2790 - Maximum Number of Groups With Increasing Length\.

Hard

You are given a 0-indexed array usageLimits of length n.

Your task is to create groups using numbers from 0 to n - 1, ensuring that each number, i, is used no more than usageLimits[i] times in total across all groups. You must also satisfy the following conditions:

• Each group must consist of distinct numbers, meaning that no duplicate numbers are allowed within a single group.

• Each group (except the first one) must have a length strictly greater than the previous group.

Return an integer denoting the maximum number of groups you can create while satisfying these conditions.

Example 1:

Input: usageLimits = 1,2,5

Output: 3

Explanation:

In this example, we can use 0 at most once, 1 at most twice, and 2 at most five times.

One way of creating the maximum number of groups while satisfying the conditions is:

Group 1 contains the number 2.

Group 2 contains the numbers 1,2.

Group 3 contains the numbers 0,1,2.

It can be shown that the maximum number of groups is 3.

So, the output is 3.

Example 2:

Input: usageLimits = 2,1,2

Output: 2

Explanation:

In this example, we can use 0 at most twice, 1 at most once, and 2 at most twice.

One way of creating the maximum number of groups while satisfying the conditions is:

Group 1 contains the number 0.

Group 2 contains the numbers 1,2.

It can be shown that the maximum number of groups is 2.

So, the output is 2.

Example 3:

Input: usageLimits = 1,1

Output: 1

Explanation:

In this example, we can use both 0 and 1 at most once.

One way of creating the maximum number of groups while satisfying the conditions is:

Group 1 contains the number 0.

It can be shown that the maximum number of groups is 1.

So, the output is 1.

Constraints:

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

• <code>1 <= usageLimitsi<= 10⁹</code>