<p>The chess knight has a <strong>unique movement</strong>,&nbsp;it may move two squares vertically and one square horizontally, or two squares horizontally and one square vertically (with both forming the shape of an <strong>L</strong>). The possible movements of chess knight are shown in this diagram:</p>

<p>A chess knight can move as indicated in the chess diagram below:</p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/18/chess.jpg" style="width: 402px; height: 402px;" />
<p>We have a chess knight and a phone pad as shown below, the knight <strong>can only stand on a numeric cell</strong>&nbsp;(i.e. blue cell).</p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/18/phone.jpg" style="width: 242px; height: 322px;" />
<p>Given an integer <code>n</code>, return how many distinct phone numbers of length <code>n</code> we can dial.</p>

<p>You are allowed to place the knight <strong>on any numeric cell</strong> initially and then you should perform <code>n - 1</code> jumps to dial a number of length <code>n</code>. All jumps should be <strong>valid</strong> knight jumps.</p>

<p>As the answer may be very large, <strong>return the answer modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 10
<strong>Explanation:</strong> We need to dial a number of length 1, so placing the knight over any numeric cell of the 10 cells is sufficient.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> 20
<strong>Explanation:</strong> All the valid number we can dial are [04, 06, 16, 18, 27, 29, 34, 38, 40, 43, 49, 60, 61, 67, 72, 76, 81, 83, 92, 94]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 3131
<strong>Output:</strong> 136006598
<strong>Explanation:</strong> Please take care of the mod.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 5000</code></li>
</ul>

class Solution {
public:
    #define ll long long int
    const ll mod = (ll)1e9 + 7;

   /* ll f_cnt(ll rem_len, ll d, unordered_map<ll, vector<ll>>& moves,vector<vector<ll>>&dp) {
        if (rem_len == 0) return 1;
        
        if(dp[rem_len][d] !=-1) return dp[rem_len][d];
        ll ways = 0;

        for (auto nd : moves[d]) {
            ways += f_cnt(rem_len - 1, nd, moves,dp);
            ways %= mod;
        }

        return dp[rem_len][d]=ways;
    }
 */
    int tab(ll n, unordered_map<ll, vector<ll>>&moves){
        vector<vector<ll>>dp(n+1,vector<ll>(10,0));
        for(int d=0;d<=9;d++) dp[0][d]=1;
        for(ll rem_len=1; rem_len<=n-1; rem_len++){
            for(ll d=0;d<=9;d++){
                ll ways = 0;               
                for (auto nd : moves[d]) {
                    ways += dp[rem_len - 1][nd];
                    ways %= mod;                  
                }
                dp[rem_len][d]=ways%mod;
            }
        }
        ll tot = 0;
        for (ll i = 0; i < 10; i++) {
            // placed the first digit at ith pos , ways to place rem n-1 digits
            tot += dp[n-1][i];
            tot %= mod;
        }
        return tot;
    }
    int knightDialer(int n) {
        unordered_map<ll, vector<ll>> moves;
        moves[0] = {4, 6};
        moves[1] = {6, 8};
        moves[2] = {7, 9};
        moves[3] = {4, 8};
        moves[4] = {0, 3, 9};
        moves[6] = {0, 1, 7};
        moves[7] = {2, 6};
        moves[8] = {1, 3};
        moves[9] = {2, 4};
       vector<vector<ll>>dp(n+1,vector<ll>(10,-1));


        return tab(n,moves);
    }
};

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