Given two integers n and k, you need to construct a list which contains n different positive integers ranging from 1 to n and obeys the following requirement: Suppose this list is [a1, a2, a3, … , an], then the list [|a1 - a2|, |a2 - a3|, |a3 - a4|, … , |an-1 - an|] has exactly k distinct integers.

If there are multiple answers, print any of them.

Example 1:

Input: n = 3, k = 1
Output: [1, 2, 3]
Explanation: The [1, 2, 3] has three different positive integers ranging from 1 to 3, and the [1, 1] has exactly 1 distinct integer: 1.

Example 2:

Input: n = 3, k = 2
Output: [1, 3, 2]
Explanation: The [1, 3, 2] has three different positive integers ranging from 1 to 3, and the [2, 1] has exactly 2 distinct integers: 1 and 2.

Note:

The n and k are in the range 1 <= k < n <= 10^4.

Solution

Time complexity : O(n)
Space complexity : O(n)

class Solution {
public:
    vector<int> constructArray(int n, int k) {
        vector<int> ans;
        int i = 1, j = n;
        while (i<=j) {
            if (1 < k)
                ans.push_back((k--)%2 ? i++ : j--);
            else
                ans.push_back(i++);
        }
        return ans;
    }
};

k = 1 : 1, 2, 3, 4, 5
k = 2 : 5, 1, 2, 3, 4
k = 3 : 1, 5, 2, 3, 4
k = 4 : 1, 5, 2, 4, 3

若 k 只剩 1，直接照順序放。
若 k 大於 1，且為偶，先放最大數。
若 k 大於 1，且為奇，先放最小數。