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)