在小于 O(n^2) 的范围内对给定的整数列表进行排名

Question

如何为给定整数列表中的元素分配等级？ 是否有时间复杂度小于 O(n^2) 的算法？

Input:  2 6 7 3 9
Output: 1 3 4 2 5

Answer 1

您可以通过排序在O(n * log n)轻松完成此操作：

int[] input = //...
int[] input = new int[]{2, 6, 7, 3, 9};
Integer[] indices = new Integer[input.length];
for (int i = 0; i < indices.length; i++) {
    indices[i] = i;
}

// find permutation of indices that would yield sorted input
Arrays.sort(indices, Comparator.comparingInt(i -> input[i]));

// invert permutation and add 1 to get rank 
int[] ranks = new int[indices.length];
for (int i = 0; i < indices.length; i++) {
    ranks[indices[i]] = i+1;
}