From b3ce28dceb4bd0b2451d59e9d391030c623bec82 Mon Sep 17 00:00:00 2001
From: Claudio Maggioni <claudio@maggioni.xyz>
Date: Thu, 4 Apr 2019 13:38:48 +0200
Subject: [PATCH] 2019-04-04 in class

---
 notes.md | 53 ++++++++++++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 52 insertions(+), 1 deletion(-)

diff --git a/notes.md b/notes.md
index 294312b..cb61c61 100644
--- a/notes.md
+++ b/notes.md
@@ -173,7 +173,58 @@ Queue has always 1 cell free to avoid confusion with full/empty
 
 Data structure for fast search
 
+A way to implement a dictionary is a *Direct-access table*
+
+## API of dictionary
+
+- `Insert(D, k)` insert a ket `k` to dictionary `D`
+- `Delete(D, k)` removes key `k`
+- `Search(D, k)` tells whether `D` contains a key `k`
+
+Many different implementations
+
 ## Direct-access table
 
-Implementation of dictionary
+- universe of keys = {1,2,...,M}
+- array `T` of size M
+- each key has its own position in T
 
+```python
+
+def Insert(D, x):
+  D[x] == True
+
+def Delete(D, x):
+  D[x] == False
+
+def Search(D, k):
+  return D[x]
+
+```
+
+Everything is O(1), but memory complexity is awful.
+
+Solve this by mapping keys to smaller keys using an hash function.
+
+Table T is a table many times smaller than the universe and different by a small
+constant factor from the set of keys stored S.
+
+Instead of using keys directly, the index returned by the hash function is used.
+
+**Pigeon hole problem:** More keys (pigeons) in the universe than holes (indexes
+for table t)
+
+### Solution
+
+For every cell in table T don't store True/False but a linked list of keys for
+each index in the table. This is called *Chained hash table*.
+
+```python
+
+def Chained_hash_insert(T, k):
+  return List_insert(T[hash(k)], k)
+
+def Chained_hash_search(T, k):
+  return List_search(T[hash(k)], k)
+
+```