Trouver les coordonnées du triangle étant donné le milieu de chaque côté
Étant donné trois coordonnées (x y) qui sont le milieu des côtés du triangle. La tâche est de trouver les coordonnées du triangle.
Exemples :
Input : midx 1 = 5 midy 1 = 3 midx 2 = 4 midy 2 = 4 midx 3 = 5 midy 3 = 5 Output : x 1 = 4 y 1 = 2 x 2 = 4 y 2 = 6 x 3 = 6 y 3 = 4
Solution can be verified by the figure.
Résolvons séparément les coordonnées X et les coordonnées Y. Pour la coordonnée X des sommets, soit x 1 x 2 x 3 . Alors la coordonnée X des points médians sera (x 1 +x 2 )/2 (x 2 +x 3 )/2 (x 3 +x 1 )/2. Observez que la somme de ces 3 expressions est égale à la somme des coordonnées X. Nous avons maintenant une somme de 3 variables et 3 expressions pour que la somme de chaque paire d'entre elles découvre les valeurs des coordonnées en résolvant des équations.
De même, nous résolvons les coordonnées Y.
Ci-dessous la mise en œuvre de cette approche :
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>
Sortir:
6 4 4 2 4 6
Complexité temporelle : O(1)
Espace auxiliaire : O(1) car il utilise un espace constant
