利用了抛物线的性质，中间最小/最大，然后向/从两端逼近。

class Solution:
    def sortTransformedArray(self, nums: List[int], a: int, b: int, c: int) -> List[int]:
        result = []
        if a == 0:
            # bx + c
            if b >= 0:
                for num in nums:
                    result.append(self.calc(num, a, b, c))
            else:
                for num in nums[::-1]:
                    result.append(self.calc(num, a, b, c))
            return result
                    
        middle = -b / 2 / a
        minVal = float('inf')
        idx = -1
        for i in range(len(nums)):
            if  abs(nums[i] - middle) < minVal:
                minVal = abs(nums[i] - middle)
                idx = i
                
        if a > 0:
            result.append(self.calc(nums[idx], a, b, c))
            left = idx - 1
            right = idx + 1
            while left >= 0 or right < len(nums):
                if left >= 0 and right < len(nums):
                    leftResult = self.calc(nums[left], a, b, c)
                    rightResult = self.calc(nums[right], a, b, c)
                    if leftResult < rightResult:
                        left -= 1
                        result.append(leftResult)
                    else:
                        right += 1
                        result.append(rightResult)
                elif left >= 0:
                    leftResult = self.calc(nums[left], a, b, c)
                    result.append(leftResult)
                    left -= 1
                elif right < len(nums):
                    rightResult = self.calc(nums[right], a, b, c)
                    result.append(rightResult)
                    right += 1
        else: # a < 0
            left = 0
            right = len(nums) - 1
            while left < right:
                if left < idx and right > idx:
                    leftResult = self.calc(nums[left], a, b, c)
                    rightResult = self.calc(nums[right], a, b, c)
                    if leftResult < rightResult:
                        left += 1
                        result.append(leftResult)
                    else:
                        right -= 1
                        result.append(rightResult)
                elif left < idx:
                    leftResult = self.calc(nums[left], a, b, c)
                    result.append(leftResult)
                    left += 1
                elif right > idx:
                    rightResult = self.calc(nums[right], a, b, c)
                    result.append(rightResult)
                    right -= 1
            result.append(self.calc(nums[idx], a, b, c))
        return result
            
    def calc(self, x, a, b, c):
        return a * (x ** 2) + b * x + c