Trending March 2024 # Number Of Triangles In A Plane If No More Than Two Points Are Collinear # Suggested April 2024 # Top 7 Popular

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Let us see how to calculate the number of triangles in a plane with n number of points given, with the constraint that not more than two points are collinear.

Computing the number of triangles in a plane with no more than two collinear points is a typical problem in computational geometry, and it is used in computer graphics, image processing, and other areas of computer science.

While creating a 2D image from a 3D scene in 3D graphics, for instance, the issue of counting triangles in a plane with no more than two points collinear can come up. The triangle counting procedure can be used to determine how many triangles are present in the final 2D image after projecting the 3D scene onto a plane in this situation. The complexity of the scene can be ascertained with this, and rendering speed can be improved.

In image processing, where we might want to count the number of unique objects or shapes in an image, this problem comes helpful. In this instance, we can represent the image as a collection of points on a plane, and then we can count the number of triangles that can be created between these points by applying the triangle counting technique. We may determine the approximate number of distinct items or shapes in the image by counting how many triangles are formed.

Explanation

Let’s understand the problem with a few examples and try to solve it.

The aim is to determine how many triangles are formed in a plane with n points such that no more than two points are collinear.

Example −

Suppose N is the number of points in a plane.

N = 3

We can draw only one triangle using these points.

So, the total number of triangles made using 3 points is 1.

Let’s N = 4

Let’s draw triangles using these four points.

The total number of triangles formed using 4 points is 4.

Let’s see some mathematics involved in calculating the number of triangles. This can be obtained using Permutations and Combinations. To construct a triangle 3 points are needed at a time from the total number of points.

So, if a plane contains n points and no more than two of them are collinear, then the number of triangles in the plane is given by the formula.

$$mathrm{n_{C_{3}}:=:frac{n(n-1):(n-2)}{6}}$$

Approach

Program to find the number of triangles in a plane if no more than two points are collinear uses the following Algorithm.

Take the number of points in a plane as input with constraints not more than two of them are collinear.

Calculate the total number of triangles using the above-mentioned formula.

Print the total number of triangles as output.

Example

C++ program to find the number of triangles in a plane if no more than two points are collinear.

using namespace std;

int main() { int number_of_points = 4; int number_of_triangle;

number_of_triangle = number_of_points * (number_of_points – 1) * (number_of_points – 2) / 6; cout << “Total number of triangles formed using ” << number_of_points<< ” points = ” << number_of_triangle << endl;

return 0; }

Output Total number of triangles formed using 4 points = 4 Complexities

Time complexity: O(1), As this code performs a fixed number of calculations, regardless of the size of the input.

Space complexity: O(1), As the code uses a fixed number of variables to store input values and results, regardless of the size of the input.

Conclusion

In this article, we have tried to explain the approach to find the total number of possible triangles with n given points, with the constraint that no two points are collinear. I hope this article helps you to learn the concept in a better way.

You're reading Number Of Triangles In A Plane If No More Than Two Points Are Collinear

How To Get The Number Of Seconds Between Two Dates In Javascript?

In this tutorial, we will learn how to get the number of seconds between two dates with JavaScript.

There are different methods for checking the number of days, hours, and seconds that are commonly used to provide information related to data. Since you can’t manually change the count of the years and months, we follow some simple tricks to get the number in JavaScript.

Using the Date getTime() Method

In JavaScript, we use different methods to calculate the days, hours, and seconds. Most popular way to calculate the time is .getTime(). However, you will get the result in milliseconds and have to convert it into seconds through division.

Syntax var x = new Date("Aug 12, 2023 19:45:25"); var y = new Date("Aug 14, 2023 19:45:25"); let seconds = Math.abs(x.getTime() - y.getTime())/1000;

Here x and y are two dates. We will use the getTime() to get the times in milliseconds of both dates. We take the absolute difference between the two times in milliseconds. Then, after subtracting the time in milliseconds, we will divide it by 1000.

Algorithm

STEP 1 − Create two dates using the new Date(). You can refer to the example for the format of a date.

STEP 2 − Use the .getTime() method to get the time in milliseconds of both dates.

STEP 3 − Subtract the old date from the recent date. Then, divide the output by 1000 to get the difference in seconds.

