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You have n
gardens, labeled from 1
to n
, and an array paths
where paths[i] = [xi, yi]
describes a bidirectional path between garden xi
to garden yi
. In each garden, you want to plant one of 4 types of flowers.
All gardens have at most 3 paths coming into or leaving it.
Your task is to choose a flower type for each garden such that, for any two gardens connected by a path, they have different types of flowers.
Return any such a choice as an array answer
, where answer[i]
is the type of flower planted in the (i+1)th
garden. The flower types are denoted 1
, 2
, 3
, or 4
. It is guaranteed an answer exists.
Example 1:
Input: n = 3, paths = [[1,2],[2,3],[3,1]]
Output: [1,2,3]
Explanation:
Gardens 1 and 2 have different types.
Gardens 2 and 3 have different types.
Gardens 3 and 1 have different types.
Hence, [1,2,3] is a valid answer. Other valid answers include [1,2,4], [1,4,2], and [3,2,1].
Example 2:
Input: n = 4, paths = [[1,2],[3,4]]
Output: [1,2,1,2]
Example 3:
Input: n = 4, paths = [[1,2],[2,3],[3,4],[4,1],[1,3],[2,4]]
Output: [1,2,3,4]
Constraints:
1 <= n <= 104
0 <= paths.length <= 2 * 104
paths[i].length == 2
1 <= xi, yi <= n
xi != yi
- Every garden has at most 3 paths coming into or leaving it.
[Graph]
Hints
Hint 1
Since each garden is connected to at most 3 gardens, there's always an available color for each garden. For example, if one garden is next to gardens with colors 1, 3, 4, then color #2 is available.