<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:
    /*
    Space optimizacija Memoizacije.Trenutni red ces generisati na osnovu prethodnog.Stoga 
      Space Complexity : O(M) , Time Complexity : O(N*M)  
    */
    bool isMatch(const string &s, const string &p) {
        int n = s.size();
        int m = p.size();
    
    // Initialize the dp array
        vector<bool> dp(m + 1, false);
        dp[0] = true;
    
    // Initialize dp array for patterns with '*'
    for (int j = 1; j <= m; ++j) {
        if (p[j - 1] == '*') {
            dp[j] = dp[j - 1];
        }
    }
    
    for (int i = 1; i <= n; ++i) {
        // Temporary array to store the results for the current row
        vector<bool> noviDP(m + 1, false);
        noviDP[0] = false; // Empty pattern cannot match non-empty string
        
        for (int j = 1; j <= m; ++j) {
            if (p[j - 1] == '*') {
                noviDP[j] = noviDP[j - 1] || dp[j];
            } else if (p[j - 1] == '?' || s[i - 1] == p[j - 1]) {
                noviDP[j] = dp[j - 1];
            } else {
                noviDP[j] = false;
            }
        }
        
        dp = noviDP;
    }

    return dp[m];
  }
    
   bool helper(int i, int j, const string &s, const string &p, vector<bool> &dp) {
  
    if (i < 0 && j < 0) return true;
    if (i >= 0 && j < 0) return false;
    if (i < 0 && j >= 0) {
        for (int z = j; z >= 0; --z) {
            if (p[z] != '*') return false;
        }
        return true;
    }
    
    if (dp[j] != -1) return dp[j];
    
    bool result = false;
    if (s[i] == p[j] || p[j] == '?') {
        result = helper(i - 1, j - 1, s, p, dp);
    } else if (p[j] == '*') {
        result = helper(i, j - 1, s, p, dp) || helper(i - 1, j, s, p, dp);
    }
    
        return dp[j] = result;
    }

};
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