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Proof theory – reasons for the inapplicability of the complete introduction to the tour expansion

It is known that the expansion of tours is a rather bad heuristic to generate short Hilton cycles even in the planar Euclidean case. This is surprising when you learn about it for the first time.
The surprise is due to the fact that the heuristic appears to resemble full induction if you start with the convex hull of the set of points as the base case and then insert the next point as the point that causes the least increase in length of the tour:

Framework:

• The relative order of the points on the convex hull is the same as for the shortest tour of all points.

Induction step:

• if that's the tour $$T_n$$ through the first $$left | CH right | + n$$ points is optimal, then the shortest tour $$T_ {n + 1}$$ with an additional point is optimal again ($$left | CH right |$$ is the number of points on the convex hull and $$n geq 0)$$,

Question:

What are the reasons that prove that the greedy expansion of the tour is not a variant of the full introduction?

What I am looking for is evidence that clearly indicates which of the conditions for the applicability of full induction are violated by a greedy extension of the tour.

problem

The problem definition is here. For a brief summary:

• An IntCode program is an array of Ints
• The program counter begins with index 0, reads an opcode there, followed by 0 or more arguments for the next indexes, and then goes to the index after the last argument
• opcode 1 takes 3 arguments, `a`. `b`, and `z`and sets `program(z) = program(a) + program(b)`
• opcode 2 does the same thing, but multiplies instead
• opcode 99 takes 0 arguments and stops the program

In part 1 we take the input, replacing index 1 with 12 and index 2 with 2 (`restore 12 2`), run the program and return index 0.

In part 2 (not shown in the link unless you solve part 1) we find which Ints have to replace indices 1 and 2 to get a result where index 0 is 19690720.

With this code, I think it could probably be easier. I tried to separate the program counter logic from the command execution logic (`interpret` vs `step`), but apparently you needed a strange combiner `whileWith`, I was wondering if there are better combiners to express this type of loop or if there is a completely different approach.

I was considering wrapping `step` in the `ContT` or `ExceptT`This would make it possible to reduce part of the nesting by using the early exit instead. However, I wasn't sure which way was the best in terms of extensibility.

code

``````import Control.Arrow (second)
import Data.Array
import Data.Array.ST
import Data.List (find)

data Status = InvalidOp | Terminated | Running | InvalidAddress
deriving (Show, Eq)

newtype Program = Program {
getInts :: Array Int Int
} deriving (Show)

-- Execute the instruction starting at `start`
step :: STArray s Int Int -> Int -> Int -> ST s Status
step arr len start = do
case op of
99 -> return Terminated
_ -> do
(i, j, store) <- forM (start+1..start+3) (readArray arr)
if not \$ all inBounds (i, j, store) then
else do
(a, b) <- forM (i, j) (readArray arr)
case op of
1 -> writeArray arr store (a+b) >> return Running
2 -> writeArray arr store (a*b) >> return Running
_ -> return InvalidOp

where inBounds ix = 0 <= ix && ix < len

interpret :: Program -> Program
interpret (Program prog) = Program \$ runSTArray \$ do
let len = succ . uncurry subtract \$ bounds prog
mArr <- thaw prog
whileWith (== Running) (0, 4..len-1)
(step mArr len)
return mArr

let nums = fmap read \$ split ',' str
in
Program \$ listArray (0, length nums - 1) nums

restore :: Int -> Int -> Program -> Program
restore a b = Program . (// ((1, a), (2, b))) . getInts

-- pt 2

findNounVerb :: Program -> Int -> Maybe (Int, Int)
findNounVerb prog target =
find ((== target) . (! 0) . getInts . interpret . (\$ prog) . uncurry restore) \$
((n, v) | n <- (0..1000), v <- (0..n))

-- util --

split :: Eq a => a -> (a) -> ((a))
split _ () = ()
split k xs = curr : split k rest
where (curr, rest) = second (drop 1) \$ span (/= k) xs

whileWith :: (Monad m) => (ret -> Bool) -> (inp) -> (inp -> m ret) -> m ()
whileWith _ () _ = return ()
whileWith pred (x:xs) step = do
res <- step x
when (pred res) \$
whileWith pred xs step

-- end util --

main :: IO ()
main = do

-- pt 1:
putStrLn "Part 1:"
let output = (! 0) . getInts . interpret . restore 12 2 \$ prog
putStrLn \$ "Output: " ++ show output
putStrLn ""

-- pt 2:
putStrLn "Part 2:"
let Just (noun, verb) = findNounVerb prog 19690720
putStrLn \$ "Noun: " ++ show noun ++ "n" ++ "Verb: " ++ show verb
print \$ 100*noun + verb

$$```$$
``````

Introduction of the Marina One residences in D01

Marina One residences is a development of M + S, a joint development of Temasek Holdings from Singapore and Khazanah Nasional Berhad from Malaysia. Marina One is a historic development collaboration, a rare integrated development with luxury residences, offices, retail stores served by 3 MRT stations and 4 MRI lines in the heart of Marina Bay. Marina One Residences Phase 2 has started and is very well received with attractive prices.

