<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 helper (int pos, int k, map<int,int>mp,int target)
    {
        if(pos==target)
        {
            return 1;
        }
        if(pos > target || k <0 || mp.find(pos)==mp.end())
        {
            return 0;
        }
        bool h1,h2;
        if(k!=0)
        {
            h1=helper(pos+k,k,mp,target);
            h2=helper(pos+k-1,k-1,mp,target);
        }
        
        bool h3=helper(pos+k+1,k+1,mp,target);

        return h1 || h2|| h3;


    }



    bool helper1(int  index, int  k, unordered_map<int,int>&mp,int &target,vector<int>&stones,vector<vector<int>>&dp)
    {
        if(stones[index]==target)
        {
            return 1;
        }
        if(stones[index]>target || k< 0)
        {
            return 0;
        }
        if(dp[index][k]!=-1)
        {
            return dp[index][k];
        }

        int h1=0,h2=0,h3=0;
        if(k!=0)
        {
            int nh1=stones[index]+k;
            int nh2=stones[index]+k-1;
            if(mp.find(nh1)!=mp.end())
            {
                h1=helper1(mp[nh1],k,mp,target,stones,dp);
            }
            if(mp.find(nh2)!=mp.end())
            {
                h2=helper1(mp[nh2],k-1,mp,target,stones,dp);
            }
        }

        int nh3=stones[index]+k+1;
        if(mp.find(nh3)!=mp.end())
        {
            h3=helper1(mp[nh3],k+1,mp,target,stones,dp);
        }

        return dp[index][k]=h1||h2||h3;
    }


    bool canCross(vector<int>& stones) {
        if(stones[1]!=1)
        {
            return 0;
        }
        unordered_map<int,int>mp;
        int n=stones.size();
        vector<vector<int>>dp(n,vector<int>(2000,-1));
        for(int i=0;i<stones.size();i++)
        {
            mp[stones[i]]=i;
        }
        return helper1(1,1,mp,stones[stones.size()-1],stones,dp);
    }
};
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