三分求极值

1142 : 三分·三分求极值

题目传送：hihoCoder - 1142 - 三分·三分求极值

二分适用于单调函数，对于需要逼近的区间做二等分，来求解某点的值等。
三分适用于凸形函数，对于需要逼近的区间做三等分。

AC代码：

#include <map>
#include <set>
#include <list>
#include <cmath>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <cctype>
#include <cstdio>
#include <string>
#include <vector>
#include <complex>
#include <cstdlib>
#include <cstring>
#include <fstream>
#include <sstream>
#include <utility>
#include <iostream>
#include <algorithm>
#include <functional>
#define LL long long
#define INF 0x7fffffff
using namespace std;

double a, b, c, x, y;

double get_dist(double xx) {
    double yy = a * xx * xx + b * xx + c;
    return sqrt((xx - x) * (xx - x) + (yy - y) * (yy - y));
}

int main() {
    double l = -500, r = 500;
    scanf("%lf %lf %lf %lf %lf", &a, &b, &c, &x, &y);
    while(r - l > 0.000001) {//这里为了保证精度，尽量开小点，因为是分治，即使再小也能够承受
        double d = (r - l) / 3;
        double rm = r - d;
        double lm = l + d;
        if(get_dist(lm) < get_dist(rm)) {
            r = rm;
        }
        else l = lm;
    }
    printf("%.3lf\n", get_dist(l));
    return 0;
}