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Contar pares cuyos productos existen en una matriz

Dada una matriz, cuente aquellos pares cuyo valor de producto está presente en la matriz. 
Ejemplos:  
 

Input : arr[] = {6 2 4 12 5 3}  
Output : 3
All pairs whose product exist in array
(6 2) (2 3) (4 3)
Input : arr[] = {3 5 2 4 15 8}
Output : 2


 


A solución sencilla es generar todos los pares de la matriz dada y verificar si el producto existe en la matriz. Si existe, incremente el recuento. Finalmente regresa el conteo.
A continuación se muestra la implementación de la idea anterior. 
 



comentario xml
C++
// C++ program to count pairs whose product exist in array #include   using namespace std; // Returns count of pairs whose product exists in arr[] int countPairs( int arr[] int n) {  int result = 0;  for (int i = 0; i < n ; i++)  {  for (int j = i+1 ; j < n ; j++)  {  int product = arr[i] * arr[j] ;  // find product in an array  for (int k = 0; k < n; k++)  {  // if product found increment counter  if (arr[k] == product)  {  result++;  break;  }  }  }  }  // return Count of all pair whose product exist in array  return result; } //Driver program int main() {  int arr[] = {6 2 4 12 5 3} ;  int n = sizeof(arr)/sizeof(arr[0]);  cout << countPairs(arr n);  return 0; } 
Java
// Java program to count pairs  // whose product exist in array import java.io.*; class GFG  {   // Returns count of pairs  // whose product exists in arr[] static int countPairs(int arr[]  int n) {  int result = 0;  for (int i = 0; i < n ; i++)  {  for (int j = i + 1 ; j < n ; j++)  {  int product = arr[i] * arr[j] ;  // find product  // in an array  for (int k = 0; k < n; k++)  {  // if product found   // increment counter  if (arr[k] == product)  {  result++;  break;  }  }  }  }  // return Count of all pair   // whose product exist in array  return result; } // Driver Code public static void main (String[] args)  { int arr[] = {6 2 4 12 5 3} ; int n = arr.length; System.out.println(countPairs(arr n)); } } // This code is contributed by anuj_67. 
Python 3
# Python program to count pairs whose # product exist in array # Returns count of pairs whose  # product exists in arr[] def countPairs(arr n): result = 0; for i in range (0 n): for j in range(i + 1 n): product = arr[i] * arr[j] ; # find product in an array for k in range (0 n): # if product found increment counter if (arr[k] == product): result = result + 1; break; # return Count of all pair whose  # product exist in array return result; # Driver program arr = [6 2 4 12 5 3] ; n = len(arr); print(countPairs(arr n)); # This code is contributed # by Shivi_Aggarwal 
C#
// C# program to count pairs  // whose product exist in array  using System; class GFG { // Returns count of pairs  // whose product exists in arr[]  public static int countPairs(int[] arr   int n) {  int result = 0;  for (int i = 0; i < n ; i++)  {  for (int j = i + 1 ; j < n ; j++)  {  int product = arr[i] * arr[j];  // find product in an array   for (int k = 0; k < n; k++)  {  // if product found   // increment counter   if (arr[k] == product)  {  result++;  break;  }  }  }  }  // return Count of all pair   // whose product exist in array   return result; } // Driver Code  public static void Main(string[] args) {  int[] arr = new int[] {6 2 4 12 5 3};  int n = arr.Length;  Console.WriteLine(countPairs(arr n)); } } // This code is contributed by Shrikant13 
JavaScript
<script> // javascript program to count pairs  // whose product exist in array  // Returns count of pairs  // whose product exists in arr  function countPairs(arr n)  {  var result = 0;  for (i = 0; i < n; i++)  {  for (j = i + 1; j < n; j++)  {  var product = arr[i] * arr[j];  // find product  // in an array  for (k = 0; k < n; k++)  {    // if product found  // increment counter  if (arr[k] == product)  {  result++;  break;  }  }  }  }  // return Count of all pair  // whose product exist in array  return result;  }  // Driver Code  var arr = [ 6 2 4 12 5 3 ];  var n = arr.length;  document.write(countPairs(arr n)); // This code is contributed by Rajput-Ji </script> 
PHP
 // PHP program to count pairs // whose product exist in array // Returns count of pairs whose // product exists in arr[] function countPairs($arr $n) { $result = 0; for ($i = 0; $i < $n ; $i++) { for ($j = $i + 1 ; $j < $n ; $j++) { $product = $arr[$i] * $arr[$j] ; // find product in an array for ($k = 0; $k < $n; $k++) { // if product found increment counter if ($arr[$k] == $product) { $result++; break; } } } } // return Count of all pair whose  // product exist in array return $result; } // Driver Code $arr = array(6 2 4 12 5 3); $n = sizeof($arr); echo countPairs($arr $n); // This code is contributed // by Akanksha Rai 

