<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 generate(const vector<int> &stones, int i, int k)
    {
        if (i == (stones.size() - 1))
        {
            return true;
        }
        bool flag = false;
        for (int j = i + 1; j != stones.size(); ++j)
        {
            if ((stones[j] - stones[i]) == (k + 1))
            {
                if (hash[j][k + 1] == INT_MIN)
                {
                    hash[j][k + 1] = generate(stones, j, k + 1);
                }
                flag |= hash[j][k + 1];
            }
            else if ((stones[j] - stones[i]) == k)
            {
                if (hash[j][k] == INT_MIN)
                {
                    hash[j][k] = generate(stones, j, k);
                }
                flag |= hash[j][k];
            }
            else if (k > 1 && (stones[j] - stones[i]) == (k - 1))
            {
                if (hash[j][k - 1] == INT_MIN)
                {
                    hash[j][k - 1] = generate(stones, j, k - 1);
                }
                flag |= hash[j][k - 1];
            }
            if (flag) return true;
        }
        return flag;
        
    }
    bool canCross(vector<int>& stones) {
        if ((stones[1] - stones[0]) != 1) return false;
        hash.resize(stones.size());
        for (int i = 0; i != hash.size(); ++i) hash[i].resize(i + 1, INT_MIN);
        return generate(stones, 1, 1);
    }
private:
    vector<vector<int>> hash;
};
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