<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:
    int f(int i, int j, string pat, string str){

        if(i < 0 && j < 0) return true;
        else if(i < 0 && j >= 0) return false;
        else if(i >= 0 && j < 0){
            for(int k=0; k<=i; k++){
                if(pat[k] != '*') return false;
            }
            return true;
        }

        if(pat[i] == str[j] && pat[i] == '?'){
            return f(i-1, j-1, pat, str);
        }

        if(pat[i] == '*'){
            return f(i-1, j-1, pat, str) | f(i, j-1, pat, str);
        }

        return false;
    }

    int fMemo(int i, int j, string pat, string str, vector<vector<int>> &dp){

        if(i == 0 && j == 0) return true;
        else if(i == 0 && j > 0) return false;
        else if(i > 0 && j == 0){
            for(int k=0; k<i; k++){
                if(pat[k] != '*') return false;
            }
            return true;
        }

        if(dp[i][j] != -1){
            return dp[i][j];
        }

        if(pat[i-1] == str[j-1] || pat[i-1] == '?'){
            return dp[i][j] = fMemo(i-1, j-1, pat, str, dp);
        }

        if(pat[i-1] == '*'){
            return dp[i][j] = fMemo(i-1, j, pat, str, dp) | fMemo(i, j-1, pat, str, dp);
        }

        return dp[i][j] = false;
    }

    int fTab(string pat, string str){
        int n = pat.size(), m = str.size();
        vector<vector<bool>> dp(n+1, vector<bool>(m+1, 0));
        dp[0][0] = true;

        for(int i=1; i<=n; i++){
            dp[i][0] = dp[i-1][0] & pat[i-1] == '*';
        }

        for(int i=1; i<=n; i++){
            for(int j=1; j<=m; j++){

                if(pat[i-1] == str[j-1] || pat[i-1] == '?'){
                    dp[i][j] = dp[i-1][j-1];
                }

                else if(pat[i-1] == '*'){
                    dp[i][j] = dp[i-1][j] | dp[i][j-1];
                }

                else dp[i][j] = false;
            }
        }

        return dp[n][m];
    }

    int fTabOpti(string pat, string str){
        int n = pat.size(), m = str.size();
        vector<bool> prev(m+1, false), curr(m+1, false);
        prev[0] = true;

        for(int i=1; i<=n; i++){
            curr[0] = prev[0] & pat[i-1] == '*';
            for(int j=1; j<=m; j++){

                if(pat[i-1] == str[j-1] || pat[i-1] == '?'){
                    curr[j] = prev[j-1];
                }

                else if(pat[i-1] == '*'){
                    curr[j] = prev[j] | curr[j-1];
                }

                else curr[j] = false;
            }
            prev = curr;
        }

        return prev[m];
    }

    bool isMatch(string s, string p) {
        int n = p.size(), m = s.size();
        // vector<vector<int>> dp(n+1, vector<int>(m+1, -1));
        // return fMemo(n, m, p, s, dp);
    
        //return fTab(p, s);

        return fTabOpti(p, s);
    }
};
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