STEP 4 − Use the innerHTML method to check the number of seconds difference between the two dates

Example 1

We have created both the dates manually using the new Date(). You can also use different methods to generate the date in JavaScript.

var

t1

=

new

Date

(

“Aug 12, 2023 19:45:25”

)

;

var

t2

=

new

Date

(

“Aug 14, 2023 19:45:25”

)

;

var

dif

=

Math

.

abs

(

t1

.

getTime

(

)

t2

.

getTime

(

)

)

/

1000

;

document

.

getElementById

(

‘date1’

)

.

innerHTML

=

“First date: “

+

t1

;

document

.

getElementById

(

‘date2’

)

.

innerHTML

=

“Second date: “

+

t2

;

document

.

getElementById

(

‘seconds’

)

.

innerHTML

+=

dif

+

” seconds”

;

Using the Math.abs() Method

Math.abs() is a method used to round the numbers to the nearest answer to avoid getting floating numbers. Hence, you can also use Math.round() method instead of Math.abs(). You can get the time difference using this method in milliseconds. The time can be converted in seconds by dividing the output by 1000.

Syntax

We will use the following syntax to get the time in milliseconds and convert it into seconds through the division method

let x = new Date(); let y = new Date(); let dif = Math.abs(x - y) / 1000;

Here, we find the number of seconds between two dates – x and y. We take the absolute difference between these two dates using the Math.abs() method. This difference is in milliseconds, so we divide by 1000 to convert it into seconds.

Example 2

In this example, there are more than 31 days of difference in both the dates. We kept the dates similar so that the output could also be checked in seconds manually.

let

date1

=

new

Date

(

“Nov 25 2023 07:24:35”

)

;

let

date2

=

new

Date

(

)

;

var

dif

=

Math

.

abs

(

date1

date2

)

/

1000

;

document

.

getElementById

(

‘date1’

)

.

innerHTML

=

“First date: “

+

date1

;

document

.

getElementById

(

‘date2’

)

.

innerHTML

=

“Second date: “

+

date2

;

document

.

getElementById

(

‘seconds’

)

.

innerHTML

+=

dif

;

The methods like .getTime() and Math.abs() are commonly used in JavaScript. You can alternatively use the Math.round() method to get similar output.

Have a look at the below example.

Example 3

let

date1

=

new

Date

(

“Nov 25 2023 07:24:35”

)

;

let

date2

=

new

Date

(

)

;

var

dif

=

Math

.

round

(

date1

date2

)

/

1000

;

document

.

getElementById

(

‘date1’

)

.

innerHTML

=

“First date: “

+

date1

;

document

.

getElementById

(

‘date2’

)

.

innerHTML

=

“Second date: “

+

date2

;

document

.

getElementById

(

‘seconds’

)

.

innerHTML

+=

dif

;

While getting the answers, you should ensure the time is converted in seconds because the output can also be in minutes or milliseconds. Hence, you can check the examples above to understand the best way to get the output in seconds.

Macos Ventura Notifications Are Broken, And There’s No Sign Of A Fix

macOS Ventura has been available to the general public since October, but there’s a problem that’s been bothering me since beta 1 – notifications. In macOS Ventura, there is a range of problems impacting the reliability and usefulness of notifications. The problems are the biggest sign yet that macOS notifications need a complete overhaul and rethink.

macOS notifications are broken

When Apple released the first beta of macOS Ventura, notifications were almost unusable. That was understandable, given it was an early beta. The experience improved through continued macOS Ventura betas. At some point, though, those improvements stopped, and macOS notifications were left in a state of disarray.

macOS Ventura 13.2 was released to everyone last month, and notifications are still unreliable for both Apple apps and third-party apps. I’ve held out hope that these point-updates would fix the problems, but they haven’t. If anything, notifications have gotten even more unreliable. Some of the issues include:

They get “stuck” in the upper-right of the display

They get “stuck” in Notification Center

They don’t appear at all

They don’t play sound when they’re supposed to, or vice versa

They “beach ball,” requiring the app that sent the notification to be force quit

Notifications appear 20-minutes late, basically like you’re running on a tape delay

The most annoying of these issues is when notifications don’t appear at all. I’ve had this problem for almost every app on my Mac, including Messages, Slack, Mail, and Twitter. This seems to mean that it’s a system-level issue, although the Mail app is the number one offender in my experience.

I’m not alone in these problems, either. Other 9to5Mac staffers are experiencing the same things. On Reddit, macOS users have regularly complained of notification issues, ranging from the Calendar app to the Weather app and more. One other common problem seems to be that notifications will show a “Not Permitted” symbol over the app icon.

9to5Mac’s Take

One possibility I’ve considered for my specific issues: I use Apple’s Focus Modes feature pretty religiously. I have Focus modes for “Work,” “Personal,” “Evenings,” and “Sleep.” These are all set to automatically enable at certain times. It could be that something to do with my Focus mode implementation that is messing up notifications on the Mac.

