone], next_step)] = 1
                            if (stone_map[next_possible_stone] == len(stones) - 1):
                                return True
        return False
        

        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        stone_map = {stones[i]: i for i in range(len(stones))}
        dp = {}
        dp[(0,0)] = 1

        for i in range(len(stones)):
            for prev_jump in range(i+1):
                if (i, prev_jump) in dp:
                    for next_jump in range(prev_jump - 1, prev_jump + 2):
                        if next_jump > 0 and (stones[i] + next_jump) in stone_map:
                            index = stone_map[stones[i] + next_jump]
                            dp[(index, next_jump)] = 1
        
        for (key1, key2) in dp:
            if key1 == len(stones)-1 and dp[(key1, key2)]:
                return True

        return False


        
21188