<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:
/*
    int n;
    unordered_map<int, int> mp;
    int t[2001][2001];
    
    bool solve(vector<int>& stones, int curr_stone_index, int prevJump) {
        if(curr_stone_index == n-1)
            return true;
        
        bool result = false;
        
        if(t[curr_stone_index][prevJump] != -1)
            return t[curr_stone_index][prevJump];
        
        for(int nextJump = prevJump-1; nextJump <= prevJump+1; nextJump++) {
            
            if(nextJump > 0) {
                int next_stone = stones[curr_stone_index] + nextJump;
                
                if(mp.find(next_stone) != mp.end()) {
                    result = result || solve(stones, mp[next_stone], nextJump);
                }
            }
            
        }
        
        return t[curr_stone_index][prevJump] = result;
        
    }
    
    bool canCross(vector<int>& stones) {
        
        if(stones[1] != 1)
            return false;
        
        n = stones.size();
        for(int i = 0; i<n; i++) {
            mp[stones[i]] = i;
        }
        
        memset(t, -1, sizeof(t));
        
        return solve(stones, 0, 0);
    }
    */
  
    bool f(vector<int>& s, int i, unordered_map<int, int>& map, int prev,vector<vector<int>>&dp) {
        if (i == s.size() - 1)
            return true;

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

        bool result = false;

        for (int next = prev - 1; next <= prev + 1; next++) {
            if (next >0) {
                int to_find = s[i] + next;
                if (map.find(to_find) != map.end()) {
                    result = result || f(s, map[to_find], map, next,dp);
                }
            }
        }
        return dp[i][prev]=result;
    }
    bool canCross(vector<int>& s) {
        unordered_map<int, int> map;
        if (s[1] != 1)
            return false;

        for (int i = 0; i < s.size(); i++) {
            map[s[i]] = i;
          
        }
        vector<vector<int>>dp(s.size(),vector<int>(2001,-1));
        return f(s, 0, map, 0,dp);
    }

};


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