Maximum Number of Groups With Increasing Length

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Problem Statement

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.

Examples

Example 1

Input: usageLimits = [1,2,5]
Output: 3
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
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
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

1 <= usageLimits.length <= 10 ^5

1 <= usageLimits[i] <= 10 ^9

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicMath