3161 - Block Placement Queries.

Hard

There exists an infinite number line, with its origin at 0 and extending towards the positive x-axis.

You are given a 2D array queries, which contains two types of queries:

• For a query of type 1, queries[i] = [1, x]. Build an obstacle at distance x from the origin. It is guaranteed that there is no obstacle at distance x when the query is asked.

• For a query of type 2, queries[i] = [2, x, sz]. Check if it is possible to place a block of size sz anywhere in the range [0, x] on the line, such that the block entirely lies in the range [0, x]. A block cannot be placed if it intersects with any obstacle, but it may touch it. Note that you do not actually place the block. Queries are separate.

Return a boolean array results, where results[i] is true if you can place the block specified in the <code>i^th</code> query of type 2, and false otherwise.

Example 1:

Input: queries = \[\[1,2],2,3,3,2,3,1,2,2,2]

Output: false,true,true

Explanation:

For query 0, place an obstacle at x = 2. A block of size at most 2 can be placed before x = 3.

Example 2:

Input: queries = \[\[1,7],2,7,6,1,2,2,7,5,2,7,6]

Output: true,true,false

Explanation:

• Place an obstacle at x = 7 for query 0. A block of size at most 7 can be placed before x = 7.

• Place an obstacle at x = 2 for query 2. Now, a block of size at most 5 can be placed before x = 7, and a block of size at most 2 before x = 2.

Constraints:

• <code>1 <= queries.length <= 15 * 10⁴</code>

• 2 <= queries[i].length <= 3

• 1 <= queries[i][0] <= 2

• <code>1 <= x, sz <= min(5 * 10⁴, 3 * queries.length)</code>

• The input is generated such that for queries of type 1, no obstacle exists at distance x when the query is asked.

• The input is generated such that there is at least one query of type 2.