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Finden Sie die Koordinaten des Dreiecks mit dem gegebenen Mittelpunkt jeder Seite

Gegeben sind drei Koordinaten (x y), die den Mittelpunkt der Seiten des Dreiecks bilden. Die Aufgabe besteht darin, die Koordinaten des Dreiecks zu finden. 

Beispiele:   

cp-Befehl unter Linux
Input : midx1 = 5 midy1 = 3 midx2 = 4 midy2 = 4 midx3 = 5 midy3 = 5 Output : x1 = 4 y1 = 2 x2 = 4 y2 = 6 x3 = 6 y3 = 4

Koordinaten des Dreiecks mit gegebenem Mittelpunkt jeder Seite' title=



Solution can be verified by the figure.

Lassen Sie uns getrennt nach X- und Y-Koordinaten auflösen. Für die X-Koordinate der Eckpunkte seien sie x1X2X3. Dann ist die X-Koordinate der Mittelpunkte (x1+ x2)/2 (x2+ x3)/2 (x3+ x1)/2. Beachten Sie, dass die Summe dieser drei Ausdrücke gleich der Summe der X-Koordinaten ist. Jetzt haben wir die Summe von 3 Variablen und 3 Ausdrücke für die Summe jedes Paars von ihnen. Finden Sie die Werte der Koordinaten durch Lösen von Gleichungen. 
Ebenso lösen wir nach Y-Koordinaten auf.

Nachfolgend finden Sie die Umsetzung dieses Ansatzes:  

