maximum-manhattan-distance-after-all-moves

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Algorithms

You are given a string <code>moves</code> consisting of the characters <code>&#39;U&#39;</code>, <code>&#39;D&#39;</code>, <code>&#39;L&#39;</code>, <code>&#39;R&#39;</code>, and <code>&#39;_&#39;</code>.

Starting from the origin <code>(0, 0)</code>, each character represents one move on a 2D plane:

<ul>
	<li><code>&#39;U&#39;</code>: Move up by 1 unit.</li>
	<li><code>&#39;D&#39;</code>: Move down by 1 unit.</li>
	<li><code>&#39;L&#39;</code>: Move left by 1 unit.</li>
	<li><code>&#39;R&#39;</code>: Move right by 1 unit.</li>
	<li><code>&#39;_&#39;</code>: Can be independently replaced with any one of <code>&#39;U&#39;</code>, <code>&#39;D&#39;</code>, <code>&#39;L&#39;</code>, or <code>&#39;R&#39;</code>.</li>
</ul>

Return the maximum Manhattan distance from the origin that can be achieved after all moves have been performed.

&nbsp;
Example 1:

<div class="example-block">
Input: moves = &quot;L_D_&quot;

Output: 4

Explanation:

One optimal choice is:

<ul>
	<li><code>&#39;L&#39;</code>: <code>(0, 0) -&gt; (-1, 0)</code></li>
	<li><code>&#39;_&#39;</code> treated as <code>&#39;D&#39;</code>: <code>(-1, 0) -&gt; (-1, -1)</code></li>
	<li><code>&#39;D&#39;</code>: <code>(-1, -1) -&gt; (-1, -2)</code></li>
	<li><code>&#39;_&#39;</code> treated as <code>&#39;L&#39;</code>: <code>(-1, -2) -&gt; (-2, -2)</code></li>
</ul>

The final Manhattan distance from the origin is <code>|0 - (-2)| + |0 - (-2)| = 4</code>.
</div>

Example 2:

<div class="example-block">
Input: moves = &quot;U_R&quot;

Output: 3

Explanation:

One optimal choice is:

<ul>
	<li><code>&#39;U&#39;</code>: <code>(0, 0) -&gt; (0, 1)</code></li>
	<li><code>&#39;_&#39;</code> treated as <code>&#39;U&#39;</code>: <code>(0, 1) -&gt; (0, 2)</code></li>
	<li><code>&#39;R&#39;</code>: <code>(0, 2) -&gt; (1, 2)</code></li>
</ul>

The final Manhattan distance from the origin is <code>|0 - 1| + |0 - 2| = 3</code>.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= moves.length &lt;= 105</code></li>
	<li><code>moves</code> consists of only <code>&#39;U&#39;</code>, <code>&#39;D&#39;</code>, <code>&#39;L&#39;</code>, <code>&#39;R&#39;</code>, and <code>&#39;_&#39;</code>.</li>
</ul>