<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>

bool canreach(vector<int>& stones, long long int k, long long int i, long long int n, map<long long int, long long int>& mpp, vector<vector<int>> &dp){
    if(i == n-1) return true;

    if(dp[i][k] != -1) return dp[i][k];

    bool first = false;
    if(k-1 > 0 && mpp[stones[i] + k - 1] > 0){
        first = canreach(stones, k-1, mpp[stones[i]+k-1], n, mpp, dp);
    }
    bool second = false;
    if(mpp[stones[i]+k] > 0){
        second = canreach(stones, k, mpp[stones[i]+k], n, mpp, dp);
    }
    bool third = false;
    if(mpp[stones[i]+k+1] > 0){
        third = canreach(stones, k+1, mpp[stones[i]+k+1], n, mpp, dp);
    }


    return dp[i][k] = first || second || third;
}
class Solution {
public:
    bool canCross(vector<int>& stones) {
        int n = stones.size();
        if(stones[1] != 1) return false;
        map<long long int, long long int> mpp;
        for(int i = 0; i<n; i++){
            mpp[stones[i]] = i;
        }
        vector<vector<int>> dp(n+1, vector<int>(n, -1));
        
        bool flag = canreach(stones, 1, 1, n, mpp, dp);

        return flag;
    }
};
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