Marina One Residences Prices can be observed excitingly in the upward trend of the real estate market. In block 21, only limited units remain with a very attractive price of 2,200 psf on average.

The Marina One Residences are located flat in the heart of Marina Bay. All units can enjoy the unparalleled accessibility with the 3 MRI and the unobstructed view of the sea or the garden "Green Heart", which is the heart of the development.

Contact the New Condo Launch 2020 development team at 6100 3447 or visit http://www.condolaunchsg.com/properties/ma…one-residences/ for more information on Marina 1.

Javascript – Is there a discussion about the introduction of aliases for window.URL.createObjectURL ()?

Is there a suggestion for ES2020 (or later) regarding the introduction of aliases for `window.URL.createObjectURL()` ?

So that I can write the following:

``````let myBlobURL = window.URL.createObjectURL(myBlob, 'my-blob-url');
``````

and then:

``````example.com/my-blob-url
``````

is a alias that points to the generated URL that was created by `window.URL.createObjectURL()` ?

Introduction!!!

Hello everybody,

I am new to this forum, my name is Debby Tompkins. I love to know why I'm here. I hope to get some really good ideas for trading and the digital ways of making money.

Many thanks

Introduction of Code 2019 Day 6

I recently solved Advent of Code 2019 Day 6 in C #.

Part 1:

You landed on the Universal Orbit Map on Mercury. because
When navigating in space is often changed between orbits
Orbit maps are useful here for efficient routes between, e.g.
Example, you and Santa. You download a map of local orbits (yours
Puzzles entry).

With the exception of the Universal Mass Center of Gravity (COM), every object is in space
is in orbit around exactly one other object. An orbit looks rough
like this:

``````

|
|
AAA--> o            o <--BBB
|
|
/
/
``````

In this diagram, the BBB object is in orbit around AAA. The way there
BBB decreases by AAA (drawn with lines) is only partially shown. In that
Map data is written this orbit relationship AAA) BBB, which means
"BBB is in orbit around AAA".

Before you use your map data to plot a course, you must ensure this
it was not damaged during the download. To check maps, the universal
Orbit Map feature uses orbit count checksums - the total number of
direct lanes (like those shown above) and indirect lanes.

Whenever A B circles around and B C circles, A indirectly circles C. This
Chain can be any number of objects long: if A B orbits, B C orbits,
and C orbits D, then A orbits D indirectly.

Suppose you have the following card:

``````COM)B
B)C
C)D
D)E
E)F
B)G
G)H
D)I
E)J
J)K
K)L
``````

The above map of the orbits visually looks like this:

``````        G - H       J - K - L
/           /
COM - B - C - D - E - F

I
``````

In this visual representation, when two objects are connected by a
The right line circles the left directly.

Here we can count the total number of orbits as follows:

D circles directly C and indirectly B and COM, a total of 3
Tracks. L circles K directly and circles J, E, D, C, B and indirectly
KOM, a total of 7 orbits. COM does not circle anything. The total number of
The direct and indirect orbit in this example is 42.

How many direct and indirect orbits does your map contain in total?
Dates?

Part 2:

Now all you have to do is find out how many orbital transfers you (SIE) make.
need to take to get to Santa (SAN).

They begin at the object that YOU circle. Your goal is that
Object SAN encircled. With an orbital transfer, you can move from anywhere
Object to an object that is orbiting or circled by this object.

Suppose you have the following card:

``````COM)B
B)C
C)D
D)E
E)F
B)G
G)H
D)I
E)J
J)K
K)L
K)YOU
I)SAN
``````

The above map of the orbits visually looks like this:

``````                          YOU
/
G - H       J - K - L
/           /
COM - B - C - D - E - F

I - SAN
``````

In this example, you are in orbit around K, and SAN is in orbit around K
I. To get from K to I, at least 4 orbital transfers are required:

``````K to J
J to E
E to D
D to I
``````

After that, the map of the orbits looks like this:

``````        G - H       J - K - L
/           /
COM - B - C - D - E - F

I - SAN

YOU
``````

How many orbital transfers are required to move from there?
The object you are in orbit of the SAN object is in orbit. (Between
the objects that orbit them - not between DIR and SAN.)

I'm new to C # and come from a C ++ background and want to learn how to improve the writing of more idiomatic and readable code. My approach to the problem is as follows:

First, I inserted the input into a text file every day and read the input from `File`, In this case, I tokenize the entries in a `List>` what I can then pass on to my `OrbitalMapCalculator`, My `OrbitalMapCalculator` then creates a list of every single body that already counts how many direct and indirect orbits it has. Since each body has its own number of orbits, a rotating body can easily increase the number of orbits of the body it orbits.

