<p>We can scramble a string s to get a string t using the following algorithm:</p>

<ol>
	<li>If the length of the string is 1, stop.</li>
	<li>If the length of the string is &gt; 1, do the following:
	<ul>
		<li>Split the string into two non-empty substrings at a random index, i.e., if the string is <code>s</code>, divide it to <code>x</code> and <code>y</code> where <code>s = x + y</code>.</li>
		<li><strong>Randomly</strong>&nbsp;decide to swap the two substrings or to keep them in the same order. i.e., after this step, <code>s</code> may become <code>s = x + y</code> or <code>s = y + x</code>.</li>
		<li>Apply step 1 recursively on each of the two substrings <code>x</code> and <code>y</code>.</li>
	</ul>
	</li>
</ol>

<p>Given two strings <code>s1</code> and <code>s2</code> of <strong>the same length</strong>, return <code>true</code> if <code>s2</code> is a scrambled string of <code>s1</code>, otherwise, return <code>false</code>.</p>

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

<pre>
<strong>Input:</strong> s1 = &quot;great&quot;, s2 = &quot;rgeat&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> One possible scenario applied on s1 is:
&quot;great&quot; --&gt; &quot;gr/eat&quot; // divide at random index.
&quot;gr/eat&quot; --&gt; &quot;gr/eat&quot; // random decision is not to swap the two substrings and keep them in order.
&quot;gr/eat&quot; --&gt; &quot;g/r / e/at&quot; // apply the same algorithm recursively on both substrings. divide at random index each of them.
&quot;g/r / e/at&quot; --&gt; &quot;r/g / e/at&quot; // random decision was to swap the first substring and to keep the second substring in the same order.
&quot;r/g / e/at&quot; --&gt; &quot;r/g / e/ a/t&quot; // again apply the algorithm recursively, divide &quot;at&quot; to &quot;a/t&quot;.
&quot;r/g / e/ a/t&quot; --&gt; &quot;r/g / e/ a/t&quot; // random decision is to keep both substrings in the same order.
The algorithm stops now, and the result string is &quot;rgeat&quot; which is s2.
As one possible scenario led s1 to be scrambled to s2, we return true.
</pre>

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

<pre>
<strong>Input:</strong> s1 = &quot;abcde&quot;, s2 = &quot;caebd&quot;
<strong>Output:</strong> false
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s1 = &quot;a&quot;, s2 = &quot;a&quot;
<strong>Output:</strong> true
</pre>

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

<ul>
	<li><code>s1.length == s2.length</code></li>
	<li><code>1 &lt;= s1.length &lt;= 30</code></li>
	<li><code>s1</code> and <code>s2</code> consist of lowercase English letters.</li>
</ul>

class Solution(object):
    def isScramble(self, s1, s2):
        """
        :type s1: str
        :type s2: str
        :rtype: bool
        """
        # Base cases

        n = len(s1)

        # If both strings are not equal in size
        if len(s2) != n:
            return False

        # If both strings are equal
        if s1 == s2:
            return True

        # If code is reached to this condition then following this are sure:
        # 1. size of both string is equal
        # 2. string are not equal
        # so size is equal (where size==1) and they are not equal then obviously false
        # example 'a' and 'b' size is equal, string are not equal
        if n == 1:
            return False

        key = s1 + " " + s2

        # Check if this problem has already been solved
        if key in self.mp:
            return self.mp[key]

        # For every iteration it can two condition
        # 1. We should proceed without swapping
        # 2. We should swap before looking next
        for i in range(1, n):
            # ex of without swap: gr|eat and rg|eat
            without_swap = (
                # Left part of first and second string
                self.isScramble(s1[:i], s2[:i])
                and
                # Right part of first and second string;
                self.isScramble(s1[i:], s2[i:])
            )

            # If without swap gives us the right answer then we do not need
            # to call the recursion with swap
            if without_swap:
                return True

            # ex of with swap: gr|eat rge|at
            # here we compare "gr" with "at" and "eat" with "rge"
            with_swap = (
                # Left part of first and right part of second
                self.isScramble(s1[:i], s2[n-i:])
                and
                # Right part of first and left part of second
                self.isScramble(s1[i:], s2[:n-i])
            )

            # If with swap gives us the right answer then we return True
            # otherwise, the for loop does its work
            if with_swap:
                return True

        self.mp[key] = False
        return False

    # for storing already solved problems
    mp = {}
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