各辺の中点が与えられた三角形の座標を見つけます

三角形の辺の中点である 3 つの座標 (x y) が与えられるとします。タスクは三角形の座標を見つけることです。

例:

CSSの背景

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

各辺の中点を与えられた三角形の座標' title=

Solution can be verified by the figure.

X 座標と Y 座標を別々に解いてみましょう。頂点の X 座標については、x とします。₁×₂×₃。この場合、中点の X 座標は (x₁+×₂)/2(x₂+×₃)/2(x₃+×₁)/2。これら 3 つの式の合計が X 座標の合計に等しいことを確認します。これで、3 つの変数の合計と、それらのすべてのペアを合計するための 3 つの式があり、方程式を解くことによって座標の値を見つけます。
同様に、Y 座標についても解きます。

以下はこのアプローチの実装です。

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# 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>

出力：

トジソン・ジャワ

6 4 4 2 4 6

時間計算量: ○(1)

補助スペース : 定数スペースを使用しているため、O(1)

文字列としてのJava int

クイズの作成