三分算法 初见 （情人节个人专场）

三分算法前人之述备矣了，咱们只需要看并且学习就好了。

几篇高质量博客

https://blog.csdn.net/Littlewhite520/article/details/70144763

https://blog.csdn.net/pi9nc/article/details/9666627

寻找区间最大值

int Three_Search(int n)
{
    int L = 1;
    int R = n;
    int mid, mmid; // mid 和 R的中点
    while (L < R - 1)
    {
        // cout << L << " " << R<< endl;
        mid = (L + R) >> 1;
        mmid = (mid + R) >> 1;
        if (a[mid] > a[mmid])
            R = mmid;
        else
            L = mid;
    }
    return a[L] < a[R] ? L : R;
}

寻找区间最小值

int Three_Search(int n)
{
    int L = 1;
    int R = n;
    int mid, mmid; // mid 和 R的中点
    while (L < R - 1)
    {
        mid = (L + R) >> 1;
        mmid = (mid + R) >> 1;
        if (a[mid] < a[mmid])
            R = mmid;
        else
            L = mid;
    }
    return a[L] < a[R] ? L : R;
}

2020牛客第五场 B题

题目链接 https://ac.nowcoder.com/acm/contest/3006/B

这题就是一个运用三分算法寻找凸函数最大值的例子。

附上代码 跟题解几乎一样

#include <iostream>
#include <malloc.h>
#include <cstdio>
#include <algorithm>
#include <queue>
#include <cmath>
#include <map>
#include <cstring>
#define IO                       \
    ios::sync_with_stdio(false); \
    cin.tie(0);                  \
    // cout.tie(0);
using namespace std;
typedef long long LL;
const int maxn = 100000 + 10;
struct p
{
    int x, y;
} p[maxn];
int n;
double dist(double x)
{
    double max = 0;
    for (int i = 1; i <= n; i++)
    {
        double t = sqrt(p[i].y * p[i].y + (p[i].x - x) * (p[i].x - x));
        if (t > max)
            max = t;
    }
    return max;
}
double Three_Search(double L, double R)
{
    int i;
    double mid, mmid;
    for (i = 0; i < 100; i++)  // 靠着循环次数不断逼近最大值嗯应该是这样
    {
        mid = L + (R - L) / 2;
        mmid = mid + (R - mid) / 2;
        if (dist(mid) > dist(mmid)) //极大值求法 
            L = mid;
        else
            R = mmid;
    }
    return mid;
}
int main()
{
#ifdef ONLINE_JUDGE
#else
    freopen("in.txt", "r", stdin);
    // freopen("out.txt", "w", stdout);
#endif
    scanf("%d", &n);
    for (int i = 1; i <= n; i++)
        scanf("%d%d", &p[i].x, &p[i].y);
    double max = Three_Search(-10000, 10000); // 左右区间
    printf("%.4lf\n", dist(max));
    return 0;
}