{ "data": { "question": { "questionId": "489", "questionFrontendId": "1643", "categoryTitle": "Algorithms", "boundTopicId": 5941, "title": "Kth Smallest Instructions", "titleSlug": "kth-smallest-instructions", "content": "
Bob is standing at cell (0, 0)
, and he wants to reach destination
: (row, column)
. He can only travel right and down. You are going to help Bob by providing instructions for him to reach destination
.
The instructions are represented as a string, where each character is either:
\n\n'H'
, meaning move horizontally (go right), or'V'
, meaning move vertically (go down).Multiple instructions will lead Bob to destination
. For example, if destination
is (2, 3)
, both "HHHVV"
and "HVHVH"
are valid instructions.
However, Bob is very picky. Bob has a lucky number k
, and he wants the kth
lexicographically smallest instructions that will lead him to destination
. k
is 1-indexed.
Given an integer array destination
and an integer k
, return the kth
lexicographically smallest instructions that will take Bob to destination
.
\n
Example 1:
\n\n\nInput: destination = [2,3], k = 1\nOutput: "HHHVV"\nExplanation: All the instructions that reach (2, 3) in lexicographic order are as follows:\n["HHHVV", "HHVHV", "HHVVH", "HVHHV", "HVHVH", "HVVHH", "VHHHV", "VHHVH", "VHVHH", "VVHHH"].\n\n\n
Example 2:
\n\n\nInput: destination = [2,3], k = 2\nOutput: "HHVHV"\n\n\n
Example 3:
\n\n\nInput: destination = [2,3], k = 3\nOutput: "HHVVH"\n\n\n
\n
Constraints:
\n\ndestination.length == 2
1 <= row, column <= 15
1 <= k <= nCr(row + column, row)
, where nCr(a, b)
denotes a
choose b
.Bob 站在单元格 (0, 0)
,想要前往目的地 destination
:(row, column)
。他只能向 右 或向 下 走。你可以为 Bob 提供导航 指令 来帮助他到达目的地 destination
。
指令 用字符串表示,其中每个字符:
\n\n'H'
,意味着水平向右移动'V'
,意味着竖直向下移动能够为 Bob 导航到目的地 destination
的指令可以有多种,例如,如果目的地 destination
是 (2, 3)
,\"HHHVV\"
和 \"HVHVH\"
都是有效 指令 。
然而,Bob 很挑剔。因为他的幸运数字是 k
,他想要遵循 按字典序排列后的第 k
条最小指令 的导航前往目的地 destination
。k
的编号 从 1 开始 。
给你一个整数数组 destination
和一个整数 k
,请你返回可以为 Bob 提供前往目的地 destination
导航的 按字典序排列后的第 k
条最小指令 。
\n\n
示例 1:
\n\n\n输入:destination = [2,3], k = 1\n输出:\"HHHVV\"\n解释:能前往 (2, 3) 的所有导航指令 按字典序排列后 如下所示:\n[\"HHHVV\", \"HHVHV\", \"HHVVH\", \"HVHHV\", \"HVHVH\", \"HVVHH\", \"VHHHV\", \"VHHVH\", \"VHVHH\", \"VVHHH\"].\n\n\n
示例 2:
\n\n\n输入:destination = [2,3], k = 2\n输出:\"HHVHV\"\n\n\n
示例 3:
\n\n\n输入:destination = [2,3], k = 3\n输出:\"HHVVH\"\n\n\n
\n\n
提示:
\n\ndestination.length == 2
1 <= row, column <= 15
1 <= k <= nCr(row + column, row)
,其中 nCr(a, b)
表示组合数,即从 a
个物品中选 b
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