<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(vector<int>& stones) {
        int n = stones.size();
        if (n >= 2)
        {
            if (stones[1] != 1)
            {
                return false;
            }

            if (n == 2)
            {
                return true;                
            }
        }

        map<pair<int,int>, bool> dict;
        set<pair<int, int>> s;        
        s.insert(pair<int,int>(1,1));
        dict[pair<int,int>(1,1)] = true;

        while (s.size() > 0)
        {
            set<pair<int,int>> news;

            for (auto elem : s)
            {
                for (int i = elem.first+1; i < n; i++)
                {
                    int jump = stones[i] - stones[elem.first];
                    if ((jump > 0) && ((jump == elem.second) || (jump == (elem.second + 1)) || (jump == (elem.second - 1))))
                    {
                        if (i == n-1)
                        {
                            return true;
                        }

                        if (dict.find(pair<int,int>(i, jump)) == dict.end())
                        {
                            news.insert(pair<int,int>(i, jump));
                            dict[pair<int,int>(i, jump)] = true;
                        }
                    }
                }
            }
            s = news;
        }

        return false;
    }
};
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