From 4ea210c9c09c714a460378f16843e0ed2c787f9d Mon Sep 17 00:00:00 2001
From: Bruno Freitas Tissei <bft15@inf.ufpr.br>
Date: Sat, 4 May 2019 23:29:01 -0300
Subject: [PATCH] Improve LCA
Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>
---
algorithms/graph/lca.cpp | 75 ++++++++++++++++++++++------------------
1 file changed, 41 insertions(+), 34 deletions(-)
diff --git a/algorithms/graph/lca.cpp b/algorithms/graph/lca.cpp
index d2d68bf..50f8701 100644
--- a/algorithms/graph/lca.cpp
+++ b/algorithms/graph/lca.cpp
@@ -4,26 +4,40 @@
/// - preprocess: O(V log V)
/// - query: O(log V)
/// Complexity (Space): O(V + E + V log V)
-///
-/// OBS: * = return sum path to LCA
-/// ** = return max value on path to LCA
-/// *** = used in both * and **
#define MAXLOG 20 //log2(MAX)
-int h[MAX];
-int par[MAX][MAXLOG];
-//*** int cost[MAX][MAXLOG];
-
-vector<int> graph[MAX]; //*** vector<ii>
+vector<ii> graph[MAX];
struct LCA {
+ vector<int> h;
+ vector<vector<int>> par, cost;
+
+ LCA(int N) :
+ h(N),
+ par(N, vector<int>(MAXLOG)),
+ cost(N, vector<int>(MAXLOG))
+ {
+ init();
+ }
+
+ void init() {
+ for (auto &i : par)
+ fill(all(i), -1);
+ for (auto &i : cost)
+ fill(all(i), 0);
+ dfs(0); // Assuming root is 0
+ }
+
+ inline int op(int a, int b) {
+ return a + b; // or max(a, b)
+ }
/// Performs DFS while filling h, par, and cost.
/// @param v root of the tree
void dfs(int v, int p = -1, int c = 0) {
par[v][0] = p;
- //*** cost[v][0] = c;
+ cost[v][0] = c;
if (p != -1)
h[v] = h[p] + 1;
@@ -31,8 +45,7 @@ struct LCA {
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];
- //** cost[v][i] = max(cost[v][i], max(cost[par[v][i-1]][i-1], cost[v][i-1]));
+ cost[v][i] = op(cost[v][i], op(cost[par[v][i-1]][i-1], cost[v][i-1]));
}
for (auto u : graph[v])
@@ -40,46 +53,40 @@ struct LCA {
dfs(u.fi, v, u.se);
}
- /// Preprocess tree.
- /// @param v root of the tree
- void preprocess(int v) {
- mset(par, -1);
- //*** mset(cost, 0);
- dfs(v);
- }
-
/// Returns LCA (or sum or max).
/// @param p,q query nodes
int query(int p, int q) {
- //*** int ans = 0;
+ 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]);
+ ans = op(ans, cost[p][i]);
p = par[p][i];
}
- if (p == q)
- return p; //*** return ans;
+ if (p == q) {
+ #ifdef COST
+ return ans;
+ #else
+ return p;
+ #endif
+ }
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]));
+ ans = op(ans, op(cost[p][i], cost[q][i])); // *
p = par[p][i];
q = par[q][i];
}
- //* 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]));
-
- return par[p][0];
+ #ifdef COST
+ if (p == q) return ans;
+ else return op(ans, op(cost[p][0], cost[q][0]));
+ #else
+ return par[p][0];
+ #endif
}
};
--
GitLab