Sort Transformed Array

Given a sorted array of integers nums and integer values a, b and c. Apply a function of the form f(x) = ax2 + bx + c to each element x in the array.

The returned array must be in sorted order.

Expected time complexity: O(n)

Example:

nums = [-4, -2, 2, 4], a = 1, b = 3, c = 5,

Result: [3, 9, 15, 33]

nums = [-4, -2, 2, 4], a = -1, b = 3, c = 5

Result: [-23, -5, 1, 7]

分析：
抛物线的中轴线可以通过-b/2a来计算，这题可以转换成按照各个点到中轴线的距离依次排列。所以，我们先找到距离中轴线最近的点 p ，然后，设置两个pointer，从p开始，一个向左走，一个向右走。看两个Pointer对应的值哪个离中轴线更近，然后取近的一个，同时移动对应的pointer.

后来发现有更好的方法，也是使用两个pointer，一个指向最左边，一个指向最右边。然后谁离中轴线越远，就选谁。
 https://discuss.leetcode.com/topic/48424/java-o-n-incredibly-short-yet-easy-to-understand-ac-solution

1 public class Solution {
2     public int[] sortTransformedArray(int[] nums, int a, int b, int c) {
3         int n = nums.length;
4         int[] sorted = new int
;
5         int i = 0, j = n - 1;
6         int index = a >= 0 ? n - 1 : 0;
7         while (i <= j) {
8             if (a >= 0) {
9                 sorted[index--] = quad(nums[i], a, b, c) >= quad(nums[j], a, b, c) ? quad(nums[i++], a, b, c) : quad(nums[j--], a, b, c);
10             } else {
11                 sorted[index++] = quad(nums[i], a, b, c) >= quad(nums[j], a, b, c) ? quad(nums[j--], a, b, c) : quad(nums[i++], a, b, c);
12             }
13         }
14         return sorted;
15     }
16
17     private int quad(int x, int a, int b, int c) {
18         return a * x * x + b * x + c;
19     }
20 }