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David Hwang
David Hwang

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5/26 TIL: Dockerfile, apt, C++ Generics, ADT in C

Dockerfile for a Go project

FROM golang:1.15 AS builder

RUN apt update && apt upgrade -y && \

apt install -y git \


# Get install script, run, and make binary

RUN curl -fLo \

&& chmod +x && sh && cp ./bin/air /bin/air

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  • Always combine RUN apt-get update with apt-get install in the same RUN statement as suggested in the Dockerfile best practices under the 'apt-get' section here:
  • The WORKDIR command is used to define the working directory of a Docker container. Any RUN, CMD, ADD, COPY, or ENTRYPOINT command will be executed in the specified working directory.

apt vs. apt-get

  • apt is a subset of apt-get and apt is usually preferred
  • apt provides all the necessary commands for package management so just go with that

apt update vs. apt upgrade

--C++ basics--

Generics in C++

#include <iostream>

using namespace std;

template <class T>

T GetMax (T a, T b) {

T result;

result = (a>b)? a : b;

return (result);


int main () {

int i=5, j=6, k;

long l=10, m=5, n;



cout << k << endl;

cout << n << endl;

return 0;


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Logical data structures—implemented using physical data structures: arrays or linked lists

  • Stack (linear, LIFO)
  • Queues (linear, FIFO)
  • Trees (non-linear)
  • Graph (non-linear)
  • Hash Table (tabular)

Abstract Data Type (ADT)

  • ADT is a type (or class) for objects whose behavior is defined by a set of value and a set of operations
  • The definition of ADT only describes what operations are to be performed but not how these operations will be implemented, making it abstract
  • List, Stack, & Queue ADTs:

--Discrete Math--

Math Theorem Example: an even integer plus an odd integer is another odd integer


  • Suppose m is even and n is odd (1. State the assumptions)
  • ∃k1 ∈ Z and ∃k2 ∈ Z so that m = 2k1 and n=2k2 + 1 (2. Formally define the assumptions)
  • Then, m + n = (2k1) + (2k2+1) = 2(k1+k2) + 1. Let k3 = k1 + k2, and note it is an integer. (3. Manipulation)
  • Hence ∃k3 ∈ Z so that m + n = 2k3 + 1 (4. Arrive at definition of conclusion)
  • Thus m + n is odd (5. Conclusion)


  • For n and d integers, d ≠ 0, d | n ↔ if ∃k ∈ Z such that n = dk
  • When we say d | n, it means n is divisible by d

∀x ∈ D, P(x) → Q(x) where we quantify with specific x values, it uses a single arrow to show implication between two statements

P(x) ⇒ Q(x) with a double arrow is an implication between two predicates; it means the same thing as above

Other Proof Methods:

  • Disproving with Counterexamples
  • Proof by division into cases
  • Proof by contradiction
  • Proof by contrapositive

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