Still, that’s not an excuse for the lackluster reliability of notifications in macOS Ventura. Focus is a feature created by Apple, it’s not a third-party hack. In fact, it’s a feature Apple has directed a lot of attention toward in the past two years.

What’s most frustrating (or impressive?) is how Apple has managed to make notifications so bad and unreliable, and yet changed absolutely nothing about notification-related features. Notifications have needed an overhaul on macOS for years — especially Notification Center itself. These issues in macOS Ventura make it clear there are some underlying issues that need to be addressed.

Finally, I want to point out that these notification bugs and reliability issues don’t seem to affect everyone running macOS Ventura. That being said, the problems appear to be widespread enough to make it clear that something isn’t quite right.

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What Is A Nan Property Of A Number Object In Javascript?

In JavaScript, the NaN property is a special value that represents “Not a Number”. It is a property of the Number object and can be accessed using Number.NaN.

The NaN property is usually produced as a result of an operation that cannot produce a meaningful result. For example, dividing 0 by 0 or trying to parse an invalid number will both produce NaN.

Here are a few examples of operations that will produce NaN −

Math.sqrt(-1); 0/0; parseInt("foo");

It is important to note that NaN is not equal to any value, including itself. So, if you want to check if a value is NaN, you cannot use the == or === operators. Instead, you should use the isNaN() function, which is designed specifically for this purpose.

Here’s an example of how to use isNaN() −

if (isNaN(someValue)) { console.log("someValue is Not a Number"); } Syntax

Following is the syntax to represent a not a umber −

NaN Number.NaN

We can call NaN from the Number objects, so even NaN represents Not a Number but a Property of a Number object.

Sometimes it is strictly required to pass a number for an operation, in that case, we can throw a NaN error to show the users that they can enter only the Number value.

Example

You can try to run the following example to learn how to use NaN −

function showValue() { var dayOfMonth = 50; dayOfMonth = Number.NaN alert(“Day of Month must be between 1 and 31.”) } Document.write(“Value of dayOfMonth : ” + dayOfMonth ); }

Example

Let’s create a function, sum which takes two parameters and converts them into Integers so that if users enter a Number in decimal or a Number in a string it will automatically change it into integers and sum those integers and print the value. Then we will call the function by passing some arguments.

function sum(a, b) { x = parseInt(a); y = parseInt(b); result = x + y; return result; } let outputDiv = document.getElementById(“output”);

Here when we either pass an Integer or a string containing Integers or Integers in the decimal value we will get the same results because all of the values can be parsed in integers and can be valid numbers but when we pass a string of alphabets we will get an error NaN, which means the value we passed is Not a Number.

Example

Let’s modify the above function, and we want this function to not allow the integers in decimal or even in the string, if the function gets a value that is strictly not a number type then we will console log the NaN to show a message that the entered number is not a number.

function sum(a, b) { if (typeof (a) === “number” && typeof (b) === “number”) { document.write(a + b); } else { document.write(NaN); } } sum(“2”, 4);

JavaScript can convert the numbers from one form to another by itself if it falls under the category of a number, it is not able to convert them into another required form, i.e., the entered number is not a number type in JavaScript, so JavaScript returns an error, NaN, it means not a number. The cool part is that the NaN is also an object of Number which we can access using the chúng tôi property. We can also manually throw the error NaN by using the chúng tôi property or directly passing NaN.

Two Of The Largest Wildfires In California’s History Are Burning Right Now

Thousands of lightning strikes across California have caused hundreds of individual fires in recent days, creating two massive blazes that mark the second and third largest in the state’s history. Officials expect more “dry lightning”—thunderstorms that don’t produce enough rain to keep the parched land below from sparking—to hit Northern California on Sunday and Monday.

More footage from the firefight taking place at the peak of Mt. Hamilton this evening (East of San Jose). Your SLO City and fellow California Firefighters are working hard to protect and defend landmarks, buildings and infrastructure. #SCULightningComplex chúng tôi San Luis Obispo City Fire Department (@SLOCityFire) August 20, 2023

The two largest wildfires currently burning in California are known as the Santa Clara Unit (SCU) Lightning Complex and the Sonoma-Lake-Napa Unit (LNU) Lightning Complex. A “complex” refers to two or more individual fire incidents that are in close enough proximity to fall under one unified containment effort.

