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| 1 | +# 2790. Maximum Number of Groups With Increasing Length |
| 2 | + |
| 3 | +- Difficulty: Hard. |
| 4 | +- Related Topics: Array, Math, Binary Search, Greedy, Sorting. |
| 5 | +- Similar Questions: Group the People Given the Group Size They Belong To. |
| 6 | + |
| 7 | +## Problem |
| 8 | + |
| 9 | +You are given a **0-indexed** array `usageLimits` of length `n`. |
| 10 | + |
| 11 | +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: |
| 12 | + |
| 13 | + |
| 14 | + |
| 15 | +- Each group must consist of **distinct **numbers, meaning that no duplicate numbers are allowed within a single group. |
| 16 | + |
| 17 | +- Each group (except the first one) must have a length **strictly greater** than the previous group. |
| 18 | + |
| 19 | + |
| 20 | +Return **an integer denoting the **maximum** number of groups you can create while satisfying these conditions.** |
| 21 | + |
| 22 | + |
| 23 | +Example 1: |
| 24 | + |
| 25 | +``` |
| 26 | +Input: usageLimits = [1,2,5] |
| 27 | +Output: 3 |
| 28 | +Explanation: In this example, we can use 0 at most once, 1 at most twice, and 2 at most five times. |
| 29 | +One way of creating the maximum number of groups while satisfying the conditions is: |
| 30 | +Group 1 contains the number [2]. |
| 31 | +Group 2 contains the numbers [1,2]. |
| 32 | +Group 3 contains the numbers [0,1,2]. |
| 33 | +It can be shown that the maximum number of groups is 3. |
| 34 | +So, the output is 3. |
| 35 | +``` |
| 36 | + |
| 37 | +Example 2: |
| 38 | + |
| 39 | +``` |
| 40 | +Input: usageLimits = [2,1,2] |
| 41 | +Output: 2 |
| 42 | +Explanation: In this example, we can use 0 at most twice, 1 at most once, and 2 at most twice. |
| 43 | +One way of creating the maximum number of groups while satisfying the conditions is: |
| 44 | +Group 1 contains the number [0]. |
| 45 | +Group 2 contains the numbers [1,2]. |
| 46 | +It can be shown that the maximum number of groups is 2. |
| 47 | +So, the output is 2. |
| 48 | +``` |
| 49 | + |
| 50 | +Example 3: |
| 51 | + |
| 52 | +``` |
| 53 | +Input: usageLimits = [1,1] |
| 54 | +Output: 1 |
| 55 | +Explanation: In this example, we can use both 0 and 1 at most once. |
| 56 | +One way of creating the maximum number of groups while satisfying the conditions is: |
| 57 | +Group 1 contains the number [0]. |
| 58 | +It can be shown that the maximum number of groups is 1. |
| 59 | +So, the output is 1. |
| 60 | +``` |
| 61 | + |
| 62 | + |
| 63 | +**Constraints:** |
| 64 | + |
| 65 | + |
| 66 | + |
| 67 | +- `1 <= usageLimits.length <= 105` |
| 68 | + |
| 69 | +- `1 <= usageLimits[i] <= 109` |
| 70 | + |
| 71 | + |
| 72 | + |
| 73 | +## Solution |
| 74 | + |
| 75 | +```javascript |
| 76 | +/** |
| 77 | + * @param {number[]} usageLimits |
| 78 | + * @return {number} |
| 79 | + */ |
| 80 | +var maxIncreasingGroups = function(usageLimits) { |
| 81 | + var count = 0; |
| 82 | + var num = 0; |
| 83 | + var minCount = 1; |
| 84 | + usageLimits.sort((a, b) => a - b); |
| 85 | + for (var i = 0; i < usageLimits.length; i++) { |
| 86 | + count += usageLimits[i]; |
| 87 | + if (count >= minCount) { |
| 88 | + num++; |
| 89 | + minCount += num + 1; |
| 90 | + } |
| 91 | + } |
| 92 | + return num; |
| 93 | +}; |
| 94 | +``` |
| 95 | + |
| 96 | +**Explain:** |
| 97 | + |
| 98 | +Math. |
| 99 | + |
| 100 | +**Complexity:** |
| 101 | + |
| 102 | +* Time complexity : O(n). |
| 103 | +* Space complexity : O(1). |
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