1331. Rank Transform of an Array
Description
Given an array of integers arr
, replace each element with its rank.
The rank represents how large the element is. The rank has the following rules:
- Rank is an integer starting from 1.
- The larger the element, the larger the rank. If two elements are equal, their rank must be the same.
- Rank should be as small as possible.
Example 1:
Input: arr = [40,10,20,30] Output: [4,1,2,3] Explanation: 40 is the largest element. 10 is the smallest. 20 is the second smallest. 30 is the third smallest.
Example 2:
Input: arr = [100,100,100] Output: [1,1,1] Explanation: Same elements share the same rank.
Example 3:
Input: arr = [37,12,28,9,100,56,80,5,12] Output: [5,3,4,2,8,6,7,1,3]
Constraints:
0 <= arr.length <= 105
-109 <= arr[i] <= 109
Solutions
Solution 1: Discretization
First, we copy an array $t$, then sort and deduplicate it to obtain an array of length $m$ that is strictly monotonically increasing.
Next, we traverse the original array $arr$. For each element $x$ in the array, we use binary search to find the position of $x$ in $t$. The position plus one is the rank of $x$.
The time complexity is $O(n \times \log n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the array $arr$.
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