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Alternating Groups II

There is a circle of red and blue tiles.

There is a circle of red and blue tiles. You are given an array of integers colors and an integer k. The color of tile i is represented by colors[i]:

An alternating group is every k contiguous tiles in the circle with alternating colors (each tile in the group except the first and last one has a different color from its left and right tiles).

Return the number of alternating groups.

Note that since colors represents a circle, the first and the last tiles are considered to be next to each other.

Alternating Groups II diagram

Example 1

Input: colors = [0,1,0,1,0], k = 3

Output: 3

Explanation: Alternating groups:

Example 2

Input: colors = [0,1,0,0,1,0,1], k = 6

Output: 2

Explanation: Alternating groups:

Example 3

Input: colors = [1,1,0,1], k = 4

Output: 0

Constraints

  • 3 <= colors.length <= 10^5
  • 0 <= colors[i] <= 1
  • 3 <= k <= colors.length

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