题目链接如下：
Online Judge
这道题挺可惜，我思路其实就差了一点点没想出来，还是看了uva 11853 paintball（好题）——yhx_yhx. live-CSDN博客 这里的文字部分才最终写出来。
dfs版本代码如下：
#include <cstdio>
#include <vector>
#include <set>
#include <cmath>
#include <algorithm>
const int maxx = 1001;
const double eps = 1e-7;
// #define debugstruct oppo{double x, y, radius;
};
int n;
bool vis[maxx];
double x, y, radius, yLeft, yRight;
std::vector<oppo> vec;
std::set<int> up;bool intersect(int a, int b){double dis1 = (vec[a].radius + vec[b].radius) * (vec[a].radius + vec[b].radius);double dis2 = (vec[a].x - vec[b].x) * (vec[a].x - vec[b].x) + (vec[a].y - vec[b].y) * (vec[a].y - vec[b].y);if (dis1 > dis2 - eps){return true;}return false;
}bool dfs(int k){vis[k] = true;if (vec[k].y < vec[k].radius + eps){return false;}if (vec[k].x < vec[k].radius + eps){yLeft = std::min(yLeft, vec[k].y - sqrt(vec[k].radius * vec[k].radius - vec[k].x * vec[k].x));}if (vec[k].x > 1000 - vec[k].radius - eps){yRight = std::min(yRight, vec[k].y - sqrt(vec[k].radius * vec[k].radius - (1000 - vec[k].x) * (1000 - vec[k].x)));}for (int i = 0; i < n; ++i){if (i != k && !vis[i] && intersect(i, k)){if (!dfs(i)){return false;}}}return true;
}void judge(){yLeft = yRight = 1000.0;for (auto it = up.begin(); it != up.end(); ++it){std::fill(vis, vis + n, false);if (!dfs(*it)){printf("IMPOSSIBLE\n");return;}}printf("0.00 %.2f 1000.00 %.2f\n", yLeft, yRight);
}int main(){#ifdef debugfreopen("0.txt", "r", stdin);freopen("1.txt", "w", stdout);#endifwhile (scanf("%d", &n) == 1){vec.resize(n);up.clear();for (int i = 0; i < n; ++i){scanf("%lf %lf %lf", &x, &y, &radius);vec[i].x = x;vec[i].y = y;vec[i].radius = radius;if (y > 1000 - radius - eps){up.insert(i);}}judge();}#ifdef debugfclose(stdin);fclose(stdout);#endifreturn 0;
}我自己最开始的想法是用连通集来做，也能AC：
#include <cstdio>
#include <vector>
#include <set>
#include <cmath>
const int maxx = 1001;
const double eps = 1e-7;
// #define debugstruct oppo{double x, y, radius;
};
int n, temp;
int fa[maxx];
double x, y, radius, yLeft, yRight;
std::vector<oppo> vec;
std::set<int> up, down, left, right;bool intersect(int a, int b){double dis1 = (vec[a].radius + vec[b].radius) * (vec[a].radius + vec[b].radius);double dis2 = (vec[a].x - vec[b].x) * (vec[a].x - vec[b].x) + (vec[a].y - vec[b].y) * (vec[a].y - vec[b].y);if (dis1 > dis2 - eps){return true;}return false;
}int findFather(int a){while (fa[a] != a){a = fa[a];}return a;
}void Union(int a, int b){int faA = findFather(a);int faB = findFather(b);fa[faA] = faB;
}bool divide(){std::set<int> top;for (auto it = up.begin(); it != up.end(); ++it){top.insert(fa[*it]);}for (auto it = down.begin(); it != down.end(); ++it){if (top.find(fa[*it]) != top.end()){return true;}}return false;
}void findPath(){yLeft = yRight = 1000.0;for (auto it = up.begin(); it != up.end(); ++it){temp = fa[*it];for (auto it1 = left.begin(); it1 != left.end(); ++it1){if (fa[*it1] == temp){yLeft = std::min(yLeft, vec[*it1].y - sqrt(vec[*it1].radius * vec[*it1].radius - vec[*it1].x * vec[*it1].x));}}for (auto it2 = right.begin(); it2 != right.end(); ++it2){if (fa[*it2] == temp){yRight = std::min(yRight, vec[*it2].y - sqrt(vec[*it2].radius * vec[*it2].radius - (1000 - vec[*it2].x) * (1000 - vec[*it2].x)));}}}printf("0.00 %.2f 1000.00 %.2f\n", yLeft, yRight);
}int main(){#ifdef debugfreopen("0.txt", "r", stdin);freopen("1.txt", "w", stdout);#endifwhile (scanf("%d", &n) == 1){vec.resize(n);up.clear();down.clear();left.clear();right.clear();for (int i = 0; i < n; ++i){fa[i] = i;}for (int i = 0; i < n; ++i){scanf("%lf %lf %lf", &x, &y, &radius);vec[i].x = x;vec[i].y = y;vec[i].radius = radius;if (x < radius + eps){left.insert(i);}if (x > 1000 - radius - eps){right.insert(i);}if (y > 1000 - radius - eps){up.insert(i);}if (y < radius + eps){down.insert(i);}for (int j = 0; j < i; ++j){if (intersect(i, j)){Union(i, j);}}}for (int i = 0; i < n; ++i){fa[i] = findFather(i);}if (divide()){printf("IMPOSSIBLE\n");} else {findPath();}}#ifdef debugfclose(stdin);fclose(stdout);#endifreturn 0;
}
)
