【牛客国庆集训派对Day1】New Game!

版权声明：欢迎加好友讨论～ QQ1336347798 https://blog.csdn.net/henu_xujiu/article/details/86549067

题目链接

L1 到 L2 之间连边权值 |C1−C2|  / √ A2+B2

线 L 与圆 i 之间连边权值 max(0, d(Oi , L1) − ri)

圆 i 与圆 j 之间连边权值 max(0, d(Oi , Oj ) − ri − rj )

求 L1 到 L2 的最短路即可。
 

#include<bits/stdc++.h>
#define ios1 ios::sync_with_stdio(0)
#define ios2 cin.tie(0)
#define inf 0x3f3f3f3f
using namespace std;
const int maxn = 5000;
int n, A, B, C1, C2;
double Map[maxn][maxn];
 
struct node{
    double x, y, r;
}circle[maxn];
 
void init() {
    for(int i = 0 ; i <= n + 1; i++){
        for(int j = 0; j <= n + 1; j++) {
            if(i == j)Map[i][j] = 0;
            else Map[i][j] = inf;
        }
    }
}
 
bool cmp (node p, node q) {
    if(p.x == q.x)return p.y < p.y;
    return p.x < p.y;
}
 
 
double dis[maxn];
bool vis[maxn];
 
 
void Dijkstra() {
    for (int i = 0; i <= n+1; i++) { 
        dis[i] = Map[0][i];
    }
    vis[0] = 1;
    for (int i = 0; i < n+1; i++) {
        double MIN = inf; 
        int x = -1;
        for (int j = 0; j <= n+1; j++) {
            if (!vis[j] && dis[j]<MIN) { 
                MIN = dis[j];
                x = j;
            }
        }
        vis[x] = 1;
        for (int j = 0; j <= n+1; j++) {
            if (!vis[j] && MIN + Map[x][j]<dis[j]) {
                dis[j] = Map[x][j] + MIN;
            }
        }
    }
}
 
 
int main() {
    ios1; ios2;
    while(cin >> n >> A >> B >> C1 >> C2) {
        for(int i = 1; i <= n; i++) {
            cin >> circle[i].x >> circle[i].y >> circle[i].r;
        }
        init();
        Map[0][n+1] = Map[n+1][0] = abs(C1-C2)/sqrt(A*A+B*B);
        for(int i = 1; i <= n; i++) {
            double k = abs(A*circle[i].x + B*circle[i].y + C1)/sqrt(A*A+B*B) - circle[i].r;
            if(k < 0)k = 0;
            Map[0][i] = Map[i][0] = k;
        }
        for(int i = 1; i <= n; i++) {
            double k = abs(A*circle[i].x + B*circle[i].y + C2)/sqrt(A*A+B*B) - circle[i].r;
            if(k < 0)k = 0;
            Map[i][n+1] = Map[n+1][i] = k;
        }
        for(int i = 1 ; i <= n; i++) {
            for(int j = 1; j <= n; j++) {
                if(i != j){
                    double k = sqrt(abs(circle[i].x - circle[j].x) * abs(circle[i].x - circle[j].x) + abs(circle[i].y - circle[j].y) * abs(circle[i].y - circle[j].y)) - circle[i].r - circle[j].r;
                    if(k < 0)k = 0;
                    Map[i][j] = k;
                }
            }
        }
        memset(vis, 0, sizeof(vis));
        Dijkstra();
        printf("%lf\n", dis[n+1]);
    }
    return 0;
}