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>

第 507 场周赛

weekly-contest-507

maxDistance

高级工程师

Maximum Manhattan Distance After All Moves

Maximum Manhattan Distance After K Changes

maximum-manhattan-distance-after-k-changes

K 次修改后的最大曼哈顿距离

Math

String

Counting

给你一个由字符 <code>'U'</code>、<code>'D'</code>、<code>'L'</code>、<code>'R'</code> 和 <code>'_'</code> 组成的字符串 <code>moves</code>。

从原点 <code>(0, 0)</code> 出发，每个字符表示二维平面上的一次移动：

<ul>
	<li><code>'U'</code>：向上移动 1 个单位。</li>
	<li><code>'D'</code>：向下移动 1 个单位。</li>
	<li><code>'L'</code>：向左移动 1 个单位。</li>
	<li><code>'R'</code>：向右移动 1 个单位。</li>
	<li><code>'_'</code>：可以独立地替换为 <code>'U'</code>、<code>'D'</code>、<code>'L'</code> 或 <code>'R'</code> 中的任意一个字符。</li>
</ul>

返回执行完所有移动后，能够达到的距离原点的&nbsp;最大曼哈顿距离&nbsp;。

两点 <code>(x1, y1)</code> 和 <code>(x2, y2)</code> 之间的&nbsp;曼哈顿距离&nbsp;为 <code>|x1 - x2| + |y1 - y2|</code>。

&nbsp;

示例 1：

<div class="example-block">
输入： moves = "L_D_"

输出： 4

解释：

一种最优选择为：

<ul>
	<li><code>'L'</code>：<code>(0, 0) -&gt; (-1, 0)</code></li>
	<li>将 <code>'_'</code> 视为 <code>'D'</code>：<code>(-1, 0) -&gt; (-1, -1)</code></li>
	<li><code>'D'</code>：<code>(-1, -1) -&gt; (-1, -2)</code></li>
	<li>将 <code>'_'</code> 视为 <code>'L'</code>：<code>(-1, -2) -&gt; (-2, -2)</code></li>
</ul>

最终位置到原点的曼哈顿距离为 <code>|0 - (-2)| + |0 - (-2)| = 4</code>。
</div>

示例 2：

<div class="example-block">
输入： moves = "U_R"

输出： 3

解释：

一种最优选择为：

<ul>
	<li><code>'U'</code>：<code>(0, 0) -&gt; (0, 1)</code></li>
	<li>将 <code>'_'</code> 视为 <code>'U'</code>：<code>(0, 1) -&gt; (0, 2)</code></li>
	<li><code>'R'</code>：<code>(0, 2) -&gt; (1, 2)</code></li>
</ul>

最终位置到原点的曼哈顿距离为 <code>|0 - 1| + |0 - 2| = 3</code>。
</div>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= moves.length &lt;= 105</code></li>
	<li><code>moves</code> 仅由 <code>'U'</code>、<code>'D'</code>、<code>'L'</code>、<code>'R'</code> 和 <code>'_'</code> 组成。</li>
</ul>