<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 solveRec(int ind, int curr_jump, vector<int> &arr, map<int,int> &mp){
        if(curr_jump<=0) return false;

        if(ind==arr.size()-1) return true;

        if(!mp[arr[ind] + curr_jump]) return 0;

        bool op1 = solveRec(mp[arr[ind]+curr_jump]-1, curr_jump, arr, mp);
        bool op2 = solveRec(mp[arr[ind]+curr_jump]-1, curr_jump+1, arr, mp);
        bool op3 = solveRec(mp[arr[ind]+curr_jump]-1, curr_jump-1, arr, mp);

        return op1 || op2 || op3;
    }

    bool solveMem(int ind, int curr_jump, vector<int> &arr, map<int,int> &mp, 
    vector<vector<int>> &dp){
        if(curr_jump<=0) return false;
        if(ind==arr.size()-1) return 1;

        if(!mp[arr[ind] + curr_jump]) return false;

        if(dp[ind][curr_jump]!=-1) return dp[ind][curr_jump];

        bool op1 = solveMem(mp[arr[ind] + curr_jump]-1, curr_jump, arr, mp, dp);
        bool op2 = solveMem(mp[arr[ind] + curr_jump]-1, curr_jump + 1, arr, mp, dp);
        bool op3 = solveMem(mp[arr[ind] + curr_jump]-1, curr_jump - 1, arr, mp, dp);


        return dp[ind][curr_jump] = op1 || op2 || op3;
    }


    bool canCross(vector<int>& stones) {
        int n = stones.size();
        map<int,int> mp;
        for(int i=0; i<n; i++){
            mp[stones[i]] = i+1;
        }

        // return solveRec(0, 1, stones, mp);
        
        vector<vector<int>> dp(n+1, vector<int>(2001, -1));
        return solveMem(0, 1, stones, mp, dp);
    }
};
397823