360. Sort Transformed Array

摘要：题目解答还是数学解法，根据这个方程图形的特征来判断最大最小值的取向

题目：
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]

解答：

//还是数学解法，根据这个方程图形的特征来判断最大最小值的取向
    public int function(int num, int a, int b, int c) {
        return a * num * num + b * num + c; 
    }
    
    public int[] sortTransformedArray(int[] nums, int a, int b, int c) {
        int len = nums.length;
        int[] result = new int[len];
        int index = a >= 0 ? len - 1 : 0;
        int i = 0, j = len - 1;
        while (i <= j) {
            if (a >= 0) {
                result[index--] = function(nums[i], a, b, c) >= function(nums[j], a, b, c) ? function(nums[i++], a, b, c) : function(nums[j--], a, b, c);
            } else {
                result[index++] = function(nums[i], a, b, c) <= function(nums[j], a, b, c) ? function(nums[i++], a, b, c) : function(nums[j--], a, b, c);
            }
        }
        return result;
    }