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Troba les coordenades del triangle donat el punt mitjà de cada costat

Donades tres coordenades (x y) que són el punt mitjà dels costats del triangle. La tasca és trobar les coordenades del triangle. 

Exemples:   

nullpointerexception
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

coordenades del triangle donat el punt mitjà de cada costat' title=



Solution can be verified by the figure.

Anem a resoldre per separat les coordenades X i les coordenades Y. Per a la coordenada X dels vèrtexs siguin x1x2x3. Aleshores la coordenada X dels punts mitjans serà (x1+ x2)/2 (x2+ x3)/2 (x3+ x1)/2. Observeu que la suma d'aquestes 3 expressions és igual a la suma de les coordenades X. Ara tenim la suma de 3 variables i 3 expressions per a la suma de cada parell d'elles esbrineu els valors de les coordenades resolent equacions. 
De la mateixa manera, resolem les coordenades Y.

edat de salman khan khan

A continuació es mostra la implementació d'aquest enfocament:  

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>

Sortida:  

6 4 4 2 4 6

Complexitat temporal: O(1)

Arquitectura de 32 bits vs 64 bits

Espai Auxiliar : O(1) perquè utilitza espai constant


 

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