From a7543847a9f12df6470734d341cae79ea10dc596 Mon Sep 17 00:00:00 2001
From: Bruno Freitas Tissei <bft15@inf.ufpr.br>
Date: Sat, 3 Feb 2018 11:26:22 -0200
Subject: [PATCH] Add LCA
Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>
---
graph/lca.cpp | 78 +++++++++++++++++++++++++++++++++++++++++++++++++++
1 file changed, 78 insertions(+)
create mode 100644 graph/lca.cpp
diff --git a/graph/lca.cpp b/graph/lca.cpp
new file mode 100644
index 0000000..f441761
--- /dev/null
+++ b/graph/lca.cpp
@@ -0,0 +1,78 @@
+/**
+ * Lowest Common Ancestor - LCA
+ *
+ * Complexity (Time):
+ * preprocess -> O(n log n)
+ * query -> O(log n)
+ * Complexity (Space): O(n + m + n log n)
+ *
+ *
+ * OBS: * = return sum path to LCA
+ * ** = return max value on path to LCA
+ */
+
+vector<ii> graph[MAX];
+
+int h[MAX];
+int par[MAX][MAXLOG], cost[MAX][MAXLOG];
+
+// Perform DFS while filling h, par, and cost
+void dfs(int v, int p = -1, int c = 0) {
+ par[v][0] = p;
+ //*** cost[v][0] = c;
+
+ if (p + 1)
+ h[v] = h[p] + 1;
+
+ for (int i = 1; i < MAXLOG; i++)
+ if (par[v][i - 1] + 1) {
+ par[v][i] = par[par[v][i - 1]][i - 1];
+ //*** cost[v][i] += cost[v][i - 1] + cost[par[v][i - 1]][i - 1];
+ }
+
+ for (auto u : graph[v])
+ if (p != u.fi)
+ dfs(u.fi, v, u.se);
+}
+
+// Preprocess tree with rooted at v
+void preprocess(int v) {
+ memset(par, -1, sizeof par);
+ memset(cost, 0, sizeof cost);
+ dfs(v);
+}
+
+// Return LCA between p and q
+int query(int p, int q) {
+ //*** int ans = 0;
+
+ if (h[p] < h[q])
+ swap(p, q);
+
+ for (int i = MAXLOG - 1; i >= 0; i--)
+ if (par[p][i] + 1 && h[par[p][i]] >= h[q]) {
+ //* ans += cost[p][i];
+ //** ans = max(ans, cost[p][i]);
+ p = par[p][i];
+ }
+
+ if (p == q)
+ return p;
+ //*** return ans;
+
+ for (int i = MAXLOG - 1; i >= 0; i--)
+ if (par[p][i] + 1 && par[p][i] != par[q][i]) {
+ //* ans += cost[p][i] + cost[q][i];
+ //** ans = max(ans, max(cost[p][i], cost[q][i]));
+ p = par[p][i];
+ q = par[q][i];
+ }
+
+ return dp[p][0];
+
+ //* if (p == q) return ans;
+ //* else return ans + cost[p][0] + cost[q][0];
+
+ //** if (p == q) return ans;
+ //** else return max(ans, max(cost[p][0], cost[q][0]));
+}
--
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