From f49fec10c62aed8c1c280626abcff9e3a581b1c0 Mon Sep 17 00:00:00 2001
From: manoflearning <77jwk0724@gmail.com>
Date: Wed, 14 Jan 2026 01:19:06 +0900
Subject: [PATCH] feat: introduce random_facts.txt

---
 .gitignore                                    |  1 +
 README.md                                     |  2 +-
 src/8-misc/facts.txt                          |  0
 src/8-misc/random_facts.txt                   | 22 +++++++++++++++++++
 ..._manhattan_distance_chebyshev_distance.txt | 20 -----------------
 5 files changed, 24 insertions(+), 21 deletions(-)
 delete mode 100644 src/8-misc/facts.txt
 create mode 100644 src/8-misc/random_facts.txt
 delete mode 100644 src/8-misc/rotation_matrix_manhattan_distance_chebyshev_distance.txt

diff --git a/.gitignore b/.gitignore
index 9099272..eae46d1 100644
--- a/.gitignore
+++ b/.gitignore
@@ -3,3 +3,4 @@
 .venv
 .DS_Store
 .ruff_cache
+references/
diff --git a/README.md b/README.md
index d60d191..099e3d8 100644
--- a/README.md
+++ b/README.md
@@ -67,9 +67,9 @@ My implementations of various data structures and algorithms for competitive pro
   - [`dp_opt.cpp`](https://github.com/manoflearning/cp-reference-codes/blob/main/src/8-misc/dp_opt.cpp)
   - [`diff_cons.cpp`](https://github.com/manoflearning/cp-reference-codes/blob/main/src/8-misc/diff_cons.cpp)
   - [`num_frac.cpp`](https://github.com/manoflearning/cp-reference-codes/blob/main/src/8-misc/num_frac.cpp)
+  - [`random_facts.txt`](https://github.com/manoflearning/cp-reference-codes/blob/main/src/8-misc/random_facts.txt)
   - [`rec_kitamasa.cpp`](https://github.com/manoflearning/cp-reference-codes/blob/main/src/8-misc/rec_kitamasa.cpp)
   - [`rnd.cpp`](https://github.com/manoflearning/cp-reference-codes/blob/main/src/8-misc/rnd.cpp)
-  - [`rotation_matrix_manhattan_distance_chebyshev_distance.txt`](https://github.com/manoflearning/cp-reference-codes/blob/main/src/8-misc/rotation_matrix_manhattan_distance_chebyshev_distance.txt)
   - [`search_ternary.cpp`](https://github.com/manoflearning/cp-reference-codes/blob/main/src/8-misc/search_ternary.cpp)
   - [`seq_lis.cpp`](https://github.com/manoflearning/cp-reference-codes/blob/main/src/8-misc/seq_lis.cpp)
   - [`simd.cpp`](https://github.com/manoflearning/cp-reference-codes/blob/main/src/8-misc/simd.cpp)
diff --git a/src/8-misc/facts.txt b/src/8-misc/facts.txt
deleted file mode 100644
index e69de29..0000000
diff --git a/src/8-misc/random_facts.txt b/src/8-misc/random_facts.txt
new file mode 100644
index 0000000..7bbb17f
--- /dev/null
+++ b/src/8-misc/random_facts.txt
@@ -0,0 +1,22 @@
+Random Facts (ICPC Team Note)
+
+- Tiny identities / tricks (no code), meant to be printed and skimmed quickly.
+- Keep each item short: setup -> formulas -> use -> pitfall.
+
+-------------------------------------------------------------------------------
+
+GEOMETRY
+
+45deg transform: Manhattan <-> Chebyshev on Z^2
+  Setup: u = x + y, v = x - y.
+  L1: |dx| + |dy| = max(|du|, |dv|).
+  L∞: max(|dx|, |dy|) = (|du| + |dv|) / 2.
+  Use: max Manhattan over points = max( max(u)-min(u), max(v)-min(v) ).
+  Note: du, dv have same parity -> (|du|+|dv|) is even -> /2 is integer.
+  Why: max(|a+b|,|a-b|)=|a|+|b| and |a+b|+|a-b|=2max(|a|,|b|).
+
+GRAPH
+
+Complete bipartite K_{n,m}: number of spanning trees
+  Formula: tau(K_{n,m}) = n^{m-1} * m^{n-1}.
+  Why: Matrix-Tree theorem (Kirchhoff).
diff --git a/src/8-misc/rotation_matrix_manhattan_distance_chebyshev_distance.txt b/src/8-misc/rotation_matrix_manhattan_distance_chebyshev_distance.txt
deleted file mode 100644
index 38c3b59..0000000
--- a/src/8-misc/rotation_matrix_manhattan_distance_chebyshev_distance.txt
+++ /dev/null
@@ -1,20 +0,0 @@
-Rotation Matrix (In Two Dimensions)
-
-x' = x * cosθ - y * sinθ
-y' = x * sinθ + y * cosθ
-
-Manhattan Distance, Chebyshev Distance
-
-For any two points (x1, y1), (x2, y2) on two-dimensional coordinates,
-- the Manhattan distance is |x1 - x2| + |y1 - y2|.
-- the Chebyshev distance is max(|x1 - x2|, |y1 - y2|).
-
-Relationship between Manhattan distance and Chebyshev distance
-
-Let x1' = x1 - y1, y1' = x1 + y1,
-x2' = x2 - y2, y2' = x2 + y2. (using Rotation matrix)
-
-Then max(|x1 - x2|, |y1 - y2|)
-= (|x1' - x2'| + |y1' - y2'|).
-
-Thus, Manhattan distance can be solved by replacing it with Chebyshev distance, and vice versa.
\ No newline at end of file