number-of-times-binary-string-is-prefix-aligned

Number of Times Binary String Is Prefix-Aligned

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You have a 1-indexed binary string of length <code>n</code> where all the bits are <code>0</code> initially. We will flip all the bits of this binary string (i.e., change them from <code>0</code> to <code>1</code>) one by one. You are given a 1-indexed integer array <code>flips</code> where <code>flips[i]</code> indicates that the bit at index <code>i</code> will be flipped in the <code>ith</code> step.

A binary string is prefix-aligned if, after the <code>ith</code> step, all the bits in the inclusive range <code>[1, i]</code> are ones and all the other bits are zeros.

Return the number of times the binary string is prefix-aligned during the flipping process.

&nbsp;
Example 1:

<pre>
Input: flips = [3,2,4,1,5]
Output: 2
Explanation: The binary string is initially &quot;00000&quot;.
After applying step 1: The string becomes &quot;00100&quot;, which is not prefix-aligned.
After applying step 2: The string becomes &quot;01100&quot;, which is not prefix-aligned.
After applying step 3: The string becomes &quot;01110&quot;, which is not prefix-aligned.
After applying step 4: The string becomes &quot;11110&quot;, which is prefix-aligned.
After applying step 5: The string becomes &quot;11111&quot;, which is prefix-aligned.
We can see that the string was prefix-aligned 2 times, so we return 2.
</pre>

Example 2:

<pre>
Input: flips = [4,1,2,3]
Output: 1
Explanation: The binary string is initially &quot;0000&quot;.
After applying step 1: The string becomes &quot;0001&quot;, which is not prefix-aligned.
After applying step 2: The string becomes &quot;1001&quot;, which is not prefix-aligned.
After applying step 3: The string becomes &quot;1101&quot;, which is not prefix-aligned.
After applying step 4: The string becomes &quot;1111&quot;, which is prefix-aligned.
We can see that the string was prefix-aligned 1 time, so we return 1.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>n == flips.length</code></li>
	<li><code>1 &lt;= n &lt;= 5 * 104</code></li>
	<li><code>flips</code> is a permutation of the integers in the range <code>[1, n]</code>.</li>
</ul>

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