I'm the first one, who stuck on this test, my program written in Kotlin (probably, same rules applies to Java).
I don't understand, what is "maximum precision"? Should I use double, float or maybe bigdecimal?

My program calculates side lengths, area of the triangle (via sides), angles (via sides and acos), and result point C_2.

Any help is really welcome!

import kotlin.math.*

class Point(val x: Int, val y: Int) {

    constructor(raw: String) :
            this(raw.split(' ')[0].toInt(), raw.split(' ')[1].toInt())

    override fun toString(): String = "$x $y"
}

class Vector(p1: Point, p2: Point) {
    private val x = p1.x - p2.x
    private val y = p1.y - p2.y
    fun length(): Double = sqrt((x*x + y*y).toDouble())
}

fun angle(v1: Vector, v2: Vector, v3: Vector): Double =
    acos(
        (v1.length().pow(2) + v2.length().pow(2) - v3.length().pow(2))
                / (2 * v1.length() * v2.length())
    )

fun triangleSquare(v1: Vector, v2: Vector, v3: Vector): Double {
    val halvedSideSum = (v1.length() + v2.length() + v3.length()) / 2.0
    return sqrt(
        halvedSideSum *
                (halvedSideSum - v1.length()) *
                (halvedSideSum - v2.length()) *
                (halvedSideSum - v3.length())
    )
}

fun Double.fuzzyEquals(other: Double): Boolean = (abs(this - other) < 1e-10)

fun Double.fuzzyEqualsLow(other: Double): Boolean = (abs(this - other) < 1e-4)

fun main() {
    // input
    val pointA = Point(readln())
    val pointB = Point(readln())
    val pointC = Point(readln())

    // solution
    val fixedPointA = Point(0, 0)
    val fixedPointB = Point(pointB.x - pointA.x, pointB.y - pointA.y)
    val fixedPointC = Point(pointC.x - pointA.x, pointC.y - pointA.y)

    val sideAB = Vector(fixedPointA, fixedPointB)
    val sideBC = Vector(fixedPointB, fixedPointC)
    val sideAC = Vector(fixedPointA, fixedPointC)

    val angleBAC = angle(sideAB, sideAC, sideBC)
    val angleACB = angle(sideAC, sideBC, sideAB)
    val angleCBA = angle(sideBC, sideAB, sideAC)

    // find h
    val h = 2.0 / sideAC.length() * triangleSquare(sideAB, sideBC, sideAC)
    // tan ACB = h / x
    val x = h / tan(angleACB)
    val subtractVectorLength = 2.0 * x
    val ratio = (sideAC.length() - subtractVectorLength) / sideAC.length()

    if (ratio <= 0.0 || ratio.fuzzyEquals(0.0) || ratio.fuzzyEqualsLow(1.0)) println("YES")
    else {
        println("NO")
        println(fixedPointA)
        println(fixedPointB)
        println(
            "%.20f".format(fixedPointC.x * ratio) +
                " ${"%.20f".format(fixedPointC.y * ratio)}")
    }
}

Edited by author 22.07.2024 22:53

Pay attention, that points given in order A, B, C. That means that angle of your triangle must equal to angle BAC

Edited by author 21.02.2022 17:07

I have got WA at 26 several times.
Is there something should i pay attention to ?
Thank you.

I keep getting wrong answer at the 2 example. Isn't it from the examples provided?
If so, why for
0 0
4 3
6 0
the solution
NO
0 0
5 0
1.6 1.2
is not correct?
A1B1 is equal to A2B2, B1C1 is equal to B2C2, C1A1 is different from C2A2, the cosine is the same, therefore the angle is the same.

For wa#3:
4 0
0 3
0 0
YES

For wa#4
0 0
5 0
6 5
YES

Look, using the theorem we could build a triangle with such vertexes:
NO
-1.0000000000 4.0000000000
0.0000000000 0.0000000000
-0.8780487805 3.9024390244
(img: http://ge.tt/9klV3HC/v/0 )

Could you help me. Why the answer in first test is YES. why not
-2 0
-1 4
4 0

0 0
0 1000
1 0
YES

0 0
1 1000
1 0
YES

0 0
1 1000
2 0
YES

Попытался разобраться как строить треугольник A2B2C2 и случайно додумался вот до такого "доказательства" теоремы Бориса:
0. Дано:
    A1B1 = A2B2,
    B1C1 = B2C2,
    ∠ B1A1C1 = ∠ B2A2C2.
1. По теореме синусов из перечисленного в п. 0 находим, что sin(∠ B2С2A2) = (A2B2 * sin(∠ B2A2C2)) / B2C2 и sin(∠ B1С1A1) = (A1B1 * sin(∠ B1A1C1)) / B1C1. Значит угол ∠ B2С2A2 = ∠ B1С1A1.
2. Соответственно, оставшийся угол A1B1C1 = A2B2C2 (следствие из суммы углов в треугольнике).
3. Теорема доказана!

Если найдете ошибку в доказательстве - значит решите задачу ;)

i mean
if:
AB<=BC
or
<ACB=90'
or
<BAC>90'
then
YES

miss something?

What is this test?