new file added on art. bridge/point

geometry/convex-hull.cpp

@@ -1,41 +1,48 @@
-struct pt {
+struct PT {
     double x, y;
+
+    PT() {}
+    PT(double _x, double _y){
+		x = _x;
+		y = _y;
+	}
 };
 
-int orientation(pt a, pt b, pt c) {
+int orientation(PT a, PT b, PT c) {
     double v = a.x*(b.y-c.y)+b.x*(c.y-a.y)+c.x*(a.y-b.y);
     if (v < 0) return -1; // clockwise
     if (v > 0) return +1; // counter-clockwise
     return 0;
 }
 
-bool cw(pt a, pt b, pt c, bool include_collinear) {
+bool cw(PT a, PT b, PT c, bool include_collinear) {
     int o = orientation(a, b, c);
     return o < 0 || (include_collinear && o == 0);
 }
-bool ccw(pt a, pt b, pt c, bool include_collinear) {
+bool ccw(PT a, PT b, PT c, bool include_collinear) {
     int o = orientation(a, b, c);
     return o > 0 || (include_collinear && o == 0);
 }
-
-void convex_hull(vector<pt>& ara, bool include_collinear = false) {
+
+// Be cautious about 'include_collinear
+void convex_hull(vector<PT>& ara, bool include_collinear = false) {
     if (ara.size() == 1)
         return;
 
-    sort(ara.begin(), ara.end(), [](pt a, pt b) {
+    sort(ara.begin(), ara.end(), [](PT a, PT b) {
         return make_pair(a.x, a.y) < make_pair(b.x, b.y);
     });
-    pt p1 = ara[0], p2 = ara.back();
-    vector<pt> up, down;
+    PT p1 = ara[0], p2 = ara.back();
+    vector<PT> up, down;
     up.push_back(p1);
     down.push_back(p1);
     for (int i = 1; i < (int)ara.size(); i++) {
-        if (i == ara.size() - 1 || cw(p1, ara[i], p2, include_collinear)) {
+        if (i == (int)ara.size() - 1 || cw(p1, ara[i], p2, include_collinear)) {
             while (up.size() >= 2 && !cw(up[up.size()-2], up[up.size()-1], ara[i], include_collinear))
                 up.pop_back();
             up.push_back(ara[i]);
         }
-        if (i == ara.size() - 1 || ccw(p1, ara[i], p2, include_collinear)) {
+        if (i == (int)ara.size() - 1 || ccw(p1, ara[i], p2, include_collinear)) {
             while (down.size() >= 2 && !ccw(down[down.size()-2], down[down.size()-1], ara[i], include_collinear))
                 down.pop_back();
             down.push_back(ara[i]);

graph/articulation-bridges.cpp

@@ -0,0 +1,37 @@
+const int N = 2e5;
+int tin[N+5], low[N+5];
+bool vis[N+5];
+vector<int> edge[N+5];
+vector<pair<int, int> > art_bridge;
+
+int timer = 0;
+void dfs(int u, int p = -1){
+	tin[u] = low[u] = timer++;
+	vis[u] = 1;
+
+	for(int to : edge[u]){
+		if(vis[to]){
+			low[u] = min(low[u], tin[to]);
+		}
+		else{
+			dfs(to, u);
+
+			low[u] = min(low[u], low[to]);
+			if(low[to] > tin[u]){
+				art_bridge.push_back({u, to});
+			}
+		}
+	}
+}
+void cut_bridge(int n)
+{
+	timer = 0;
+	art_bridge.clear();
+	for(int K = 1; K <= n; K++) vis[K] = 0;
+
+	for(int K = 1; K <= n; K++){
+		if(!vis[K]){
+			dfs(K);
+		}
+	}
+}

graph/articulation-point.cpp

@@ -0,0 +1,77 @@
+const int N = 2e5;
+int tin[N+5], low[N+5];
+bool vis[N+5];
+vector<int> art_point, edge[N+5];
+
+int timer = 0;
+void dfs(int u, int p = -1){
+	tin[u] = low[u] = timer++;
+	vis[u] = 1;
+
+	int child = 0;
+	for(int to : edge[u]){
+		if(to == p) continue;
+
+		if(vis[to]){
+			low[u] = min(low[u], tin[to]);
+		}
+		else{
+			dfs(to, u);
+
+			low[u] = min(low[u], low[to]);
+			if(low[to] >= tin[u] && p != -1){
+				art_point.push_back(u);
+			}
+			++child;
+		}
+	}
+	if(p == -1 && child >= 2){
+		art_point.push_back(u);
+	}
+}
+void cut_point(int n)
+{
+	timer = 0;
+	art_point.clear();
+	for(int K = 1; K <= n; K++) vis[K] = 0;
+
+	for(int K = 1; K <= n; K++){
+		if(!vis[K]){
+			dfs(K);
+		}
+	}
+}
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