2592. Maximize Greatness of an Array
Description
You are given a 0-indexed integer array nums
. You are allowed to permute nums
into a new array perm
of your choosing.
We define the greatness of nums
be the number of indices 0 <= i < nums.length
for which perm[i] > nums[i]
.
Return the maximum possible greatness you can achieve after permuting nums
.
Example 1:
Input: nums = [1,3,5,2,1,3,1] Output: 4 Explanation: One of the optimal rearrangements is perm = [2,5,1,3,3,1,1]. At indices = 0, 1, 3, and 4, perm[i] > nums[i]. Hence, we return 4.
Example 2:
Input: nums = [1,2,3,4] Output: 3 Explanation: We can prove the optimal perm is [2,3,4,1]. At indices = 0, 1, and 2, perm[i] > nums[i]. Hence, we return 3.
Constraints:
1 <= nums.length <= 105
0 <= nums[i] <= 109
Solutions
Solution 1: Greedy
We can sort the array $nums$ first.
Then we define a pointer $i$ pointing to the first element of the array $nums$. We traverse the array $nums$, and for each element $x$ we encounter, if $x$ is greater than $nums[i]$, then we move the pointer $i$ to the right.
Finally, we return the value of the pointer $i$.
The time complexity is $O(n \times \log n)$, and the space complexity is $O(\log n)$, where $n$ is the length of the array $nums$.
1 2 3 4 5 6 7 |
|
1 2 3 4 5 6 7 8 9 10 11 12 |
|
1 2 3 4 5 6 7 8 9 10 11 |
|
1 2 3 4 5 6 7 8 9 10 |
|
1 2 3 4 5 6 7 8 9 10 |
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