From d0883b193fc8d098586bc6af5d6891589934e7ee Mon Sep 17 00:00:00 2001
From: Bruno Freitas Tissei <bft15@inf.ufpr.br>
Date: Sat, 4 May 2019 23:07:39 -0300
Subject: [PATCH] Add Centroid Decomposition
Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>
---
algorithms/graph/centroid_decomposition.cpp | 65 +++++++++++++++++++++
1 file changed, 65 insertions(+)
create mode 100644 algorithms/graph/centroid_decomposition.cpp
diff --git a/algorithms/graph/centroid_decomposition.cpp b/algorithms/graph/centroid_decomposition.cpp
new file mode 100644
index 0000000..80a783d
--- /dev/null
+++ b/algorithms/graph/centroid_decomposition.cpp
@@ -0,0 +1,65 @@
+/// Centroid Decomposition
+///
+/// Complexity (Time): O(V log V)
+/// Complexity (Space): O(V + E)
+
+// Must be a tree
+vector<int> graph[MAX];
+
+struct CentroidDecomposition {
+ vector<int> par, size, marked;
+
+ CentroidDecomposition(int N) :
+ par(N), size(N), marked(N)
+ {
+ init();
+ }
+
+ void init() {
+ fill(all(marked), 0);
+ build(0, -1);
+ }
+
+ /// Builds the centroid decomposition of the tree recursively.
+ /// @param x initial node
+ /// @param p parent node
+ void build(int x, int p) {
+ int n = dfs(x, -1);
+ int centroid = get_centroid(x, -1, n);
+
+ marked[centroid] = 1;
+ par[centroid] = p;
+
+ for (auto i : graph[centroid])
+ if (!marked[i])
+ build(i, centroid);
+ }
+
+ /// Calculates size of every subtree (in the original tree).
+ /// @param x initial node
+ /// @param p parent node
+ int dfs(int x, int p) {
+ size[x] = 1;
+ for (auto i : graph[x])
+ if (i != p && !marked[i])
+ size[x] += dfs(i, x);
+
+ return size[x];
+ }
+
+ /// Finds centroid by recursively searching for it in the subtree
+ /// with more than n / 2 nodes in it.
+ /// @param x initial node
+ /// @param p parent node
+ /// @param n size of initial subtree
+ int get_centroid(int x, int p, int n) {
+ for (auto i : graph[x])
+ if (i != p && size[i] > n / 2 && !marked[i])
+ return get_centroid(i, x, n);
+ return x;
+ }
+
+ int operator[](int i) {
+ return par[i];
+ }
+};
--
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