题目：原题链接（困难）
标签：几何、数学
| 解法 | 时间复杂度 | 空间复杂度 | 执行用时 |
|---|---|---|---|
| Ans 1 (Python) | O ( 1 ) O(1) O(1) | O ( 1 ) O(1) O(1) | 44ms (38.46%) |
| Ans 2 (Python) | |||
| Ans 3 (Python) |
解法一：
class Solution:
def intersection(self, start1: List[int], end1: List[int], start2: List[int], end2: List[int]) -> List[float]:
k1 = (end1[1] - start1[1]) / (end1[0] - start1[0]) if end1[0] != start1[0] else float("inf")
k2 = (end2[1] - start2[1]) / (end2[0] - start2[0]) if end2[0] != start2[0] else float("inf")
# 处理两条线段均垂直于X轴的情况
if k1 == k2 == float("inf"):
if (start1[0] != start2[0]
or min(start1[1], end1[1]) > max(start2[1], end2[1])
or max(start1[1], end1[1]) < min(start2[1], end2[1])):
return []
return [start1[0], max(start1[1], start2[1])]
b1 = start1[1] - k1 * start1[0] if k1 != float("inf") else start1[0]
b2 = start2[1] - k2 * start2[0] if k2 != float("inf") else start2[0]
# 处理两条线段为平行线的情况
if k1 == k2:
if (b1 != b2
or min(start1[1], end1[1]) > max(start2[1], end2[1])
or max(start1[1], end1[1]) < min(start2[1], end2[1])):
return []
return [max(start1[0], start2[0]), max(start1[1], start2[1])]
# 处理有一条线段平行与X轴的情况
if k1 == float("inf"):
k1, k2, b1, b2 = k2, k1, b2, b1
if k2 == float("inf"):
x = b2
y = k1 * x + b1
if (min(start1[1], end1[1]) <= y <= max(start1[1], end1[1])
and min(start2[1], end2[1]) <= y <= max(start2[1], end2[1])):
return [x, y]
else:
return []
# 计算两条线段的交点
x = (b1 - b2) / (k2 - k1)
y = k1 * x + b1
if (not min(start1[0], end1[0]) <= x <= max(start1[0], end1[0])
or not min(start1[1], end1[1]) <= y <= max(start1[1], end1[1])
or not min(start2[0], end2[0]) <= x <= max(start2[0], end2[0])
or not min(start2[1], end2[1]) <= y <= max(start2[1], end2[1])):
return []
return [x, y]
