[leetcode-667-Beautiful Arrangement II]

Posted 2020-10-05 hellowOOOrld

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.

思路：

The requirement of k distinct distance can be achieved from 1, 2, ..., k+1 (<= n), by the following strategy:

1, k+1, 2, k, 3, k-1 ...;
The distance of this sequence is k, k-1, k-2, ..., 2, 1

Then append the remaining numbers to the list.

vector<int> constructArray(int n, int k) {
        int l = 1, r = k+1;
        vector<int> ans;
        while (l <= r) {
            ans.push_back(l++);
            if (l <= r) ans.push_back(r--);
        }
        for (int i = k+2; i <= n; i++)
            ans.push_back(i);
        return ans;
    }

参考：

https://discuss.leetcode.com/topic/101135/c-concise-code-o-n