C++
// C++ program to find coordinate of the // triangle given midpoint of each side #include   #define N 3 using namespace std; // Return after solving the equations and // finding the vertices coordinate. vector<int> solve(int v[]) {  vector<int> res;  // Finding sum of all three coordinate.  int all3 = v[0] + v[1] + v[2];  // Solving the equation.  res.push_back(all3 - v[1]*2);  res.push_back(all3 - v[2]*2);  res.push_back(all3 - v[0]*2);  return res; } // Finds vertices of a triangles from given // middle vertices. void findVertex(int xmid[] int ymid[]) {  // Find X coordinates of vertices.  vector<int> V1 = solve(xmid);  // Find Y coordinates of vertices.  vector<int> V2 = solve(ymid);  // Output the solution.  for (int i = 0; i < 3; i++)  cout << V1[i] << ' '  << V2[i] <<endl; } // Driver code int main() {  int xmid[N] = { 5 4 5 };  int ymid[N] = { 3 4 5 };  findVertex(xmid ymid);  return 0; } 
Java
import java.util.Vector; // Java program to find coordinate of the  // triangle given midpoint of each side  class GFG { //static final int N = 3;  // Return after solving the equations and  // finding the vertices coordinate.   static Vector<Integer> solve(int v[]) {  Vector<Integer> res = new Vector<Integer>();  // Finding sum of all three coordinate.   int all3 = v[0] + v[1] + v[2];  // Solving the equation.   res.add(all3 - v[1] * 2);  res.add(all3 - v[2] * 2);  res.add(all3 - v[0] * 2);  return res;  } // Finds vertices of a triangles from given  // middle vertices.   static void findVertex(int xmid[] int ymid[]) {  // Find X coordinates of vertices.   Vector<Integer> V1 = solve(xmid);  // Find Y coordinates of vertices.   Vector<Integer> V2 = solve(ymid);  // Output the solution.   for (int i = 0; i < 3; i++) {  System.out.println(V1.get(i) + ' ' + V2.get(i));  }  } // Driver code   public static void main(String[] args) {  int xmid[] = {5 4 5};  int ymid[] = {3 4 5};  findVertex(xmid ymid);  } } // This code is contributed by // PrinciRaj1992 
Python3
# Python3 program to find coordinate of the # triangle given midpoint of each side N = 3 # Return after solving the equations and # finding the vertices coordinate. def solve(v): res = [] # Finding sum of all three coordinate. all3 = v[0] + v[1] + v[2] # Solving the equation. res.append(all3 - v[1] * 2) res.append(all3 - v[2] * 2) res.append(all3 - v[0] * 2) return res # Finds vertices of a triangles from given # middle vertices. def findVertex(xmid ymid): # Find X coordinates of vertices. V1 = solve(xmid) # Find Y coordinates of vertices. V2 = solve(ymid) # Output the solution. for i in range(0 3): print(V1[i] end=' ') print(V2[i]) # Driver code if __name__=='__main__': xmid = [5 4 5] ymid = [3 4 5] findVertex(xmid ymid) # This code is contributed by # Sanjit_Prasad 
C#
// C# program to find coordinate of the  // triangle given midpoint of each side  using System; using System.Collections; class GFG  {   //static final int N = 3;   // Return after solving the equations and   // finding the vertices coordinate.   static ArrayList solve(int []v)  {   ArrayList res = new ArrayList();   // Finding sum of all three coordinate.   int all3 = v[0] + v[1] + v[2];   // Solving the equation.   res.Add(all3 - v[1] * 2);   res.Add(all3 - v[2] * 2);   res.Add(all3 - v[0] * 2);   return res;   }   // Finds vertices of a triangles from given   // middle vertices.   static void findVertex(int []xmid int []ymid)  {   // Find X coordinates of vertices.   ArrayList V1 = solve(xmid);   // Find Y coordinates of vertices.   ArrayList V2 = solve(ymid);   // Output the solution.   for (int i = 0; i < 3; i++)  {   Console.WriteLine(V1[i] + ' ' + V2[i]);   }   }   // Driver code   public static void Main()   {   int []xmid = {5 4 5};   int []ymid = {3 4 5};   findVertex(xmid ymid);   }  }  // This code is contributed by mits 
PHP
 // PHP program to find coordinate of the  // triangle given midpoint of each side  $N = 3; // Return after solving the equations and  // finding the vertices coordinate.  function solve($v) { $res = array(); // Finding sum of all three coordinate.  $all3 = $v[0] + $v[1] + $v[2]; // Solving the equation.  array_push($res $all3 - $v[1] * 2); array_push($res $all3 - $v[2] * 2); array_push($res $all3 - $v[0] * 2); return $res; } // Finds vertices of a triangles from  // given middle vertices.  function findVertex($xmid $ymid) { // Find X coordinates of vertices.  $V1 = solve($xmid); // Find Y coordinates of vertices.  $V2 = solve($ymid); // Output the solution.  for ($i = 0; $i < 3; $i++) print($V1[$i] . ' ' . $V2[$i] . 'n'); } // Driver code  $xmid = array(5 4 5); $ymid = array(3 4 5); findVertex($xmid $ymid) // This code is contributed by mits ?> 
JavaScript
<script>  // JavaScript program to find coordinate of the  // triangle given midpoint of each side  // Return after solving the equations and  // finding the vertices coordinate.  function solve(v) {  var res = [];  // Finding sum of all three coordinate.  var all3 = v[0] + v[1] + v[2];  // Solving the equation.  res.push(all3 - v[1] * 2);  res.push(all3 - v[2] * 2);  res.push(all3 - v[0] * 2);  return res;  }  // Finds vertices of a triangles from given  // middle vertices.  function findVertex(xmid ymid) {  // Find X coordinates of vertices.  var V1 = solve(xmid);  // Find Y coordinates of vertices.  var V2 = solve(ymid);  // Output the solution.  for (var i = 0; i < 3; i++) {  document.write(V1[i] + ' ' + V2[i] + '  
'
); } } // Driver code var xmid = [5 4 5]; var ymid = [3 4 5]; findVertex(xmid ymid); </script>

Ausgabe:  

string.compare c#
6 4 4 2 4 6

Zeitkomplexität: O(1)

Hilfsraum : O(1), weil es konstanten Platz verwendet


 

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