# 885. Spiral Matrix III 螺旋矩阵 III

@TOC

## # 题目描述

On a 2 dimensional grid with R rows and C columns, we start at (r0, c0) facing east.

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.

Now, we walk in a clockwise spiral shape to visit every position in this grid.

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.)

Eventually, we reach all R * C spaces of the grid.

Return a list of coordinates representing the positions of the grid in the order they were visited.

Example 1:

``````Input: R = 1, C = 4, r0 = 0, c0 = 0
Output: [[0,0],[0,1],[0,2],[0,3]]
``````

Example 2:

``````Input: R = 5, C = 6, r0 = 1, c0 = 4
Output: [[1,4],[1,5],[2,5],[2,4],[2,3],[1,3],[0,3],[0,4],[0,5],[3,5],[3,4],[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],[0,1],[4,0],[3,0],[2,0],[1,0],[0,0]]
``````

Note:

1. 1 <= R <= 100
2. 1 <= C <= 100
3. 0 <= r0 < R
4. 0 <= c0 < C

## # 解题方法

``````class Solution(object):
def spiralMatrixIII(self, R, C, r0, c0):
"""
:type R: int
:type C: int
:type r0: int
:type c0: int
:rtype: List[List[int]]
"""
def nxt(r, c):
step = 1
yield (r, c)
while True:
for _ in range(step):
c += 1
yield (r, c)
for _ in range(step):
r += 1
yield (r, c)
step += 1
for _ in range(step):
c -= 1
yield (r, c)
for _ in range(step):
r -= 1
yield (r, c)
step += 1
ans = []
for r, c in nxt(r0, c0):
if 0 <= r < R and 0 <= c < C:
ans.append([r, c])
if len(ans) == R * C:
break
return ans
``````

C++代码如下：

``````class Solution {
public:
vector<vector<int>> spiralMatrixIII(int R, int C, int r0, int c0) {
vector<vector<int>> res;
int dx = 0, dy = 1;
int step = 1;
int count = 1;
res.push_back(vector<int>{r0, c0});
while (count < R * C) {
dx = 0, dy = 1;
for (int s = 0; s < step; s++) {
r0 += dx;
c0 += dy;
if (r0 >= 0 && r0 < R && c0 >= 0 && c0 < C) {
res.push_back(vector<int>{r0, c0});
count ++;
if (count >= R * C) return res;
}
}
dx = 1, dy = 0;
for (int s = 0; s < step; s++) {
r0 += dx;
c0 += dy;
if (r0 >= 0 && r0 < R && c0 >= 0 && c0 < C) {
res.push_back(vector<int>{r0, c0});
count ++;
if (count >= R * C) return res;
}
}
step ++;
dx = 0, dy = -1;
for (int s = 0; s < step; s++) {
r0 += dx;
c0 += dy;
if (r0 >= 0 && r0 < R && c0 >= 0 && c0 < C) {
res.push_back(vector<int>{r0, c0});
count ++;
if (count >= R * C) return res;
}
}
dx = -1, dy = 0;
for (int s = 0; s < step; s++) {
r0 += dx;
c0 += dy;
if (r0 >= 0 && r0 < R && c0 >= 0 && c0 < C) {
res.push_back(vector<int>{r0, c0});
count ++;
if (count >= R * C) return res;
}
}
step ++;
}
return res;
}
};
``````

https://leetcode.com/problems/spiral-matrix-iii/discuss/158995/python-infinite-generator-(yield)

## # 日期

2018 年 9 月 4 日 —— 迎接明媚的阳光！ 2018 年 12 月 4 日 —— 周二啦！