Kattis

Kattis - amsterdamdistance【数学】

题意

给出两个点 算出从第一个点到第二个点的最短距离，只不过这里不是直角坐标系， 是雷达图

思路
因为内圈的圆的路径要比外圈的小，所以我们要尽可能先往内圈走，加一个判断条件 走到哪里就好了

AC代码

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <deque>
#include <vector>
#include <queue>
#include <string>
#include <cstring>
#include <map>
#include <stack>
#include <set>
#include <cstdlib>
#include <ctype.h>
#include <numeric>
#include <sstream>
using namespace std;

typedef long long LL;
const double PI  = 3.14159265358979323846264338327;
const double E   = 2.718281828459;  
const double eps = 1e-6;
const int MAXN   = 0x3f3f3f3f;
const int MINN   = 0xc0c0c0c0;
const int maxn   = 1e5 + 5; 
const int MOD    = 1e9 + 7;

int main()
{
    int n, m;
    double r;
    scanf("%d%d%lf", &n, &m, &r);
    double ave = r * 1.0 / m;
    int x1, y1, x2, y2;
    scanf("%d%d%d%d", &x1, &y1, &x2, &y2);
    double ans = 0.0;
    ans += (max(y1, y2) - min(y1, y2)) * ave * 1.0;
    int y = min(y1, y2);
    double rec = (max(x1, x2) - min(x1, x2)) * 1.0 / n; // 份数 
    while (y)
    {
        double dis1, dis2;
        dis1 = 2.0 * ave + 1.0 * rec * (PI * (y - 1) * ave);
        dis2 = rec * PI * y * ave * 1.0;
        if (dis1 <= dis2)
        {
            ans += 2 * ave;
            y--;    
        }       
        else 
        {
            ans += dis2;
            break;  
        }                                                          
    }
    if (fabs(ans - 0.0) < eps)
        cout << 0 << endl;
    else
        printf("%.14lf
", ans);
}