luogu P1663 山

题目链接

luogu P1663 山

题解

只需要求出下凸包的最低点就好了

显然是由两个斜率相反的直线相交来的

盼下最低点为直线的情况

代码

#include<cstdio>
#include<iostream>
#include<algorithm>
inline int read() {
    int x = 0,f = 1;
    char c = getchar();
    while(c < '0' || c > '9')c = getchar();
    while(c <= '9' && c >= '0') x = x * 10 + c - '0',c = getchar();
    return x * f;
}
const int maxn = 10007;
int n;
double x[maxn],y[maxn];
double k[maxn],b[maxn];
int main() {
    n = read();
    scanf("%lf%lf",&x[1],&y[1]);
    for(int i = 2;i <= n;++ i) {
        scanf("%lf%lf",x + i,y + i);
        k[i] = (y[i] - y[i - 1]) / (x[i] - x[i - 1]);
        b[i] = y[i] - k[i] * x[i];
    }
    double ans = 0.0;
    for(int i = 1;i <= n;++ i)
        for(int j = i + 1;j <= n;++ j) {
            if((k[j] > 0 && k[i] < 0) || (k[i] > 0 && k[j] < 0))  {
                double X = (b[i] - b[j]) / (k[j] - k[i]);
                if(X * k[i] + b[i] > ans) ans = X * k[i] + b[i];
            }
            else if(!k[j] && !k[i] && b[i] == b[j])
                if(ans < b[i]) ans = b[i];
        }
    printf("%.7lf",ans);
    return 0;
}