<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>

#include <bits/stdc++.h>
using namespace std;


template<class Fun> class y_combinator_result { Fun fun_;
public:
    template<class T> explicit y_combinator_result(T &&fun): fun_(std::forward<T>(fun)) {}
    template<class ...Args> decltype(auto) operator()(Args &&...args) { return fun_(std::ref(*this), std::forward<Args>(args)...); }
};
template<class Fun> decltype(auto) y_combinator(Fun &&fun) { return y_combinator_result<std::decay_t<Fun>>(std::forward<Fun>(fun)); }

int cache[2005][2005];

class Solution {
public:
    bool isMatch(string S, string P) {
        int N = S.size(), M = P.size();

        auto solve = y_combinator([&] (auto solve, int sInd, int pInd) -> bool {      
            if(sInd == N && pInd == M) {
                return true;
            }
            if(cache[sInd][pInd] != -1) return cache[sInd][pInd];

            if(sInd >= N) {
                for(int index = pInd; index < M; index++) {
                    if(P[index] != '*') return false;
                }
                return true;
            }

            if(pInd >= M) return cache[sInd][pInd] = false;

            if(S[sInd] == P[pInd]) return cache[sInd][pInd] = solve(sInd +1, pInd + 1);
            char pChar = P[pInd];

            if(pChar != '*' && pChar != '?') return cache[sInd][pInd] = false;

            if(pChar == '?') return cache[sInd][pInd] = solve(sInd + 1, pInd + 1);

            return cache[sInd][pInd] = solve(sInd + 1, pInd) | solve(sInd, pInd + 1);
            
        });
        memset(cache, -1, sizeof(cache));
        return solve(0, 0);        
    }
};
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