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Recompte de paral·lelograms en un pla

Donats alguns punts d'un pla que són diferents i cap d'ells no es troben en la mateixa línia. Hem de trobar el nombre de paral·lelograms amb els vèrtexs com a punts donats. Exemples:

Input : points[] = {(0 0) (0 2) (2 2) (4 2) (1 4) (3 4)} Output : 2 Two Parallelograms are possible by choosing above given point as vertices which are shown in below diagram.

Podem resoldre aquest problema utilitzant una propietat especial dels paral·lelograms que les diagonals d'un paral·lelogram es tallen entre si al mig. Així, si obtenim un punt mitjà que és el punt mitjà de més d'un segment de línia, podem concloure que un paral·lelogram existeix amb més precisió si un punt mig es produeix x vegades, llavors es poden triar diagonals de possibles paral·lelograms.xC2maneres, és a dir, hi haurà x*(x-1)/2 paral·lelograms corresponents a aquest punt mitjà concret amb una freqüència x. Així que iterem sobre tots els parells de punts i calculem el seu punt mitjà i augmentem la freqüència del punt mitjà en 1. Al final comptem el nombre de paral·lelograms segons la freqüència de cada punt mitjà diferent, tal com s'ha explicat anteriorment. Com que només necessitem que la freqüència de la divisió del punt mitjà per 2 s'ignora mentre es calcula el punt mitjà per simplicitat. 

CPP
// C++ program to get number of Parallelograms we // can make by given points of the plane #include    using namespace std; // Returns count of Parallelograms possible // from given points int countOfParallelograms(int x[] int y[] int N) {  // Map to store frequency of mid points  map<pair<int int> int> cnt;  for (int i=0; i<N; i++)  {  for (int j=i+1; j<N; j++)  {  // division by 2 is ignored to get  // rid of doubles  int midX = x[i] + x[j];  int midY = y[i] + y[j];  // increase the frequency of mid point  cnt[make_pair(midX midY)]++;  }  }  // Iterating through all mid points  int res = 0;  for (auto it = cnt.begin(); it != cnt.end(); it++)  {  int freq = it->second;  // Increase the count of Parallelograms by  // applying function on frequency of mid point  res += freq*(freq - 1)/2;  }  return res; } // Driver code to test above methods int main() {  int x[] = {0 0 2 4 1 3};  int y[] = {0 2 2 2 4 4};  int N = sizeof(x) / sizeof(int);  cout << countOfParallelograms(x y N) << endl;  return 0; } 
Java
/*package whatever //do not write package name here */ import java.io.*; import java.util.*; public class GFG {    // Returns count of Parallelograms possible  // from given points  public static int countOfParallelograms(int[] x int[] y int N)  {  // Map to store frequency of mid points  HashMap<String Integer> cnt = new HashMap<>();  for (int i=0; i<N; i++)  {  for (int j=i+1; j<N; j++)  {  // division by 2 is ignored to get  // rid of doubles  int midX = x[i] + x[j];  int midY = y[i] + y[j];  // increase the frequency of mid point  String temp = String.join(' ' String.valueOf(midX) String.valueOf(midY));  if(cnt.containsKey(temp)){  cnt.put(temp cnt.get(temp) + 1);  }  else{  cnt.put(temp 1);  }  }  }  // Iterating through all mid points  int res = 0;  for (Map.Entry<String Integer> it : cnt.entrySet()) {  int freq = it.getValue();  // Increase the count of Parallelograms by  // applying function on frequency of mid point  res = res + freq*(freq - 1)/2;  }  return res;  }    public static void main(String[] args) {  int[] x = {0 0 2 4 1 3};  int[] y = {0 2 2 2 4 4};  int N = x.length;  System.out.println(countOfParallelograms(x y N));  } } // The code is contributed by Nidhi goel.  
Python3
# python program to get number of Parallelograms we # can make by given points of the plane # Returns count of Parallelograms possible # from given points def countOfParallelograms(x y N): # Map to store frequency of mid points cnt = {} for i in range(N): for j in range(i+1 N): # division by 2 is ignored to get # rid of doubles midX = x[i] + x[j]; midY = y[i] + y[j]; # increase the frequency of mid point if ((midX midY) in cnt): cnt[(midX midY)] += 1 else: cnt[(midX midY)] = 1 # Iterating through all mid points res = 0 for key in cnt: freq = cnt[key] # Increase the count of Parallelograms by # applying function on frequency of mid point res += freq*(freq - 1)/2 return res # Driver code to test above methods x = [0 0 2 4 1 3] y = [0 2 2 2 4 4] N = len(x); print(int(countOfParallelograms(x y N))) # The code is contributed by Gautam goel.  
C#
using System; using System.Collections.Generic; public class GFG {  // Returns count of Parallelograms possible  // from given points  public static int CountOfParallelograms(int[] x int[] y int N)  {  // Map to store frequency of mid points  Dictionary<string int> cnt = new Dictionary<string int>();  for (int i = 0; i < N; i++)  {  for (int j = i + 1; j < N; j++)  {  // division by 2 is ignored to get  // rid of doubles  int midX = x[i] + x[j];  int midY = y[i] + y[j];  // increase the frequency of mid point  string temp = string.Join(' ' midX.ToString() midY.ToString());  if (cnt.ContainsKey(temp))  {  cnt[temp]++;  }  else  {  cnt.Add(temp 1);  }  }  }  // Iterating through all mid points  int res = 0;  foreach (KeyValuePair<string int> it in cnt)  {  int freq = it.Value;  // Increase the count of Parallelograms by  // applying function on frequency of mid point  res += freq * (freq - 1) / 2;  }  return res;  }  public static void Main(string[] args)  {  int[] x = { 0 0 2 4 1 3 };  int[] y = { 0 2 2 2 4 4 };  int N = x.Length;  Console.WriteLine(CountOfParallelograms(x y N));  } } 
JavaScript
// JavaScript program to get number of Parallelograms we // can make by given points of the plane // Returns count of Parallelograms possible // from given points function countOfParallelograms(x y N) {  // Map to store frequency of mid points  // map int> cnt;  let cnt = new Map();  for (let i=0; i<N; i++)  {  for (let j=i+1; j<N; j++)  {  // division by 2 is ignored to get  // rid of doubles  let midX = x[i] + x[j];  let midY = y[i] + y[j];  // increase the frequency of mid point  let make_pair = [midX midY];  if(cnt.has(make_pair.join(''))){  cnt.set(make_pair.join('') cnt.get(make_pair.join('')) + 1);  }  else{  cnt.set(make_pair.join('') 1);  }  }  }  // Iterating through all mid points  let res = 0;  for (const [key value] of cnt)  {  let freq = value;  // Increase the count of Parallelograms by  // applying function on frequency of mid point  res = res + Math.floor(freq*(freq - 1)/2);  }  return res; } // Driver code to test above methods let x = [0 0 2 4 1 3]; let y = [0 2 2 2 4 4]; let N = x.length; console.log(countOfParallelograms(x y N)); // The code is contributed by Gautam goel (gautamgoel962) 

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Complexitat temporal: O (n2logn) ja que estem iterant a través de dos bucles fins a n i utilitzant també un mapa que pren logn.
Espai auxiliar: O(n)



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