<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:
        mem = [[None]*len(stones) for _ in stones]
        return can_cross(1, 0, stones, max(stones), mem, 0)

def can_cross(jump: int, pos: int, stones: List[int], finish: int, mem: List[Optional[bool]], n) -> bool:
    indent = "\t"*n
    # print(f'{indent}{jump} {pos}({stones[pos]}) ---')
    if pos == len(stones) - 1:
        return True

    # print(pos, jump-1, len(mem), len(mem[0]))
    if mem[pos][jump-1] is not None:
        return mem[pos][jump-1]

    pos_to_move = 1
    while pos + pos_to_move < len(stones) and stones[pos + pos_to_move] < stones[pos] + jump:
        pos_to_move += 1

    if pos + pos_to_move >= len(stones) or stones[pos + pos_to_move] != stones[pos] + jump:
        # print('\t'*(n+1), jump, f'{pos}({stones[pos]})', f'{pos + pos_to_move}')
        mem[pos][jump-1] = False
        return False

    slow_down_works = jump != 1 and can_cross(jump-1, pos+pos_to_move, stones, finish, mem, n+1)
    same_works = can_cross(jump, pos+pos_to_move, stones, finish, mem, n+1)
    accelerate_works = can_cross(jump+1, pos+pos_to_move, stones, finish, mem, n+1)
    mem[pos][jump-1] = slow_down_works or same_works or accelerate_works
    # print('\t'*(n+1), jump, pos, slow_down_works, same_works, accelerate_works)
    return mem[pos][jump-1]



# 0 1 3 4 6 8 12 17

# k
# can_cross(curr_jump)
49065