원호 구간에 포인트가 존재하는지 확인하세요.

원점(0 0)을 중심으로 하는 원이 있습니다. 입력으로 원 구간의 시작 각도와 원 구간의 크기(%)가 제공됩니다.

예:

Input : Radius = 8 StartAngle = 0 Percentage = 12 x = 3 y = 4 Output : Point (3 4) exists in the circle sector Input : Radius = 12 Startangle = 45 Percentage = 25 x = 3 y = 4 Output : Point (3 4) does not exist in the circle sector

출처:Wikibook.org

이 이미지에서 시작 각도는 반경 r 0도이고 색상 영역의 백분율이 12%라고 가정하면 끝 각도를 다음과 같이 계산합니다. 360/퍼센트 + 시작 각도 .

원점(원점 중심)에 점(xy)이 존재하는지 여부를 확인하기 위해 해당 점의 극좌표를 찾은 후 다음 단계를 수행합니다.

이것을 사용하여 x y를 극좌표로 변환합니다.
각도 = 부재(y/x); 반경 = sqrt(x * y y y y y y);
그런 다음 각도는 StartingAngle과 EndingAngle 사이에 있어야 하고 반경은 0과 반경 사이에 있어야 합니다.

C++

// C++ program to check if a point lies inside a circle // sector. #include   using namespace std; void checkPoint(int radius int x int y float percent  float startAngle) {  // calculate endAngle  float endAngle = 360/percent + startAngle;  // Calculate polar co-ordinates  float polarradius = sqrt(x*x+y*y);  float Angle = atan(y/x);  // Check whether polarradius is less then radius of circle  // or not and Angle is between startAngle and endAngle  // or not  if (Angle>=startAngle && Angle<=endAngle && polarradius<radius)  printf('Point (%d %d) exist in the circle sectorn' x y);  else  printf('Point (%d %d) does not exist in the circle sectorn'  x y); } // Driver code int main() {  int radius = 8 x = 3 y = 4;  float percent = 12 startAngle = 0;  checkPoint(radius x y percent startAngle);  return 0; }

Java

// Java program to check if // a point lies inside a circle // sector. class GFG { static void checkPoint(int radius int x int y float percent  float startAngle) {  // calculate endAngle  float endAngle = 360/percent + startAngle;    // Calculate polar co-ordinates  double polarradius = Math.sqrt(x*x+y*y);  double Angle = Math.atan(y/x);    // Check whether polarradius is  // less then radius of circle  // or not and Angle is between  // startAngle and endAngle  // or not  if (Angle>=startAngle && Angle<=endAngle && polarradius<radius)  System.out.print('Point'+'('+x+''+y+')'+  ' exist in the circle sectorn');  else  System.out.print('Point'+'('+x+''+y+')'+  ' exist in the circle sectorn'); } // Driver Program to test above function public static void main(String arg[]) {  int radius = 8 x = 3 y = 4;  float percent = 12 startAngle = 0;  checkPoint(radius x y percent startAngle); } } // This code is contributed // by Anant Agarwal.

Python3

# Python3 program to check if a point  # lies inside a circle sector. import math def checkPoint(radius x y percent startAngle): # calculate endAngle endAngle = 360 / percent + startAngle # Calculate polar co-ordinates polarradius = math.sqrt(x * x + y * y) Angle = math.atan(y / x) # Check whether polarradius is less # then radius of circle or not and  # Angle is between startAngle and  # endAngle or not if (Angle >= startAngle and Angle <= endAngle and polarradius < radius): print('Point (' x '' y ') ' 'exist in the circle sector') else: print('Point (' x '' y ') ' 'does not exist in the circle sector') # Driver code radius x y = 8 3 4 percent startAngle = 12 0 checkPoint(radius x y percent startAngle) # This code is contributed by # Smitha Dinesh Semwal

// C# program to check if a point lies // inside a circle sector. using System.IO; using System; class GFG {    static void checkPoint(int radius int x int y  float percent float startAngle)  {    // calculate endAngle  float endAngle = 360 / percent + startAngle;    // Calculate polar co-ordinates  float polarradius =   (float)Math.Sqrt(x * x + y * y);    float Angle = (float)Math.Atan(y / x);    // Check whether polarradius is less then   // radius of circle or not and Angle is   // between startAngle and endAngle or not  if (Angle >= startAngle && Angle <= endAngle  && polarradius < radius)  Console.Write('Point ({0} {1}) exist in '  + 'the circle sector' x y);  else  Console.Write('Point ({0} {1}) does not '  + 'exist in the circle sector' x y);  }    // Driver code  public static void Main()  {  int radius = 8 x = 3 y = 4;  float percent = 12 startAngle = 0;  checkPoint(radius x y percent startAngle);  } } // This code is contributed by Smitha Dinesh Semwal

JavaScript

<script> // Javascript program to check if // a point lies inside a circle // sector. function checkPoint(radius x y percent startAngle) {    // Calculate endAngle  let endAngle = 360 / percent + startAngle;    // Calculate polar co-ordinates  let polarradius = Math.sqrt(x * x + y * y);  let Angle = Math.atan(y / x);    // Check whether polarradius is  // less then radius of circle  // or not and Angle is between  // startAngle and endAngle  // or not  if (Angle >= startAngle &&   Angle <= endAngle &&   polarradius < radius)  document.write('Point' + '(' + x +   '' + y + ')' +  ' exist in the circle sectorn');  else  document.write('Point' + '(' + x +   '' + y + ')' +  ' exist in the circle sectorn'); }   // Driver code  let radius = 8 x = 3 y = 4; let percent = 12 startAngle = 0; checkPoint(radius x y percent startAngle); // This code is contributed by splevel62   </script>

출력 :

Point(3 4) exists in the circle sector

시간 복잡도: 오(1)
보조 공간: 오(1)

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