<p>Given an input string (<code>s</code>) and a pattern (<code>p</code>), implement wildcard pattern matching with support for <code>&#39;?&#39;</code> and <code>&#39;*&#39;</code> where:</p>

<ul>
	<li><code>&#39;?&#39;</code> Matches any single character.</li>
	<li><code>&#39;*&#39;</code> Matches any sequence of characters (including the empty sequence).</li>
</ul>

<p>The matching should cover the <strong>entire</strong> input string (not partial).</p>

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

<pre>
<strong>Input:</strong> s = &quot;aa&quot;, p = &quot;a&quot;
<strong>Output:</strong> false
<strong>Explanation:</strong> &quot;a&quot; does not match the entire string &quot;aa&quot;.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;aa&quot;, p = &quot;*&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong>&nbsp;&#39;*&#39; matches any sequence.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;cb&quot;, p = &quot;?a&quot;
<strong>Output:</strong> false
<strong>Explanation:</strong>&nbsp;&#39;?&#39; matches &#39;c&#39;, but the second letter is &#39;a&#39;, which does not match &#39;b&#39;.
</pre>

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

<ul>
	<li><code>0 &lt;= s.length, p.length &lt;= 2000</code></li>
	<li><code>s</code> contains only lowercase English letters.</li>
	<li><code>p</code> contains only lowercase English letters, <code>&#39;?&#39;</code> or <code>&#39;*&#39;</code>.</li>
</ul>

class Solution {
public:
    bool findAnsRecur(string s, string p, int row, int col, vector<vector<int>> &dp){
        if(row < 0 && col < 0) return true;

        if(row < 0) {
            for(int i=0;i<=col;i++) if(p[i] != '*') return false;
            return true;
        }
        if(col < 0) return false;
        if(dp[row][col] != -1) return dp[row][col];
        
        if(p[col] == '*'){
            return dp[row][col] = findAnsRecur(s, p, row-1, col, dp) || findAnsRecur(s, p, row, col-1, dp);
        }
        if(p[col] == '?' || s[row] == p[col]){
            return dp[row][col] = findAnsRecur(s, p, row-1, col-1, dp);
        }
        return dp[row][col] = false;
    }

    bool findAnsIter(string s, string p){
        vector<vector<bool>> dp(s.size() + 1, vector<bool> (p.size() + 1, 0));
        dp[0][0] = true; // If both strings are exhausted.

        // If just second string got exhausted.
        for(int i=1;i<=s.size();i++){
            dp[i][0] = false;
        }
        // If just first string got exhausted.
        for(int i=1;i<=p.size();i++){
            dp[0][i] = (p[i-1] == '*') & dp[0][i-1];
        }

        for(int row=1;row<=s.size();row++){
            for(int col=1;col<=p.size();col++){
                if(s[row-1] == p[col-1] || p[col-1] == '?') dp[row][col] = dp[row-1][col-1];
                else if(p[col-1] == '*'){
                    dp[row][col] = dp[row][col-1] | dp[row-1][col];
                }
                else dp[row][col] = false;
            }
        }
        return dp[s.size()][p.size()];
    }

    bool isMatch(string s, string p) {
        // vector<vector<int>> dp(s.size(), vector<int> (p.size(), -1));
        // return findAnsRecur(s, p, s.size()-1, p.size()-1, dp);
        return findAnsIter(s, p);
    }
};
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