uf + geom

Author: atcoder-live

README.md

@@ -15,6 +15,7 @@ AtCoder解説放送ライブラリ集
 |名前|コード|説明|
 |:--|:--|:--|
 |BIT|[bit.cpp](bit.cpp)|Binary Indexed Tree (Fenwick Tree)|
+|UnionFind|[uf.cpp](uf.cpp)|Union Find|
 
 ### 数学
 |名前|コード|説明|
@@ -35,4 +36,6 @@ AtCoder解説放送ライブラリ集
 ### 幾何
 |名前|コード|説明|
 |:--|:--|:--|
-|Vector|[vector.cpp](vector.cpp)|ベクトル（点を扱う際にも使う）|
+|基本|[geom.cpp](geom.cpp)|幾何のベース＋目次|
+|Vector|[geom/vector.cpp](geom/vector.cpp)|ベクトル（点を扱う際にも使う）|
+|Circle|[geom/circle.cpp](geom/circle.cpp)|円|

geom.cpp

@@ -0,0 +1,6 @@
+// Geometry
+const double eps = 1e-9;
+bool equal(double a, double b) { return abs(a-b) < eps;}
+
+[geom/vector]
+[geom/circle]

geom/circle.cpp

@@ -0,0 +1,25 @@
+// Circle
+// coding: https://youtu.be/TdR816rqc3s?t=1750
+// comment: https://youtu.be/TdR816rqc3s?t=11609
+struct Circle {
+  V o; double r;
+  Circle(V o=V(), double r=0) : o(o), r(r) {}
+  vector<V> crossPoint(const Circle& c) {
+    V v = c.o-o;
+    double l = v.norm();
+    if (equal(l, 0)) return {};
+    if (equal(l+r+c.r, max({l,r,c.r})*2)) {
+      if (equal(l+r,c.r)) return {o - v*(r/l)};
+      return {o + v*(r/l)};
+    }
+    if (l+r+c.r < max({l,r,c.r})*2) return {};
+    double x = (l*l + r*r - c.r*c.r) / (2*l);
+    double y = sqrt(r*r - x*x);
+    V mid = o + v*(x/l);
+    v = v.rotate90();
+    return {mid + v*(y/l), mid - v*(y/l)};
+  }
+  bool isInside(const V& p) const {
+    return (p-o).norm() < r+eps;
+  }
+};

vector.cpp geom/vector.cppvector.cpp renamed to geom/vector.cpp

@@ -1,6 +1,5 @@
-// vector
+// Vector
 // https://youtu.be/UWbGRhF3Ozw?t=9564
-const double eps = 1e-9;
 struct V {
   double x, y;
   V(double x=0, double y=0): x(x), y(y) {}
@@ -16,7 +15,7 @@ struct V {
   double cross(const V& v) const { return x*v.y - v.x*y;}
   double norm2() const { return x*x + y*y;}
   double norm() const { return sqrt(norm2());}
-  
+  V rotate90() const { return V(y, -x);}
   int ort() const { // orthant
     if (abs(x) < eps && abs(y) < eps) return 0;
     if (y > 0) return x>0 ? 1 : 2;

uf.cpp

@@ -0,0 +1,21 @@
+// UnionFind
+// coding: https://youtu.be/TdR816rqc3s?t=726
+// comment: https://youtu.be/TdR816rqc3s?t=6822
+struct UnionFind {
+  vector<int> d;
+  UnionFind(int n=0): d(n,-1) {}
+  int find(int x) {
+    if (d[x] < 0) return x;
+    return d[x] = find(d[x]);
+  }
+  bool unite(int x, int y) {
+    x = find(x); y = find(y);
+    if (x == y) return false;
+    if (d[x] > d[y]) swap(x,y);
+    d[x] += d[y];
+    d[y] = x;
+    return true;
+  }
+  bool same(int x, int y) { return find(x) == find(y);}
+  int size(int x) { return -d[find(x)];}
+};