For part one, I simply add the total orbits of all the bodies.

For the second part I find the distance from "YOU" to the center and from "SAN" to the center. I then find the first common orbit. From there I find the two distances and add them.

Here is the tokenizer:

``````using System;
using System.IO;
using System.Collections.Generic;

{
class ProcessInput
{
internal List> GenerateOrbitalPairs(string textFile)
{
List> orbitalTokens = new List>();

if (File.Exists(textFile))
{
foreach (string pair in tokenPairs)
{
string() splitPair = pair.Split(')');
}
}

return orbitalTokens;
}
}
}
``````

The bulk of the work will be in the `OrbitalMapCalculator`:

``````using System;
using System.Collections.Generic;

{
internal class OrbitalMapCalculator
{
private class Node
{
public Node orbitingNode;
public int numberOfOrbits;
public string ID;

public Node(string id)
{
orbitingNode = null;
numberOfOrbits = 0;
ID = id;
}

public Node(Node orbiting, string id)
{
orbitingNode = orbiting;
numberOfOrbits = orbiting.numberOfOrbits + 1;
ID = id;
}
}

private List orbitalMap = new List();

{
string centerOfMass = "COM";
Node centerNode = new Node(centerOfMass);
Queue centerNames = new Queue();
centerNames.Enqueue(centerOfMass);

while (centerNames.Count > 0)
{
centerOfMass = centerNames.Dequeue();

foreach (Node node in orbitalMap)
{
if (node.ID == centerOfMass)
{
centerNode = node;
break;
}
}

foreach (Tuple pair in orbitalPairs)
{
if (centerOfMass == pair.Item1)
{
centerNames.Enqueue(pair.Item2);
}
}
}
}

public int CountOrbits()
{
int orbits = 0;
foreach (Node node in orbitalMap)
{
orbits += node.numberOfOrbits;
}
return orbits;
}

public int DistanceToSanta()
{
string yourID = "YOU";
string santasID = "SAN";
Node you = null;
Node santa = null;

foreach (Node node in orbitalMap)
{
if (node.ID == yourID)
{
you = node;
}
if (node.ID == santasID)
{
santa = node;
}
}

List youToCenter = new List();
List santaToCenter = new List();
Node pivotNode = FindPivotNode(youToCenter, santaToCenter);

int youToPivot = you.numberOfOrbits - pivotNode.numberOfOrbits - 1;
int santaToPivot = santa.numberOfOrbits - pivotNode.numberOfOrbits - 1;

return youToPivot + santaToPivot;
}

private void AddNodesTilCenter(Node sentinal, List nodes)
{
while (sentinal.orbitingNode != null)
{
sentinal = sentinal.orbitingNode;
}
}

private Node FindPivotNode(List lhs, List rhs)
{
foreach (Node leftNode in lhs)
{
foreach (Node rightNode in rhs)
{
if (leftNode.ID == rightNode.ID)
{
return leftNode;
}
}
}
return null;
}
}
}
``````

And finally the `Program.cs`:

``````using System;
using System.Collections.Generic;

{
class Program
{
static void Main(string() args)
{
string inputFile =
ProcessInput processor = new ProcessInput();
OrbitalMapCalculator calculator = new OrbitalMapCalculator();
List> orbitalPairs = processor.GenerateOrbitalPairs(inputFile);

// Part One only

// Part Two Only

}
}
}
``````

Data Structures – Should I read all these books? Introduction to algorithms, algorithms and the art of computer programming

There, many data structure and algorithmic books from other software engineers were recommended Introduction to the algorithm. algorithm. The art of computer programming and so on.

Should I buy and read all these books, or should I just have to buy one of them, is more than enough? Because all books talk about data structure and algorithm.

genesys – Preliminary system introduction: Where should I start?

Genesys was recommended to me as a system for it possibly is consistent with some things I've searched for in RPG systems. I want to get a feel for it and make an assessment of suitability for my needs before deciding whether to spend time and money fully on it.

Different systems and game lines have different preliminary introduction materials. GURPS Has GURPS Lite and used to have that Everything in one night's work CYOA (back in 3e as part of the basic equipment). sublime has a wonderful fan-generated interactive tutorial. Various other systems have their own quick start and introduction kits.

What kind of Genesys material can I use to quickly familiarize myself with the basic principles and feel of the system and make an informed decision as to whether it is worthwhile to dive deeply?

Introduction to Modern Geometry shively Chapter 3 Exercise 10

Intersects a circle at the points P, P & #; to the sides BC, CA and AB of the triangle ΔABC; Q, Q & # 39 ;; R, R & # 39 ;, and if AP, BQ, and CR are simultaneous, then AP & quot ;, BQ & quot; YCR & # 39; simultaneously.