feat: introduce random_facts.txt

.gitignore

@@ -3,3 +3,4 @@
 .venv
 .DS_Store
 .ruff_cache
+references/

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)

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).