[洛谷P3382]【模板】三分法

题目大意：给出一个$N$次函数，保证在范围$[l,r]$内存在一点x，使得$[l,x]$上单调增，$[x,r]$上单调减。试求出$x$的值。

题解：求导，就变成了求零点，二分答案即可

卡点：无

C++ Code：

#pragma GCC optimize($1 orz)

#pragma GCC optimize(3)

#pragma GCC optimize("Ofast")

#pragma GCC optimize("inline")

#pragma GCC optimize("-fgcse")

#pragma GCC optimize("-fgcse-lm")

#pragma GCC optimize("-fipa-sra")

#pragma GCC optimize("-ftree-pre")

#pragma GCC optimize("-ftree-vrp")

#pragma GCC optimize("-fpeephole2")

#pragma GCC optimize("-ffast-math")

#pragma GCC optimize("-fsched-spec")

#pragma GCC optimize("unroll-loops")

#pragma GCC optimize("-falign-jumps")

#pragma GCC optimize("-falign-loops")

#pragma GCC optimize("-falign-labels")

#pragma GCC optimize("-fdevirtualize")

#pragma GCC optimize("-fcaller-saves")

#pragma GCC optimize("-fcrossjumping")

#pragma GCC optimize("-fthread-jumps")

#pragma GCC optimize("-funroll-loops")

#pragma GCC optimize("-fwhole-program")

#pragma GCC optimize("-freorder-blocks")

#pragma GCC optimize("-fschedule-insns")

#pragma GCC optimize("inline-functions")

#pragma GCC optimize("-ftree-tail-merge")

#pragma GCC optimize("-fschedule-insns2")

#pragma GCC optimize("-fstrict-aliasing")

#pragma GCC optimize("-fstrict-overflow")

#pragma GCC optimize("-falign-functions")

#pragma GCC optimize("-fcse-skip-blocks")

#pragma GCC optimize("-fcse-follow-jumps")

#pragma GCC optimize("-fsched-interblock")

#pragma GCC optimize("-fpartial-inlining")

#pragma GCC optimize("no-stack-protector")

#pragma GCC optimize("-freorder-functions")

#pragma GCC optimize("-findirect-inlining")

#pragma GCC optimize("-fhoist-adjacent-loads")

#pragma GCC optimize("-frerun-cse-after-loop")

#pragma GCC optimize("inline-small-functions")

#pragma GCC optimize("-finline-small-functions")

#pragma GCC optimize("-ftree-switch-conversion")

#pragma GCC optimize("-foptimize-sibling-calls")

#pragma GCC optimize("-fexpensive-optimizations")

#pragma GCC optimize("-funsafe-loop-optimizations")

#pragma GCC optimize("inline-functions-called-once")

#pragma GCC optimize("-fdelete-null-pointer-checks")

#include <cstdio>

#define maxn 20

using namespace std;

const double eps = 1e-5;

int n;

double s[maxn];

double l, r, p, mid;

bool check(double mid) {

    double tmp = 1, ans = 0;

    for (int i = 0; i < n; i++) ans += s[i] * tmp, tmp *= mid;

    return ans > 0;

}

int main(){

    scanf("%d%lf%lf", &n, &l, &r);

    for (int i = n; i; i--) {

        scanf("%lf", &s[i - 1]);

        s[i - 1] *= i;

    }

    while (r - l > eps) {

        mid = (l + r) / 2;

        if (check(mid)) l = mid;

        else r = mid;

    }

    printf("%.5lf\n", l);

}