932. Beautiful Array

For some fixed N, an array A is beautiful if it is a permutation of the integers 1, 2, ..., N, such that:

For every i < j, there is no k with i < k < j such that A[k] * 2 = A[i] + A[j].

Given N, return any beautiful array A.  (It is guaranteed that one exists.)

 

Example 1:

Input: 4
Output: [2,1,4,3]

Example 2:

Input: 5
Output: [3,1,2,5,4]

 

Note:

• 1 <= N <= 1000

 

Approach #1: divide and conquer. [C++]

class Solution {
public:
    vector<int> beautifulArray(int N) {
        vector<int> ans;
        ans.push_back(1);
        while (ans.size() < N) {
            vector<int> temp;
            for (int i : ans) if (i * 2 - 1 <= N) temp.push_back(i*2-1);
            for (int i : ans) if (i * 2 <= N) temp.push_back(i*2);
            ans = temp;
        }
        return ans;
    }
};

　　

Approach #2: [Python]

class Solution(object):
    def beautifulArray(self, N):
        """
        :type N: int
        :rtype: List[int]
        """
        res = [1]
        while len(res) < N:
            res = [i * 2 - 1 for i in res] + [i * 2 for i in res]
        return [i for i in res if i <= N]

　　

Analysis:

https://leetcode.com/problems/beautiful-array/discuss/186679/C%2B%2BJavaPython-Odd-%2B-Even-Pattern-O(N)