3245 - Alternating Groups III.

Hard

There are some red and blue tiles arranged circularly. You are given an array of integers colors and a 2D integers array queries.

The color of tile i is represented by colors[i]:

• colors[i] == 0 means that tile i is red.

• colors[i] == 1 means that tile i is blue.

An alternating group is a contiguous subset of tiles in the circle with alternating colors (each tile in the group except the first and last one has a different color from its adjacent tiles in the group).

You have to process queries of two types:

• <code>queriesi = 1, size_i</code>, determine the count of alternating groups with size <code>size_i</code>.

• <code>queriesi = 2, index_i, color_i</code>, change <code>colorsindex_i</code> to <code>color_i</code>.

Return an array answer containing the results of the queries of the first type in order.

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

Example 1:

Input: colors = 0,1,1,0,1, queries = \[\[2,1,0],1,4]

Output: 2

Explanation:

First query:

Change colors[1] to 0.

Second query:

Count of the alternating groups with size 4:

Example 2:

Input: colors = 0,0,1,0,1,1, queries = \[\[1,3],2,3,0,1,5]

Output: 2,0

Explanation:

First query:

Count of the alternating groups with size 3:

Second query: colors will not change.

Third query: There is no alternating group with size 5.

Constraints:

• <code>4 <= colors.length <= 5 * 10⁴</code>

• 0 <= colors[i] <= 1

• <code>1 <= queries.length <= 5 * 10⁴</code>

• queries[i][0] == 1 or queries[i][0] == 2

• For all i that: