# Leetcode

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360. Sort Transformed Array

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?

Solution(Python3):

# two pointers

class Solution:

def sortTransformedArray(self, nums: List[int], a: int, b: int, c: int) -> List[int]:

nums = [x*x*a + x* b + c for x in nums] ret = [0] * len(nums)

p1, p2 = 0, len(nums) - 1

i, d = (p1, 1) if a < 0 else (p2, -1) # coefficients

while p1 <= p2: if nums[p1] * -d > nums[p2] * -d: # return a sorted

ret[i] = nums[p1]

p1 += 1 else:

ret[i] = nums[p2]

p2 -= 1

i += d

return ret

Complexity Analysis:

Time: O(n), because two pointers traverse the array once

Space: O(n)