feat: centroid decomposition was added

LuchoBazz · web-flow · commit 0ea61bbeefc3 · 2022-07-14T18:52:27.000-05:00
diff --git a/graph/graph_centroid_decomposition.cpp b/graph/graph_centroid_decomposition.cpp
@@ -0,0 +1,65 @@
+// const int N = @@;
+// int n;
+// vector<int> adj[N];
+
+namespace decomposition {
+    int subtree[N], depth[N], f[N];
+
+    int dfs(int u, int p = -1) {
+        subtree[u] = 1;
+        for(const auto &v: adj[u])
+            if(v != p)
+                subtree[u] += dfs(v, u);
+        return subtree[u];
+    }
+
+    int get_centroid(int u, int sz, int p = -1) {
+        for(const auto &v: adj[u])
+            if(!depth[v] && v != p && subtree[v] > sz)
+                return get_centroid(v, sz, u);
+        return u;
+    }
+
+    int decompose(int u, int d=1) {
+        int centroid = get_centroid(u, dfs(u) / 2);
+        depth[u] = d;
+        for(const auto &v: adj[u])
+            if(!depth[v])
+                f[decompose(v, d + 1)] = centroid;
+        return centroid;
+    }
+
+    int lca(int u, int v) {
+        for(; u != v; u = f[u])
+            if(depth[v] > depth[u])
+                swap(u, v);
+        return u;
+    }
+
+    void clean(int n) {
+        for(int i = 0; i < n; ++i){
+            subtree[i] = 0;
+            depth[i] = 0;
+            f[i] = 0;
+        }
+    }
+
+    vector<int> get_centroids() {
+        vector<int> centroids;
+        // clean(n);
+        dfs(0);
+        int centroid = get_centroid(0, n / 2);
+        centroids.push_back(centroid);
+        clean(n);
+        dfs(centroid);
+        for(const auto &v: adj[centroid]) {
+            if((subtree[centroid] - subtree[v]) == n / 2) {
+                centroids.push_back(v);
+            }
+        }
+        assert(0 < (int) centroids.size() && (int) centroids.size() <= 2);
+        return centroids;
+    }
+}
+
+using namespace decomposition;
