3624 - Number of Integers With Popcount-Depth Equal to K II.

Hard

You are given an integer array nums.

For any positive integer x, define the following sequence:

• <code>p₀ = x</code>

• <code>p_i+1 = popcount(p_i)</code> for all i >= 0, where popcount(y) is the number of set bits (1's) in the binary representation of y.

This sequence will eventually reach the value 1.

The popcount-depth of x is defined as the smallest integer d >= 0 such that <code>p_d = 1</code>.

For example, if x = 7 (binary representation "111"). Then, the sequence is: 7 → 3 → 2 → 1, so the popcount-depth of 7 is 3.

You are also given a 2D integer array queries, where each queries[i] is either:

• [1, l, r, k] - Determine the number of indices j such that l <= j <= r and the popcount-depth of nums[j] is equal to k.

• [2, idx, val] - Update nums[idx] to val.

Return an integer array answer, where answer[i] is the number of indices for the <code>i^th</code> query of type [1, l, r, k].

Example 1:

Input: nums = 2,4, queries = [1,0,1,1,2,1,1,1,0,1,0]

Output: 2,1

Explanation:

Thus, the final answer is [2, 1].

Example 2:

Input: nums = 3,5,6, queries = [1,0,2,2,2,1,4,1,1,2,1,1,0,1,0]

Output: 3,1,0

Explanation:

Thus, the final answer is [3, 1, 0].

Example 3:

Input: nums = 1,2, queries = [1,0,1,1,2,0,3,1,0,0,1,1,0,0,2]

Output: 1,0,1

Explanation:

Thus, the final answer is [1, 0, 1].

Constraints:

• <code>1 <= n == nums.length <= 10⁵</code>

• <code>1 <= numsi<= 10¹⁵</code>

• <code>1 <= queries.length <= 10⁵</code>

• queries[i].length == 3 or 4