<p>You are given two strings <code>s</code> and <code>t</code>.</p>

<p>You are allowed to remove any number of characters from the string <code>t</code>.</p>

<p>The score of the string is <code>0</code> if no characters are removed from the string <code>t</code>, otherwise:</p>

<ul>
	<li>Let <code>left</code> be the minimum index among all removed characters.</li>
	<li>Let <code>right</code> be the maximum index among all removed characters.</li>
</ul>

<p>Then the score of the string is <code>right - left + 1</code>.</p>

<p>Return <em>the minimum possible score to make </em><code>t</code><em>&nbsp;a subsequence of </em><code>s</code><em>.</em></p>

<p>A <strong>subsequence</strong> of a string is a new string that is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (i.e., <code>&quot;ace&quot;</code> is a subsequence of <code>&quot;<u>a</u>b<u>c</u>d<u>e</u>&quot;</code> while <code>&quot;aec&quot;</code> is not).</p>

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

<pre>
<strong>Input:</strong> s = &quot;abacaba&quot;, t = &quot;bzaa&quot;
<strong>Output:</strong> 1
<strong>Explanation:</strong> In this example, we remove the character &quot;z&quot; at index 1 (0-indexed).
The string t becomes &quot;baa&quot; which is a subsequence of the string &quot;abacaba&quot; and the score is 1 - 1 + 1 = 1.
It can be proven that 1 is the minimum score that we can achieve.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;cde&quot;, t = &quot;xyz&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> In this example, we remove characters &quot;x&quot;, &quot;y&quot; and &quot;z&quot; at indices 0, 1, and 2 (0-indexed).
The string t becomes &quot;&quot; which is a subsequence of the string &quot;cde&quot; and the score is 2 - 0 + 1 = 3.
It can be proven that 3 is the minimum score that we can achieve.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length, t.length &lt;= 10<sup>5</sup></code></li>
	<li><code>s</code> and <code>t</code> consist of only lowercase English letters.</li>
</ul>

from collections import deque

class Solution:
    
    def getLeftIndices(leftString, rightString):
        rightIdx = 0
        leftCand = deque()
        for idx, letter in enumerate(leftString):
            if letter == rightString[rightIdx]:
                leftCand.append(idx)
                rightIdx += 1
                if rightIdx >= len(rightString):
                    break
        return leftCand

    def getRightIndices(leftString, rightString):
        rightIdx = len(rightString) - 1
        rightCand = deque()
        for idx, letter in enumerate(leftString[::-1]):
            if letter == rightString[rightIdx]:
                rightCand.appendleft(len(leftString) - 1 - idx)
                rightIdx -= 1
                if rightIdx < 0:
                    break
        return rightCand

    def minimumScore(self, s: str, t: str) -> int:
        leftCand = Solution.getLeftIndices(s, t)
        rightUsed = Solution.getRightIndices(s, t)

        minRemove = 0
        maxRemove = len(t) - 1 - len(rightUsed)
        minScore = maxRemove - minRemove + 1

        score = minScore
        while minScore > 0 and len(leftCand) > 0: 
            if len(rightUsed) == 0 or leftCand[0] < rightUsed[0]:
                minRemove += 1
                leftCand.popleft()
            else:
                maxRemove += 1
                rightUsed.popleft()
            score = maxRemove - minRemove + 1
            minScore = min(score, minScore)

        return minScore
20700