J. The Volcano Eruption（圆相交+并查集）

题目链接：https://codeforces.com/gym/101915/problem/J

思路：将所有相交的圆用并查集维护看做一个整体，然后枚举每个整体的左边界和右边界，判断能不能同时覆盖整个路。

AC代码：

 #include<bits/stdc++.h>
 using namespace std;
 typedef long long ll;
 const int maxn = 1e5 + ;
 int n;
 struct circle{
     ll x, y, r;
 };
 circle c[maxn];
 bool intercircle(circle a, circle b)
 {
     ll d = (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
     ll r = a.r + b.r;
     if(d <= r * r) return true;
     else return false;
 }
 int far[maxn], L[maxn], R[maxn];
 int find(int x)
 {
     if(far[x] == x) return x;
     else return far[x] = find(far[x]);
 }
 void unite(int x, int y)
 {
     x = find(x);
     y = find(y);
     if(x == y) return;
     far[x] = y;
 }
 void init(int n)
 {
     for(int i = ;i <= n;i++)
     {
         far[i] = i;
         L[i] = R[i] = ;
     }
 }
 int main()
 {
     std::ios::sync_with_stdio(false);
     int t;
     cin >> t;
     while(t--)
     {
         ll w, l;
         cin >> n >> w >> l;
         init(n);
         for(int i = ;i < n;i++) cin >> c[i].x >> c[i].y >> c[i].r;
         for(int i = ;i < n;i++)
         {
             for(int j = ;j < i;j++)
             {
                 if(intercircle(c[i],c[j])) unite(i, j);
             }
         }
         for(int i = ;i < n;i++)
         {
             if(c[i].x - c[i].r <= ) L[find(i)] = ;
             if(c[i].x + c[i].r >= w) R[find(i)] = ;
         }
         int ans = ;
         for(int i = ;i < n;i++)
         {
             if(L[i] && R[i]) ans++;
         }
         cout << ans << endl;
     }
     return ;
 }

最近又做了一道从左上角走到右下角的：那么就会多了俩个方向的约数条件：GYM12346A

 #include<bits/stdc++.h>
 using namespace std;
 const int maxn = 1e5 +;
 typedef long long ll;
 int n;
 struct circle{
     ll x, y, r;
 };
 circle c[maxn];
 bool intercircle(circle a, circle b)
 {
     ll d = (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
     ll r = a.r + b.r;
     if(d <= r * r) return true;
     else return false;
 }
 int far[maxn], L[maxn], R[maxn], U[maxn], D[maxn];
 int find(int x)
 {
     if(far[x] == x) return x;
     else return far[x] = find(far[x]);
 }
 void unite(int x, int y)
 {
     x = find(x);
     y = find(y);
     if(x == y) return;
     far[x] = y;
     U[y] = max(U[x], U[y]);
     D[y] = min(D[x], D[y]);
     L[y] = min(L[x], L[y]);
     R[y] = max(R[x], R[y]);
 }
 void init(int n)
 {
     for(int i = ;i <= n;i++)
     {
         far[i] = i;
         L[i] = R[i] = D[i] = U[i] =;
     }
 }
 int main()
 {
     std::ios::sync_with_stdio(false);
     ll n, m, k;
     cin >> m >> n >> k;
     init(k);
     for(int i = ;i <= k;i++)
     {
         cin >> c[i].x >> c[i].y >> c[i].r;
         U[i] = c[i].y + c[i].r;
         D[i] = c[i].y - c[i].r;
         L[i] = c[i].x - c[i].r;
         R[i] = c[i].x + c[i].r;
     }
     for(ll i = ; i <= k; i++){
         for(ll j = i+; j <= k; j++){
             if(intercircle(c[i],c[j])) unite(i, j);
         }
     }
     int flag = ;
     for(ll i = ; i <= k; i++)
     {
         if(far[i])
         {
             if((U[i] >= n && D[i] <= ) ||(L[i] <=  && R[i] >= m) ||
                (D[i] <=  && L[i] <= ) ||(U[i] >= n && R[i] >= m))
             {
                 flag = ;
                 break;
             }
         }
     }
     if(flag) cout <<"N"<<endl;
     else cout <<"S"<<endl;
     return ;
 }