<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 solve(int idx,int curr_jump,vector<int>& stones,vector<vector<int>>&dp)
    {

        if(idx==stones.size()-1)
        {
            return true;
        }


        if(dp[idx][curr_jump]!=-1)
        {
            if(dp[idx][curr_jump]==1)
            {
                return true;
            }
            else
            {
                return false;
            }
        }
        
        for(int i=curr_jump-1; i<=curr_jump+1; i++)
        {
            if(i>0)
            {
                int ele = stones[idx]+i;
                int a = lower_bound(stones.begin()+idx,stones.end(),ele)-stones.begin();

                if(a==stones.size())
                {
                    continue;
                }
                else if(stones[a]!=ele)
                {
                    continue;
                }
                else
                {
                    bool z = solve(a,i,stones,dp);
                    if(z==true)
                    {
                        dp[idx][curr_jump]=1;
                        return true;
                    }
                }
            }
        }

        dp[idx][curr_jump]=0;
        return false;
    }

    bool canCross(vector<int>& stones) {
        

        int idx = 0;
        int curr_jump = 0;
        vector<vector<int>>dp(stones.size()+1,vector<int>(2001,-1));
        bool ans  = solve(idx,curr_jump,stones,dp);

        return ans;
    }
};
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