<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>

#include<bits/stdc++.h>
class Solution {
int mod=1000000007;

private:
    int solve(int prev,int n,unordered_map<int,list<int>>&mapping,vector<vector<int>>&dp)
    {
        if(n==0)
        {
            return 1;
        }
        if(dp[prev][n]!=-1)
        {
            return dp[prev][n];
        }
        int ans=0;
        for(auto i:mapping[prev])
        {
            ans+=(solve(i,n-1,mapping,dp)%mod);
            ans=ans%mod;
        }
        return dp[prev][n]=ans;
    }
public:
    int knightDialer(int n) {
        if(n==1)
        {
            return 10;
        }
        int temp=0;
        unordered_map<int,list<int>>mapping;
        mapping[0].push_back(4);
        mapping[0].push_back(6);
        mapping[1].push_back(6);
        mapping[1].push_back(8);
        mapping[2].push_back(7);
        mapping[2].push_back(9);
        mapping[3].push_back(4);
        mapping[3].push_back(8);
        mapping[4].push_back(0);
        mapping[4].push_back(3);
        mapping[4].push_back(9);
        mapping[6].push_back(0);
        mapping[6].push_back(1);
        mapping[6].push_back(7);
        mapping[7].push_back(2);
        mapping[7].push_back(6);
        mapping[8].push_back(1);
        mapping[8].push_back(3);
        mapping[9].push_back(4);
        mapping[9].push_back(2);
        vector<vector<int>>dp(10,vector<int>(n+1,-1));
        for(int i=0;i<5;i++)
        {
            temp+=(solve(i,n-1,mapping,dp)%mod);
            temp=temp%mod;
        }
        for(int i=6;i<10;i++)
        {
            temp+=(solve(i,n-1,mapping,dp)%mod);
            temp=temp%mod;
        }
        return temp;
        
    }
};
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