[HiHoCoder]三分·三分求极值[hiho一下 第四十周]

时间限制:10000ms

单点时限:1000ms

内存限制:256MB

描述

在直角坐标系中有一条抛物线y=ax^2+bx+c和一个点P(x,y)，求点P到抛物线的最短距离d。

提示：三分法

输入

第1行：5个整数a,b,c,x,y。前三个数构成抛物线的参数，后两个数x,y表示P点坐标。-200≤a,b,c,x,y≤200

输出

第1行：1个实数d，保留3位小数(四舍五入)

样例输入

2 8 2 -2 6

样例输出

2.437

import java.math.BigDecimal;import java.util.Scanner;public class Main {private static String minLen(int a,int b,int c,int x,int y){double zhou = -((double)b)/(2*a);double left = -1;double right = -1;if(b*b-4*a*(c-y)<0){left = zhou<x?zhou:x;right = zhou<x?x:zhou;}else{double as = x<zhou?(-b-Math.sqrt(b*b-4*a*(c-y)))/(2*a):(-b+Math.sqrt(b*b-4*a*(c-y)))/(2*a);left = as<x?as:x;right = as<x?x:as;}/*left = x>zhou?zhou:left;right = x<=zhou?zhou:right;*/BigDecimal res = null;while(true){double lm = left+(right-left)/3;double rm = left+(right-left)/3*2;double lmval = len(a,b,c,x,y,lm);double rmval = len(a,b,c,x,y,rm);BigDecimal lvStr = new BigDecimal(lmval).setScale(3,BigDecimal.ROUND_HALF_UP);BigDecimal rvStr = new BigDecimal(rmval).setScale(3,BigDecimal.ROUND_HALF_UP);if(lvStr.equals(rvStr)&&right-left<0.0001){res = lvStr;break;}if(lmval<rmval){right = rm;}else{left = lm;}}return res.setScale(3,BigDecimal.ROUND_HALF_UP)+"";}private static double len(int a,int b,int c,int x,int y,double xx){return Math.sqrt((xx-x)*(xx-x)+Math.pow(a*xx*xx+b*xx+c-y, 2));}public static void main(String args[]){Scanner sc = new Scanner(System.in);int a = sc.nextInt();int b = sc.nextInt();int c = sc.nextInt();int x = sc.nextInt();int y = sc.nextInt();System.out.println(minLen(a, b, c, x, y));sc.close();}}