From f4d4687cdb524f3cc771bfbffb8e9cd70f4508a9 Mon Sep 17 00:00:00 2001
From: Caio <caiofeliperro@gmail.com>
Date: Mon, 19 Aug 2024 15:37:22 -0300
Subject: [PATCH] feat(graphs): add binary lifting

---
 algorithms/graphs/binary-lifting.cpp | 14 ++++++++++++++
 algorithms/graphs/binary-lifting.tex |  3 +++
 2 files changed, 17 insertions(+)
 create mode 100644 algorithms/graphs/binary-lifting.cpp
 create mode 100644 algorithms/graphs/binary-lifting.tex

diff --git a/algorithms/graphs/binary-lifting.cpp b/algorithms/graphs/binary-lifting.cpp
new file mode 100644
index 0000000..1a2c767
--- /dev/null
+++ b/algorithms/graphs/binary-lifting.cpp
@@ -0,0 +1,14 @@
+const int MAXN = 2e5, MAXLOG2 = 60;
+int bl[MAXN][MAXLOG2 + 1];
+
+int jump(int u, ll k) {
+  for (int i = 0; i <= MAXLOG2; i++)
+    if (k & (1LL << i)) u = bl[u][i];
+
+  return u;
+}
+
+void build(int N) {
+  for (int i = 1; i <= MAXLOG2; i++)
+    for (int j = 0; j < N; j++) bl[j][i] = bl[bl[j][i - 1]][i - 1];
+}
diff --git a/algorithms/graphs/binary-lifting.tex b/algorithms/graphs/binary-lifting.tex
new file mode 100644
index 0000000..3179e27
--- /dev/null
+++ b/algorithms/graphs/binary-lifting.tex
@@ -0,0 +1,3 @@
+\subsection{Binary Lifting}
+
+Time: $O(N \cdot \log_2 K)$