Deriving Average Without Totals
Even an old dog like me learns something new every day.
Let’s say you need a program that receives a sequence of numbers and output the current average. How do you do this efficiently? The naive solution is to to keep track of two variables:
total # add up all numbers seen so far
count # a count of how many numbers seen so farThis way, at any step, you can calculate the current average using total/count.
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Vocabulary
- bind
- Sometimes a synonym for “map”
- conflate
- combine
- disjoint
- separate, e.g., odd numbers and even numbers are disjoint
- disjunction
- inclusive or – if one of the inputs is
True - extrinsic
- not intrinsic
- federated
- Top-down delegation of responsibilities; Has a single point of failure at the top.
- PID controller
- control loop feedback mechanism
- e.g., curise control
- 99%ile
- Abbreviation of percentile
- EBNF
- Extended Backus-Naur Form
- Useful for defining the syntax of a programming language
- EBNF terminal
- a token/word/chunk in EBNF
- Alpha
- Αα
- Beta
- Ββ
- Gamma
- Γγ
- Delta
- Δδ
- Commonly denotes ‘difference’
- Epsilon
- Εε
- Used in Greedy-Epsilon algo for multi-armed bandit problems
- Error margin in floating point comparisons.
- Zeta
- Ζζ
- Eta
- Ηη
- Theta
- Θθ
- Iota
- Ιι
- Kappa
- Κκ
- Lambda
- Λλ
- Mu
- Μμ
- Nu
- Νν
- Xi
- Ξξ
- Omicron
- Οο
- Pi
- Ππ
- Rho
- Ρρ
- Sigma
- Σσς
- Tau
- Ττ
- Upsilon
- Υυ
- Phi
- Φφ
- Chi
- Χχ
- Psi
- Ψψ
- Union
- ∪
- Aleph
- ℵ
- Symbol for cardinal numbers. ℵ is pronounced as Aleph-null.
- Empty Set
- ∅
- Such That
- Commonly represented as a colon,
: - Example,
D={x^2|x ∈ N, x >=1, x <= 4}. This reads D is the set of all x^2 SUCH THAT: 1) x is a natural number; 2) x is greater or equal to 1; 3) x is less than or equal to 4. - Intersection
- ∩
- Subset
- ⊂ or ⊆
- e.g., if A = {1,4,9} and B = {1,4}, then B ⊂ A (B is a subset of A).
- Belongs To
- ∈
- ∉ Means “not belong”.
- To say that 1 belongs to S, we write 1 ∈ S.
- e.g., if A = {1,4,9} and e = 4, then we say e∈A, meaning “e belongs to A”. However, one would not say e⊂A – e is a single element, not a set. Similarly, if B = {1,4}, one would not say B∈A or “B belongs to A”, as B is a set not a single element.
- Complements
- Difference between two sets
- Relative Complement
- A\B means objects that belong to A and not to B. i.e., {1,2,3}{3} == {1,2}
- Omega
- Ωω
- P(A|B)
- The likelihood of event A occurring given that B is true.
- P(A^C)
- The probability that A doesn’t happen
- Precision Recall
- Precision = probability that some retreived doc is relevant; Recall = probability that some relevant doc was retreived.
- Narrow Integration Tests
- exercise only that portion of the code in a service that talks to a separate service; uses test doubles of those services, either in process or remote; thus consist of many narrowly scoped tests, often no larger in scope than a unit test (and usually run with the same test framework that’s used for unit tests)
- Broad Integration Tests
- require live versions of all services, requiring substantial test environment and networ access; exercise code paths through all services, not just code responsible for interactions
- Balanced Binary Search Tree
- For example, red-black tree or AVL tree.
- Natural Numbers
- ℕ
- double-struck N
- Cardinal numbers,
- Complex Numbers
- ℂ
- double-struck C