## Tuesday, August 29, 2017

### LeetCode 667 - Beautiful Arrangement II

https://leetcode.com/problems/beautiful-arrangement-ii
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:
1. The `n` and `k` are in the range 1 <= k < n <= 104.

https://discuss.leetcode.com/topic/101113/c-java-clean-code-4-liner
if you have `n` number, the maximum `k` can be `n - 1`;
if `n` is 9, max `k` is 8.
This can be done by picking numbers interleavingly from head and tail,
``````// start from i = 1, j = n;
// i++, j--, i++, j--, i++, j--

1   2   3   4   5
9   8   7   6
out: 1 9 2 8 3 7 6 4 5
dif:  8 7 6 5 4 3 2 1
``````
This is a case where `k` is exactly `n - 1`
When k is less than that, simply lay out the rest `(i, j)` in incremental
order(all diff is 1). Say if k is 5:
``````i++, j--, i++, j--, i++, i++, i++ ...
1   9   2   8    3 4 5 6 7
8   7   6   5    1 1 1 1 ``````
``````    public int[] constructArray(int n, int k) {
int[] res = new int[n];
for (int i = 0, l = 1, r = n; l <= r; i++)
res[i] = k > 1 ? (k-- % 2 != 0 ? l++ : r--) : (k % 2 != 0? l++ : r--);
return res;
}``````