<img alt="" src="https://assets.leetcode.com/uploads/2020/01/02/leetcode_keyboard.png" style="width: 349px; height: 209px;" />
<p>You have a keyboard layout as shown above in the <strong>X-Y</strong> plane, where each English uppercase letter is located at some coordinate.</p>

<ul>
	<li>For example, the letter <code>&#39;A&#39;</code> is located at coordinate <code>(0, 0)</code>, the letter <code>&#39;B&#39;</code> is located at coordinate <code>(0, 1)</code>, the letter <code>&#39;P&#39;</code> is located at coordinate <code>(2, 3)</code> and the letter <code>&#39;Z&#39;</code> is located at coordinate <code>(4, 1)</code>.</li>
</ul>

<p>Given the string <code>word</code>, return <em>the minimum total <strong>distance</strong> to type such string using only two fingers</em>.</p>

<p>The <strong>distance</strong> between coordinates <code>(x<sub>1</sub>, y<sub>1</sub>)</code> and <code>(x<sub>2</sub>, y<sub>2</sub>)</code> is <code>|x<sub>1</sub> - x<sub>2</sub>| + |y<sub>1</sub> - y<sub>2</sub>|</code>.</p>

<p><strong>Note</strong> that the initial positions of your two fingers are considered free so do not count towards your total distance, also your two fingers do not have to start at the first letter or the first two letters.</p>

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

<pre>
<strong>Input:</strong> word = &quot;CAKE&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> Using two fingers, one optimal way to type &quot;CAKE&quot; is: 
Finger 1 on letter &#39;C&#39; -&gt; cost = 0 
Finger 1 on letter &#39;A&#39; -&gt; cost = Distance from letter &#39;C&#39; to letter &#39;A&#39; = 2 
Finger 2 on letter &#39;K&#39; -&gt; cost = 0 
Finger 2 on letter &#39;E&#39; -&gt; cost = Distance from letter &#39;K&#39; to letter &#39;E&#39; = 1 
Total distance = 3
</pre>

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

<pre>
<strong>Input:</strong> word = &quot;HAPPY&quot;
<strong>Output:</strong> 6
<strong>Explanation:</strong> Using two fingers, one optimal way to type &quot;HAPPY&quot; is:
Finger 1 on letter &#39;H&#39; -&gt; cost = 0
Finger 1 on letter &#39;A&#39; -&gt; cost = Distance from letter &#39;H&#39; to letter &#39;A&#39; = 2
Finger 2 on letter &#39;P&#39; -&gt; cost = 0
Finger 2 on letter &#39;P&#39; -&gt; cost = Distance from letter &#39;P&#39; to letter &#39;P&#39; = 0
Finger 1 on letter &#39;Y&#39; -&gt; cost = Distance from letter &#39;A&#39; to letter &#39;Y&#39; = 4
Total distance = 6
</pre>

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

<ul>
	<li><code>2 &lt;= word.length &lt;= 300</code></li>
	<li><code>word</code> consists of uppercase English letters.</li>
</ul>

class Solution:
    def minimumDistance(self, word):
    # Create the keyboard layout where each letter corresponds to a coordinate (x, y)
        def getPos(c):
            return divmod(ord(c) - ord('A'), 6)

        # Memoization table
        memo = {}

        # dp function definition: i is the index in the word, f1 and f2 are the positions of the two fingers
        def dp(i, f1, f2):
            if i == len(word):
                return 0  # Base case: no more characters to type

            if (i, f1, f2) in memo:
                return memo[(i, f1, f2)]

            # Position of the current letter in the word
            pos = getPos(word[i])

            # Move finger 1 to the current letter
            if f1 is None:  # If finger 1 hasn't typed anything yet
                dist1 = 0
            else:
                dist1 = abs(f1[0] - pos[0]) + abs(f1[1] - pos[1])

            # Move finger 2 to the current letter
            if f2 is None:  # If finger 2 hasn't typed anything yet
                dist2 = 0
            else:
                dist2 = abs(f2[0] - pos[0]) + abs(f2[1] - pos[1])

            # Recursively calculate the minimum cost for typing the rest of the word
            useFinger1 = dist1 + dp(i + 1, pos, f2)
            useFinger2 = dist2 + dp(i + 1, f1, pos)

            # Take the minimum of the two options
            memo[(i, f1, f2)] = min(useFinger1, useFinger2)
            return memo[(i, f1, f2)]

        # Start with both fingers not having typed anything
        return dp(0, None, None)

27100