On Sunday, local outlets were reporting that both the SCU and LNU complexes had surpassed 340,000 acres, with the record for California’s second-largest wildfire being volleyed back and forth as the blazes spread. The pair are surpassed only by 2023′s Mendocino Complex.

During their assignment on the #SCULightningComplex OES 385 and Strike Team 5806A continued to mop up hot spots after the main fire front burned around the @LickObservatory property to keep hot spots from flaring back up. chúng tôi San Luis Obispo City Fire Department (@SLOCityFire) August 22, 2023

On Saturday evening, The New York Times reported that SCU had burned through at least 339,968 acres in Contra Costa County, Alameda County, Santa Clara County, Stanislaus County, and San Joaquin County. Fortunately, SCU has so far burned mostly less populated areas than the 2023 blaze—because the fires that grew to form the Mendocino Complex were caused by human activity, the flames quickly devastated many communities. This is not to say, however, that the SCU Lightning Complex does not pose a major threat: Local news report two civilian injuries and two injured first responders as of Sunday, and several counties are under mandatory evacuation orders.

Devastating images coming out of the #LNULightningComplex Fire in Northern California. Please stay safe out there and I cannot stress this enough: heed any warnings and evacuation orders from local officials. chúng tôi Vice President Kamala Harris (@VP) August 19, 2023

The LNU Lightning Complex has reportedly burned through more than 341,000 acres in Napa, Yolo, Sonoma, and Solano counties, and has killed at least four civilians so far. Multiple counties are under mandatory evacuation orders, as storms on Sunday and Monday are expected to spark more fires to join the complex.

California governor Gavin Newsom said in a Friday press briefing that Cal Fire had already called out 96 percent of its available fire engines. He emphasized that the state’s annual fire season has just begun, and put out a call for assistance from Canada and Australia’s firefighting personnel.

On Saturday, President Donald Trump declared the fires a “major disaster” and ordered federal aid to assist affected areas. According to a White House statement, the funds could include “grants for temporary housing and home repairs, low-cost loans to cover uninsured property losses, and other programs to help individuals and business owners recover from the effects of the disaster.”

Evacuation efforts are complicated by the COVID-19 pandemic, which is actively spreading in many parts of California. Officials have suggested that evacuees stay with friends or family outside the endangered zone whenever possible, and shelters are reportedly enforcing social distancing as best they can. You can read more about how COVID-19 has affected preparations for fire season here.

The LSU and SCU complexes may be particularly massive, but they are far from California’s only concern. Two other, smaller complexes are also raging in Northern California this weekend, in addition to multiple individual wildfires. As Popular Science has previously reported, California’s natural propensity to burn has collided disastrously with the effects of climate change. That, combined with the pandemic, may make for a particularly dangerous fire season.

How To Print A Number With Commas As Thousands Of Separators In Javascript?

In this tutorial, we will look at a few ways to print a number with commas as thousands of separators in JavaScript and compare them to understand which one is suitable in a given context.

Why do we do number formatting? In English, commas are used to separate numbers bigger than 999. Dot is the thousands separator in Germany. Sweden uses space. The separator is added after every three digits from the right.

Let’s briefly introduce the methods.

Using the toLocaleString() Method

Here, the built-in locale string method localizes the number format based on the country.

Syntax

Users can follow the syntax below.

number.toLocaleString(locale)

Here, the number is the number that we are going to separate with commas.

Parameters

locale − The locale code of the country. For the USA, it is ‘en-US’. ‘en’ is the English language, and ‘US’ is the USA. Other examples are en-GB, hi-EN, and ar-EG. hi-EN uses a comma after every two digits.

Example

In this program, the toLocaleString() returns the comma-separated number of the input.

const

num

=

1234567890

;

document

.

getElementById

(

“inp”

)

.

innerHTML

=

“Input : “

+

num

;

const

result

=

num

.

toLocaleString

(

‘en-US’

)

;

document

.

getElementById

(

“out”

)

.

innerHTML

=

“Output: “

+

result

;

Using Intl.NumberFormatter() Object

Intl is the internationalization namespace in JavaScript. Language-sensitive number formatting is one of the uses of this method.

Syntax

Users can follow the syntax below.

new Intl.NumberFormat() new Intl.NumberFormat(locale) new Intl.NumberFormat(locale, options)

Here, Intl refers to internationalization.

Parameters

locale − The locale code. For example, ‘en-IN’, ‘de-DE’, ’ja-JP.’

options − There are many options available, like style, currency, etc.

Example

const

num

=

1234567890

;

document

.

getElementById

(

“inp”

)

.

innerHTML

=

“Input : “

+

num

;

const

result

=

Intl

.

