Algorithms
Hard
2790
2919
Maximum Number of Groups With Increasing Length
maximum-number-of-groups-with-increasing-length
"""
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:

 * 1 <= usageLimits.length <= 105
 * 1 <= usageLimits[i] <= 109
"""
class Solution:
    def maxIncreasingGroups(self, usageLimits: List[int]) -> int:
        
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:

 * 1 <= usageLimits.length <= 105
 * 1 <= usageLimits[i] <= 109


Please complete the code below to solve above prblem:
```python
class Solution:
    def maxIncreasingGroups(self, usageLimits: List[int]) -> int:
        
```

my_solution = Solution()

test_input = { "usageLimits": [1,2,5] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [2,1,2] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [1,1] }
assert my_solution.maxIncreasingGroups(**test_input) == 1

test_input = { "usageLimits": [1,4] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [1,5] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [1,7] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [1,8] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [2,1] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [2,2] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [2,3] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [2,4] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [2,5] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [2,7] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [2,8] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [2,9] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [3,1] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [3,4] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [3,7] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [3,10] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [4,1] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [4,2] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [4,4] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [4,5] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [4,7] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [4,10] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [5,8] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [5,10] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [6,2] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [6,3] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [6,4] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [6,5] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [6,6] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [6,7] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [6,9] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [6,19] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [7,1] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [7,2] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [7,3] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [7,4] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [7,7] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [7,13] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [8,3] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [8,6] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [9,1] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [9,3] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [9,4] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [9,6] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [9,8] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [9,10] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [10,2] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [10,3] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [10,8] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [10,11] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [13,11] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [13,13] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [16,9] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [18,6] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [32,42] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [1,1,5] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [1,1,10] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [1,4,3] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [1,4,5] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [1,6,4] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [1,6,8] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [1,7,19] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [1,8,6] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [1,9,5] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [1,9,6] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [1,10,6] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [2,2,2] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [2,3,8] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [2,6,10] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [2,7,2] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [2,7,7] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [2,8,7] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [2,9,9] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [3,1,1] }
assert my_solution.maxIncreasingGroups(**test_input) == 2

test_input = { "usageLimits": [3,5,5] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [3,5,8] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [3,6,5] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [3,7,4] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [3,7,10] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [3,8,1] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [3,9,9] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [3,10,9] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [4,2,5] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [4,2,15] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [4,5,5] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [4,7,9] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [4,8,2] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [4,8,4] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [4,10,3] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [4,10,4] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [5,1,5] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [5,2,9] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [5,2,10] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [5,6,1] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [5,6,5] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [5,7,4] }
assert my_solution.maxIncreasingGroups(**test_input) == 3

test_input = { "usageLimits": [5,10,3] }
assert my_solution.maxIncreasingGroups(**test_input) == 3