Merge pull request matthewsamuel95#270 from ThiagoWhispher/patch-3

Created Centroid Decomposition

Author: matthewsamuel95

Graph/Centroid Decomposition/centroid_decomposition.cpp

@@ -0,0 +1,76 @@
+#include <bits/stdc++.h>
+ 
+using namespace std;
+ 
+#define N 100100
+ 
+int n, x, y;
+vector < int > graph[N];
+ 
+struct CentroidDec {
+    int root, visited[N], siz[N], layer[N], parent[N];
+    vector < int > centroidTree[N];
+ 
+    void init() {
+        for (int i = 0; i < N; i++) {
+            visited[i] = siz[i] = layer[i] = parent[i] = 0;
+            centroidTree[i].clear();
+        }
+    }
+ 
+    int getCentroid(int u, int p = 0) {
+        siz[u] = 1;
+        for (int v : graph[u])
+            if (v != p && !visited[v]) {
+                getCentroid(v, u);
+                siz[u] += siz[v];
+            }
+        if (p) return 0;
+ 
+        int par = 0, aux = u, nxt = 0;
+        while (1) {
+            for (int v : graph[aux])
+                if (!visited[v] && v != par && siz[v] > siz[u] / 2)
+                    nxt = v;
+ 
+            if (!nxt) return aux;
+            else { par = aux; aux = nxt; nxt = 0; }
+        }
+    }
+ 
+    void buildTree(int u = 0) {
+        if (u == 0) {
+            u = root = getCentroid(1);
+            visited[u] = 1; layer[u] = 1;
+        }
+ 
+        for (int v : graph[u])
+            if (!visited[v]) {
+                int x = getCentroid(v);
+                visited[x] = 1; layer[x] = layer[u] + 1; parent[x] = u;
+                centroidTree[u].push_back(x);
+                centroidTree[x].push_back(u);
+                buildTree(x);
+            }
+    }
+} centroid;
+ 
+int main() {
+    scanf("%d", &n);
+    for (int i = 0; i < n-1; i++) {
+        scanf("%d %d", &x, &y);
+        graph[x].push_back(y);
+        graph[y].push_back(x);
+    }
+ 
+    centroid.init();
+    centroid.buildTree();
+ 
+    for (int i = 1; i <= n; i++) {
+        if (i > 1) printf(" ");
+        printf("%c", centroid.layer[i] - 1 + 'A');
+    }
+    printf("\n");
+ 
+    return 0;
+}