Producción:  
 

3  


Complejidad del tiempo: En3)

Espacio Auxiliar: O(1)
Un Solución eficiente es utilizar 'hash' que almacena todos los elementos de la matriz. Genere todos los pares posibles de la matriz dada 'arr' y verifique que el producto de cada par esté en 'hash'. Si existe, incremente el recuento. Finalmente regresa el conteo. 
A continuación se muestra la implementación de la idea anterior. 
 

C++
// A hashing based C++ program to count pairs whose product // exists in arr[] #include   using namespace std; // Returns count of pairs whose product exists in arr[] int countPairs(int arr[]  int n) {  int result = 0;  // Create an empty hash-set that store all array element  set< int > Hash;  // Insert all array element into set  for (int i = 0 ; i < n; i++)  Hash.insert(arr[i]);  // Generate all pairs and check is exist in 'Hash' or not  for (int i = 0 ; i < n; i++)  {  for (int j = i + 1; j<n ; j++)  {  int product = arr[i]*arr[j];  // if product exists in set then we increment  // count by 1  if (Hash.find(product) != Hash.end())  result++;  }  }  // return count of pairs whose product exist in array  return result; } // Driver program int main() {  int arr[] = {6 2 4 12 5 3};  int n = sizeof(arr)/sizeof(arr[0]);  cout << countPairs(arr n) ;  return 0; } 
Java
// A hashing based Java program to count pairs whose product // exists in arr[] import java.util.*; class GFG {  // Returns count of pairs whose product exists in arr[]  static int countPairs(int arr[] int n) {  int result = 0;  // Create an empty hash-set that store all array element  HashSet< Integer> Hash = new HashSet<>();  // Insert all array element into set  for (int i = 0; i < n; i++)  {  Hash.add(arr[i]);  }  // Generate all pairs and check is exist in 'Hash' or not  for (int i = 0; i < n; i++)  {  for (int j = i + 1; j < n; j++)  {  int product = arr[i] * arr[j];  // if product exists in set then we increment  // count by 1  if (Hash.contains(product))  {  result++;  }  }  }  // return count of pairs whose product exist in array  return result;  }  // Driver program  public static void main(String[] args)   {  int arr[] = {6 2 4 12 5 3};  int n = arr.length;  System.out.println(countPairs(arr n));  } }  // This code has been contributed by 29AjayKumar 
Python3
# A hashing based C++ program to count  # pairs whose product exists in arr[] # Returns count of pairs whose product  # exists in arr[] def countPairs(arr n): result = 0 # Create an empty hash-set that  # store all array element Hash = set() # Insert all array element into set for i in range(n): Hash.add(arr[i]) # Generate all pairs and check is # exist in 'Hash' or not for i in range(n): for j in range(i + 1 n): product = arr[i] * arr[j] # if product exists in set then  # we increment count by 1 if product in(Hash): result += 1 # return count of pairs whose  # product exist in array return result # Driver Code if __name__ == '__main__': arr = [6 2 4 12 5 3] n = len(arr) print(countPairs(arr n)) # This code is contributed by # Sanjit_Prasad 
C#
// A hashing based C# program to count pairs whose product // exists in arr[] using System; using System.Collections.Generic; class GFG {  // Returns count of pairs whose product exists in arr[]  static int countPairs(int []arr int n)   {  int result = 0;  // Create an empty hash-set that store all array element  HashSet<int> Hash = new HashSet<int>();  // Insert all array element into set  for (int i = 0; i < n; i++)  {  Hash.Add(arr[i]);  }  // Generate all pairs and check is exist in 'Hash' or not  for (int i = 0; i < n; i++)  {  for (int j = i + 1; j < n; j++)  {  int product = arr[i] * arr[j];  // if product exists in set then we increment  // count by 1  if (Hash.Contains(product))  {  result++;  }  }  }  // return count of pairs whose product exist in array  return result;  }  // Driver code  public static void Main(String[] args)   {  int []arr = {6 2 4 12 5 3};  int n = arr.Length;  Console.WriteLine(countPairs(arr n));  } } /* This code contributed by PrinciRaj1992 */ 
JavaScript
<script> // A hashing based javascript program to count pairs whose product // exists in arr  // Returns count of pairs whose product exists in arr  function countPairs(arr  n) {  var result = 0;  // Create an empty hash-set that store all array element  var Hash = new Set();  // Insert all array element into set  for (i = 0; i < n; i++) {  Hash.add(arr[i]);  }  // Generate all pairs and check is exist in 'Hash' or not  for (i = 0; i < n; i++) {  for (j = i + 1; j < n; j++) {  var product = arr[i] * arr[j];  // if product exists in set then we increment  // count by 1  if (Hash.has(product)) {  result++;  }  }  }  // return count of pairs whose product exist in array  return result;  }  // Driver program    var arr = [ 6 2 4 12 5 3 ];  var n = arr.length;  document.write(countPairs(arr n)); // This code contributed by Rajput-Ji </script> 

