<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 {
public:
  bool canCross(const std::vector<int>& stones) {
    std::vector<std::vector<std::optional<bool>>> memo(stones.size()+1, std::vector<std::optional<bool>>(stones.size()+1));
    return go(stones, stones.cbegin(), 0, memo);
  }

private:
  bool go(const auto& stones, std::vector<int>::const_iterator it, long last_jump, auto& memo) {
    if(it == stones.cend()-1)
      return true;
    if(not memo[std::distance(stones.begin(),it)][last_jump]){
      std::array<bool, 3> jump_options;
      for(int j = -1, i = 0; i<3; ++i, ++j) {
        auto next_it = std::lower_bound(it, stones.cend(), *it+last_jump+j);
        if(next_it == stones.cend() or next_it == it or *it+last_jump+j != *next_it)
          jump_options[i] = false;
        else
          jump_options[i] = go(stones, next_it, last_jump + j, memo);
      }
      memo[std::distance(stones.begin(), it)][last_jump].emplace(std::ranges::any_of(jump_options, std::identity{}));
    }
    return *memo[std::distance(stones.begin(), it)][last_jump];
  }
};


121301