NumberFormat

(

‘en-US’

)

.

format

(

num

)

;

document

.

getElementById

(

“out”

)

.

innerHTML

=

“Output: “

+

result

;

Using Regular Expression

We can write our code using regex to format numbers.

Syntax

Users can follow the syntax below.

number.toString().split("."); number.replace(replace, ",");

Here, the string split and replace syntax used in the example is given.

Algorithm

STEP 1 − Covert the number to a string.

STEP 2 − Split into a number and a possible decimal.

STEP 3 − Use regex to find and add commas to thousands (3-digit group) in the number.

STEP 4 − Separate the number and decimal with a dot.

Example

In this example, the input is grouped into three digits using the custom regex.

const

regxNum

=

192837.4650

;

var

regxInpEl

=

document

.

getElementById

(

“regxInp”

)

;

var

regxOutEl

=

document

.

getElementById

(

“regxOut”

)

;

var

regxBtnWrapEl

=

document

.

getElementById

(

“regxWrap”

)

;

regxInpEl

.

innerHTML

=

“Input = “

+

regxNum

;

function

regxDoFormat

(

)

{

function

formatNum

(

n

)

{

var

splits

=

n

.

toString

(

)

.

split

(

“.”

)

;

const

numSplit

=

splits

[

0

]

;

const

decimalSplit

=

splits

[

1

]

;

const

thousands

=

/

B(?=(d{3})+(?!d))

/

g

;

return

numSplit

.

replace

(

thousands

,

“,”

)

+

(

decimalSplit

?

“.”

+

decimalSplit

:

“”

)

;

}

const

regxFormt

=

formatNum

(

regxNum

)

;

regxOutEl

.

innerHTML

=

“Output = “

+

regxFormt

;

regxBtnWrapEl

.

style

.

display

=

“none”

;

}

By Creating Custom Function

Here we have written custom code to comma separate the number by checking decimal places and signs.

Syntax number.toString().includes('.); number.toString().split('.')[0]; for (initialize; condition; loop control) {}

Here the syntax of string operations and loop used in the example is given.

Algorithm

Check for the decimal point and number sign.

Remove the sign, loop through, and add commas to 3 digits group accordingly.

Add the sign back and display the output.

Example

Here, the negative floating point input is processed by the custom code based on the algorithm above, and the desired output is obtained.

let

custNum

=

987654.4650

;

var

custInpEl

=

document

.

getElementById

(

“custInp”

)

;

var

custOutEl

=

document

.

getElementById

(

“custOut”

)

;

var

custBtnWrapEl

=

document

.

getElementById

(

“custWrap”

)

;

custInpEl

.

innerHTML

=

“Input = “

+

custNum

;

function

custDoFormat

(

)

{

function

addComma

(

numVal

)

{

var

numSign

=

1

;

if

(

numVal

<

0

)

{

numSign

=

1

;

numVal

=

numVal

;

}

let

num

=

numVal

.

toString

(

)

.

includes

(

‘.’

)

?

numVal

.

toString

(

)

.

split

(

‘.’

)

[

0

]

:

numVal

.

toString

(

)

;

let

len

=

num

.

toString

(

)

.

length

;

let

numResult

=

;

let

numCount

=

1

;

numResult

=

num

.

toString

(

)

[

i

]

+

numResult

;

if

(

numCount

%

3

===

0

&&

numCount

!==

0

&&

i

!==

0

)

{

numResult

=

‘,’

+

numResult

;

}

numCount

++

;

}

if

(

numVal

.

toString

(

)

.

includes

(

‘.’

)

)

{

numResult

=

numResult

+

‘.’

+

numVal

.

toString

(

)

.

split

(

‘.’

)

[

1

]

;

}

return

numSign

<

0

?

‘-‘

+

numResult

:

numResult

;

}

let

custFormt

=

addComma

(

custNum

)

;

custOutEl

.

innerHTML

=

“Output = “

+

custFormt

;

custBtnWrapEl

.

style

.

display

=

“none”

;

}

This article discusses three ways to print a number with commas as thousands of separators in JavaScript.

The locale string and Intl number format method must first look for the localization chosen by the JavaScript engine. Then only formatting is done.

The regex and string replace method is faster than the toLocaleString() method. You can go for this method when there are a huge number of formatting requests.

Update the detailed information about Number Of Triangles In A Plane If No More Than Two Points Are Collinear on the Moimoishop.com website. We hope the article's content will meet your needs, and we will regularly update the information to provide you with the fastest and most accurate information. Have a great day!