# Notion Cheat Sheet

Probability Cheat Sheet Distributions Unifrom Distribution notation Ua;b cdf x a b a for x2a;b pdf 1 b a for x2a;b expectation 1 2 (a+ b) variance 1 12 (b a)2 mgf etb eta t(b a) story: all intervals of the same length on the distribution’s support are equally probable. Gamma Distribution notation Gamma(k; ) pdf kx 1e x ( k) I x0 ( k. Cheat Sheet of Mathemtical Notation and Terminology Logic and Sets Notation Terminology Explanation and Examples a:=b deﬁned by The objectaon the side of the colon is deﬁned byb. Examples:x:= 5means thatxis deﬁned to be5, orf.x/:=x2.1means that the functionf is deﬁned to bex2. 1, orA:= ^1;5;7‘means that the setAis deﬁned to be^1;5:7‘.

## Common Data Structure Operations

Data StructureTime ComplexitySpace Complexity
AverageWorstWorst
AccessSearchInsertionDeletionAccessSearchInsertionDeletion
Array`Θ(1)``Θ(n)``Θ(n)``Θ(n)``O(1)``O(n)``O(n)``O(n)``O(n)`
Stack`Θ(n)``Θ(n)``Θ(1)``Θ(1)``O(n)``O(n)``O(1)``O(1)``O(n)`
Queue`Θ(n)``Θ(n)``Θ(1)``Θ(1)``O(n)``O(n)``O(1)``O(1)``O(n)`
Singly-Linked List`Θ(n)``Θ(n)``Θ(1)``Θ(1)``O(n)``O(n)``O(1)``O(1)``O(n)`
Doubly-Linked List`Θ(n)``Θ(n)``Θ(1)``Θ(1)``O(n)``O(n)``O(1)``O(1)``O(n)`
Skip List`Θ(log(n))``Θ(log(n))``Θ(log(n))``Θ(log(n))``O(n)``O(n)``O(n)``O(n)``O(n log(n))`
Hash Table`N/A``Θ(1)``Θ(1)``Θ(1)``N/A``O(n)``O(n)``O(n)``O(n)`
Binary Search Tree`Θ(log(n))``Θ(log(n))``Θ(log(n))``Θ(log(n))``O(n)``O(n)``O(n)``O(n)``O(n)`
Cartesian Tree`N/A``Θ(log(n))``Θ(log(n))``Θ(log(n))``N/A``O(n)``O(n)``O(n)``O(n)`
B-Tree`Θ(log(n))``Θ(log(n))``Θ(log(n))``Θ(log(n))``O(log(n))``O(log(n))``O(log(n))``O(log(n))``O(n)`
Red-Black Tree`Θ(log(n))``Θ(log(n))``Θ(log(n))``Θ(log(n))``O(log(n))``O(log(n))``O(log(n))``O(log(n))``O(n)`
Splay Tree`N/A``Θ(log(n))``Θ(log(n))``Θ(log(n))``N/A``O(log(n))``O(log(n))``O(log(n))``O(n)`
AVL Tree`Θ(log(n))``Θ(log(n))``Θ(log(n))``Θ(log(n))``O(log(n))``O(log(n))``O(log(n))``O(log(n))``O(n)`
KD Tree`Θ(log(n))``Θ(log(n))``Θ(log(n))``Θ(log(n))``O(n)``O(n)``O(n)``O(n)``O(n)`

## Array Sorting Algorithms AlgorithmTime ComplexitySpace Complexity
BestAverageWorstWorst
Quicksort`Ω(n log(n))``Θ(n log(n))``O(n^2)``O(log(n))`
Mergesort`Ω(n log(n))``Θ(n log(n))``O(n log(n))``O(n)`
Timsort`Ω(n)``Θ(n log(n))``O(n log(n))``O(n)`
Heapsort`Ω(n log(n))``Θ(n log(n))``O(n log(n))``O(1)`
Bubble Sort`Ω(n)``Θ(n^2)``O(n^2)``O(1)`
Insertion Sort`Ω(n)``Θ(n^2)``O(n^2)``O(1)`
Selection Sort`Ω(n^2)``Θ(n^2)``O(n^2)``O(1)`
Tree Sort`Ω(n log(n))``Θ(n log(n))``O(n^2)``O(n)`
Shell Sort`Ω(n log(n))``Θ(n(log(n))^2)``O(n(log(n))^2)``O(1)`
Bucket Sort`Ω(n+k)``Θ(n+k)``O(n^2)``O(n)`
Radix Sort`Ω(nk)``Θ(nk)``O(nk)``O(n+k)`
Counting Sort`Ω(n+k)``Θ(n+k)``O(n+k)``O(k)`
Cubesort`Ω(n)``Θ(n log(n))``O(n log(n))``O(n)`
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## How To Setup The Database

### Notion Format Date

• Create one Child relation property connected both ways. Search for the database you are currently in. The second relation property that appears will be the Parent. Rename both properties accordingly.

• Create one rollup property called Grandparents. Configure it to grab the parent and show that parent’s parent. A.k.a the grandparent of the current entry.

## How To Create A Template To Navigate To Grandparents And Grandchildren

• If you want the ability to navigate to the grandparent and grandchildren relations, something the above technique alone will not allow (rollups are only windows, not links), follow these instructions.

• First, create another rollup property called Grandchildren and configure it to grab the current entry’s child’s child.

• Next, create a template and insert TWO linked databases (trigger: /linked database) into the body of the page and search for the current database.

• Create two columns labeled Grandparents and Grandchildren inside the template page and drag the two linked databases underneath. I switched the default table to list view.

• Configure the filter of the Grandparents like this:

• Grandchildren Rollup contains Name of Template

• Configure the filter of the Grandchildren like this:

• Grandparents Rollup contains Name of Template

### Formulas In Notion

This is a small segment of my work-in-progress family tree. Finding automatic connections between grandparents/children is essential for my setup.