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# 0360. Sort Transformed Array

<https://leetcode.com/problems/sort-transformed-array>

## Description

Given a **sorted** integer array `nums` and three integers `a`, `b` and `c`, apply a quadratic function of the form `f(x) = ax2 + bx + c` to each element `nums[i]` in the array, and return *the array in a sorted order*.

**Example 1:**

```
**Input:** nums = [-4,-2,2,4], a = 1, b = 3, c = 5
**Output:** [3,9,15,33]
```

**Example 2:**

```
**Input:** nums = [-4,-2,2,4], a = -1, b = 3, c = 5
**Output:** [-23,-5,1,7]
```

**Constraints:**

* `1 <= nums.length <= 200`
* `-100 <= nums[i], a, b, c <= 100`
* `nums` is sorted in **ascending** order.

**Follow up:** Could you solve it in `O(n)` time?

## ac

```java
class Solution {
    public int[] sortTransformedArray(int[] nums, int a, int b, int c) {
        // edge cases
        if (nums == null || nums.length == 0) return new int[0];

        int[] res = new int[nums.length];

        // 2 pointers
        int l = 0, r = res.length - 1;
        if (a < 0) {
            int i = l;
            while (l <= r) {
                int left = a * nums[l] * nums[l] + b * nums[l] + c;
                int right = a * nums[r] * nums[r] + b * nums[r] + c;
                if (left < right) {
                    res[i++] = left;
                    l++;
                } else {
                    res[i++] = right;
                    r--;
                }
            }
        } else {
            int i = r;
            while (l <= r) {
                int left = a * nums[l] * nums[l] + b * nums[l] + c;
                int right = a * nums[r] * nums[r] + b * nums[r] + c;
                if (left > right) {
                    res[i--] = left;
                    l++;
                } else {
                    res[i--] = right;
                    r--;
                }
            }
        }

        return res;
    }
}
/*
upward, downward


*/
```