{ "data": { "question": { "questionId": "3754", "questionFrontendId": "3443", "categoryTitle": "Algorithms", "boundTopicId": 3060799, "title": "Maximum Manhattan Distance After K Changes", "titleSlug": "maximum-manhattan-distance-after-k-changes", "content": "

You are given a string s consisting of the characters 'N', 'S', 'E', and 'W', where s[i] indicates movements in an infinite grid:

\n\n\n\n

Initially, you are at the origin (0, 0). You can change at most k characters to any of the four directions.

\n\n

Find the maximum Manhattan distance from the origin that can be achieved at any time while performing the movements in order.

\nThe Manhattan Distance between two cells (xi, yi) and (xj, yj) is |xi - xj| + |yi - yj|.\n

 

\n

Example 1:

\n\n
\n

Input: s = "NWSE", k = 1

\n\n

Output: 3

\n\n

Explanation:

\n\n

Change s[2] from 'S' to 'N'. The string s becomes "NWNE".

\n\n\n\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\n\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\n
MovementPosition (x, y)Manhattan DistanceMaximum
s[0] == 'N'(0, 1)0 + 1 = 11
s[1] == 'W'(-1, 1)1 + 1 = 22
s[2] == 'N'(-1, 2)1 + 2 = 33
s[3] == 'E'(0, 2)0 + 2 = 23
\n\n

The maximum Manhattan distance from the origin that can be achieved is 3. Hence, 3 is the output.

\n
\n\n

Example 2:

\n\n
\n

Input: s = "NSWWEW", k = 3

\n\n

Output: 6

\n\n

Explanation:

\n\n

Change s[1] from 'S' to 'N', and s[4] from 'E' to 'W'. The string s becomes "NNWWWW".

\n\n

The maximum Manhattan distance from the origin that can be achieved is 6. Hence, 6 is the output.

\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "K 次修改后的最大曼哈顿距离", "translatedContent": "

给你一个由字符 'N'、'S'、'E' 和 'W' 组成的字符串 s，其中 s[i] 表示在无限网格中的移动操作：

\n\n\n\n

初始时，你位于原点 (0, 0)。你 最多 可以修改 k 个字符为任意四个方向之一。

\n\n

请找出在 按顺序 执行所有移动操作过程中的 任意时刻 ，所能达到的离原点的 最大曼哈顿距离 。

\n\n

曼哈顿距离 定义为两个坐标点 (xi, yi) 和 (xj, yj) 的横向距离绝对值与纵向距离绝对值之和，即 |xi - xj| + |yi - yj|。

\n\n

 

\n\n

示例 1：

\n\n
\n

输入：s = \"NWSE\", k = 1

\n\n

输出：3

\n\n

解释：

\n\n

将 s[2] 从 'S' 改为 'N' ，字符串 s 变为 \"NWNE\" 。

\n\n\n\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\n\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\t\n\t\t\n\t\n
移动操作位置 (x, y)曼哈顿距离最大值
s[0] == 'N'(0, 1)0 + 1 = 11
s[1] == 'W'(-1, 1)1 + 1 = 22
s[2] == 'N'(-1, 2)1 + 2 = 33
s[3] == 'E'(0, 2)0 + 2 = 23
\n\n

执行移动操作过程中，距离原点的最大曼哈顿距离是 3 。

\n
\n\n

示例 2：

\n\n
\n

输入：s = \"NSWWEW\", k = 3

\n\n

输出：6

\n\n

解释：

\n\n

将 s[1] 从 'S' 改为 'N' ，将 s[4] 从 'E' 改为 'W' 。字符串 s 变为 \"NNWWWW\" 。

\n\n

执行移动操作过程中，距离原点的最大曼哈顿距离是 6 。

\n
\n\n

 

\n\n

提示：

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\\u60a8\\u7684\\u4ee3\\u7801\\u5c06\\u4f1a\\u88ab\\u4e0d\\u7f16\\u8bd1\\u76f4\\u63a5\\u8fd0\\u884c<\\/p>\"],\"cangjie\":[\"Cangjie\",\"
\\u7248\\u672c\\uff1a1.0.0 LTS (cjnative)<\\/p>\\r\\n\\r\\n
\\u7f16\\u8bd1\\u53c2\\u6570\\uff1a-O2 --disable-reflection<\\/code><\\/p>\\r\\n\\r\\n
\\u5feb\\u901f\\u5165\\u95e8\\u8bf7\\u67e5\\u9605\\u300c\\u4ed3\\u9889\\u7f16\\u7a0b\\u8bed\\u8a00\\u5f00\\u53d1\\u6307\\u5357\\u300d<\\/a><\\/p>\"]}",
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}