<p>You are given a <strong>0-indexed</strong> binary string <code>s</code> and two integers <code>minJump</code> and <code>maxJump</code>. In the beginning, you are standing at index <code>0</code>, which is equal to <code>&#39;0&#39;</code>. You can move from index <code>i</code> to index <code>j</code> if the following conditions are fulfilled:</p>

<ul>
	<li><code>i + minJump &lt;= j &lt;= min(i + maxJump, s.length - 1)</code>, and</li>
	<li><code>s[j] == &#39;0&#39;</code>.</li>
</ul>

<p>Return <code>true</code><i> if you can reach index </i><code>s.length - 1</code><i> in </i><code>s</code><em>, or </em><code>false</code><em> otherwise.</em></p>

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

<pre>
<strong>Input:</strong> s = &quot;<u>0</u>11<u>0</u>1<u>0</u>&quot;, minJump = 2, maxJump = 3
<strong>Output:</strong> true
<strong>Explanation:</strong>
In the first step, move from index 0 to index 3. 
In the second step, move from index 3 to index 5.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;01101110&quot;, minJump = 2, maxJump = 3
<strong>Output:</strong> false
</pre>

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

<ul>
	<li><code>2 &lt;= s.length &lt;= 10<sup>5</sup></code></li>
	<li><code>s[i]</code> is either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>
	<li><code>s[0] == &#39;0&#39;</code></li>
	<li><code>1 &lt;= minJump &lt;= maxJump &lt; s.length</code></li>
</ul>

class Solution:
    def canReach(self, s: str, minJump: int, maxJump: int) -> bool:
        # jump ranges
        q = deque([0])
        mx = 0
        while q:
            i = q.popleft()
            if i == len(s) - 1: return True
            for j in range(max(mx, i + minJump), min(i + maxJump + 1, len(s))):
                if s[j] == '1': continue
                q.append(j)
            mx = max(mx, min(i + maxJump + 1, len(s)))
        return False


        # TLE
        # if s[-1] == '1': return False
        # @cache
        # def dfs(i: int) -> bool:
        #     if i == len(s) - 1: return True
        #     if i in visited: return False
        #     visited.add(i)
        #     if s[i] == '1': return False
        #     return any(dfs(j) for j in range(i + minJump, min(i + maxJump, (len(s) - 1)) + 1))

        # visited = set()
        # return dfs(0)



        # # at each position, check if it is reachable
        #     # if yes, mark following posisitions can be jumped to
        # positions = [True] + [False] * (len(s) - 1)
        # for i in range(len(s)):
        #     # boundary
        #     if not positions[i]: continue
        #     if s[i] == '1': continue
        #     for j in range(i + minJump, min(i + maxJump, (len(s) - 1)) + 1):
        #         if s[j] != '1': positions[j] = True
        
        # return positions[-1]
460