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55 lines
2.5 KiB
Markdown
Executable File
55 lines
2.5 KiB
Markdown
Executable File
# [885. Spiral Matrix III](https://leetcode.com/problems/spiral-matrix-iii/)
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## 题目
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On a 2 dimensional grid with `R` rows and `C` columns, we start at `(r0, c0)` facing east.
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Here, the north-west corner of the grid is at the first row and column, and the south-east corner of the grid is at the last row and column.
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Now, we walk in a clockwise spiral shape to visit every position in this grid.
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Whenever we would move outside the boundary of the grid, we continue our walk outside the grid (but may return to the grid boundary later.)
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Eventually, we reach all `R * C` spaces of the grid.
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Return a list of coordinates representing the positions of the grid in the order they were visited.
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**Example 1:**
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Input: R = 1, C = 4, r0 = 0, c0 = 0
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Output: [[0,0],[0,1],[0,2],[0,3]]
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**Example 2:**
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Input: R = 5, C = 6, r0 = 1, c0 = 4
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Output: [[1,4],[1,5],[2,5],[2,4],[2,3],[1,3],[0,3],[0,4],[0,5],[3,5],[3,4],
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[3,3],[3,2],[2,2],[1,2],[0,2],[4,5],[4,4],[4,3],[4,2],[4,1],[3,1],[2,1],[1,1],
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[0,1],[4,0],[3,0],[2,0],[1,0],[0,0]]
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**Note:**
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1. `1 <= R <= 100`
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2. `1 <= C <= 100`
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3. `0 <= r0 < R`
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4. `0 <= c0 < C`
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## 题目大意
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在 R 行 C 列的矩阵上，我们从 (r0, c0) 面朝东面开始。这里，网格的西北角位于第一行第一列，网格的东南角位于最后一行最后一列。现在，我们以顺时针按螺旋状行走，访问此网格中的每个位置。每当我们移动到网格的边界之外时，我们会继续在网格之外行走（但稍后可能会返回到网格边界）。最终，我们到过网格的所有 R * C 个空间。
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要求输出按照访问顺序返回表示网格位置的坐标列表。
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## 解题思路
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- 给出一个二维数组的行 `R`，列 `C`，以及这个数组中的起始点 `(r0,c0)`。从这个起始点开始出发，螺旋的访问数组中各个点，输出途径经过的每个坐标。注意每个螺旋的步长在变长，第一个螺旋是 1 步，第二个螺旋是 1 步，第三个螺旋是 2 步，第四个螺旋是 2 步……即 1，1，2，2，3，3，4，4，5……这样的步长。
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- 这一题是第 59 题的加强版。除了有螺旋以外，还加入了步长的限制。步长其实是有规律的，第 0 次移动的步长是 `0/2+1`，第 1 次移动的步长是 `1/2+1`，第 n 次移动的步长是 `n/2+1`。其他的做法和第 59 题一致。
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