calculate sorted y of function y = ax^2 + bx + c given sorted x array

本文介绍了一种算法，该算法接收一个一元二次方程和一个已排序的数组，将数组中的每个元素代入方程计算结果，并返回一个按升序排列的计算结果列表。算法首先判断方程开口方向，再根据不同情况分段计算，最后合并两个部分的计算结果。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

给定一个一元二次方程式y = ax^2 + bx + c, 一个sorted array X, 将X中所有元素代入方程中，返回sorted的Y

solution: 看a< or > 0,，搞出两边的y们，然后merge

public class Ax2 {
    public static void main(String[] args) {
    }

    // x is sorted array
    private static ArrayList<Integer> sorted(int a, int b, int c, int[] x) {
        ArrayList<Integer> result = new ArrayList<Integer>();
        if (a == 0) {
            return result;
        }
        // the tredence is decresing first then increasing 
        if (a > 0) {
            ArrayList<Integer> list1 = new ArrayList<Integer>();
            list1.add(getFun(a, b, c, x[0]));
            int i;
            for (i = 1; i < x.length; i++) {
                int y = getFun(a, b, c, x[i]);
                if (y > list1.get(i - 1)) {
                    break;
                }
                list1.add(y);
            }
            //now the i is the index of first element is larger than previous 
            ArrayList<Integer> list2 = new ArrayList<Integer>();
            for (; i < x.length; i++) {
                int y = getFun(a, b, c, x[i]);
                list2.add(y);
            }
            //merge two arraylist
            result = mergeList(list1, list2);
        } else { //increasing first then decreasing
            ArrayList<Integer> list1 = new ArrayList<Integer>();
            list1.add(getFun(a, b, c, x[0]));
            int i;
            for (i = 1; i < x.length; i++) {
                int y = getFun(a, b, c, x[i]);
                if (y < list1.get(i - 1)) {
                    break;
                }
                list1.add(y);
            }
            //now the i is the index of first element is larger than previous 
            ArrayList<Integer> list2 = new ArrayList<Integer>();
            for (; i < x.length; i++) {
                int y = getFun(a, b, c, x[i]);
                list2.add(y);
            }
            //merge two arraylist
            result = mergeList(list1, list2);
        }
        return result;
    }

    private static int getFun(int a, int b, int c, int num) {
        return (int) (a * Math.pow(num, 2) + b * num + c);
    }

    private static ArrayList<Integer> mergeList(ArrayList<Integer> list1, ArrayList<Integer> list2) {
        ArrayList<Integer> result = new ArrayList<Integer>();
        if (list1 == null && list2 != null) {
            return list2;
        } else if (list1 != null && list2 == null) {
            return list1;
        }
        int i = 0;
        int j = 0;
        while (i < list1.size() && j < list2.size()) {
            if (list1.get(i) < list2.get(j)) {
                result.add(list1.get(i));
                i++;
            } else {
                result.add(list2.get(j));
                j++;
            }
        }
        if (i != list1.size()) {
            for (; i < list1.size(); i++) {
                result.add(list1.get(i));
            }
        }
        if (j != list2.size()) {
            for (; j < list2.size(); j++) {
                result.add(list2.get(j));
            }
        }
        return result;
    }