<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:
    int mod = 1e9 + 7;
    
    int solve(int n, int r, int c, vector<vector<int>>& dialer, vector<vector<vector<int>>>& dp, int dr[], int dc[]) {
        if (n == 1) {
            return 1;
        }

        if (dp[n][r][c]!=-1) {
            return dp[n][r][c];
        }

        int ans=0;

        for (int k = 0; k < 8; ++k) {
            int nrow =r+dr[k];
            int ncol = c+dc[k];

            if (nrow >= 0 && nrow < 4 && ncol >= 0 && ncol < 3 && dialer[nrow][ncol] != -1) {
                ans=(ans + solve(n - 1, nrow, ncol, dialer, dp, dr, dc)) % mod;
            }
        }

        return dp[n][r][c] = ans;
    }

    int knightDialer(int n) {
        vector<vector<int>> dialer = {
            {1, 2, 3},
            {4, 5, 6},
            {7, 8, 9},
            {-1, 0, -1} 
        };

       
        vector<vector<vector<int>>> dp(n + 1, vector<vector<int>>(4, vector<int>(3, -1)));

        int dr[] = {-2, -2, -1, -1, 1, 2, 2, 1};
        int dc[] = {-1, 1, -2, 2, -2, -1, 1, 2};

        int ans = 0;

        
        for (int r =0; r<4;r++) {
            for (int c=0; c<3;c++) {
                if (dialer[r][c]!=-1) {
                    ans=(ans+solve(n,r,c,dialer,dp,dr,dc)) % mod;
                }
            }
        }

        return ans;
    }
};

109847