Producción:  
 

características de una serie de pandas
3  


Complejidad del tiempo: En2) 'Bajo el supuesto, la operación de inserción y búsqueda toma O(1) Tiempo '

Espacio Auxiliar: En)

Método 3: usar un mapa desordenado

Acercarse:

1.Cree un mapa vacío para almacenar los elementos de la matriz y sus frecuencias.
2.Recorre la matriz e inserta cada elemento en el mapa junto con su frecuencia.
3.Inicialice una variable de recuento en 0 para realizar un seguimiento del número de pares.
4.Recorra la matriz nuevamente y para cada elemento verifique si tiene algún factor (que no sea él mismo) que esté presente en el mapa.
5.Si ambos factores están presentes en el mapa, incremente el recuento de pares.
6.Devuelve el recuento de pares.

Implementación:

C++
#include    using namespace std; // Function to count pairs whose product value is present in array int count_Pairs(int arr[] int n) {  map<int int> mp; // Create a map to store the elements of the array and their frequencies    // Initialize the map with the frequencies of the elements in the array  for (int i = 0; i < n; i++) {  mp[arr[i]]++;  }    int count = 0; // Initialize the count of pairs to zero    // Traverse the array and check if arr[i] has a factor in the map  for (int i = 0; i < n; i++) {  for (int j = 1; j*j <= arr[i]; j++) {  if (arr[i] % j == 0) {  int factor1 = j;  int factor2 = arr[i] / j;    // If both factors are present in the map then increment the count of pairs  if (mp.count(factor1) && mp.count(factor2)) {  if (factor1 == factor2 && mp[factor1] < 2) {  continue;  }  count++;  }  }  }  }    // Return the count of pairs  return count; } // Driver code int main() {  // Example input  int arr[] = {6 2 4 12 5 3};  int n = sizeof(arr) / sizeof(arr[0]);    // Count pairs whose product value is present in array  int count = count_Pairs(arr n);    // Print the count  cout << count << endl;    return 0; } 
Java
import java.util.HashMap; import java.util.Map; public class Main {  // Function to count pairs whose product value is  // present in the array  static int countPairs(int[] arr)  {  Map<Integer Integer> frequencyMap  = new HashMap<>();  // Initialize the map with the frequencies of the  // elements in the array  for (int num : arr) {  frequencyMap.put(  num frequencyMap.getOrDefault(num 0) + 1);  }  int count  = 0; // Initialize the count of pairs to zero  // Traverse the array and check if arr[i] has a  // factor in the map  for (int num : arr) {  for (int j = 1; j * j <= num; j++) {  if (num % j == 0) {  int factor1 = j;  int factor2 = num / j;  // If both factors are present in the  // map then increment the count of  // pairs  if (frequencyMap.containsKey(factor1)  && frequencyMap.containsKey(  factor2)) {  if (factor1 == factor2  && frequencyMap.get(factor1)  < 2) {  continue;  }  count++;  }  }  }  }  // Return the count of pairs  return count;  }  public static void main(String[] args)  {  // Example input  int[] arr = { 6 2 4 12 5 3 };  // Count pairs whose product value is present in the  // array  int count = countPairs(arr);  // Print the count  System.out.println(count);  } } 
Python
# Function to count pairs whose product value is present in the array def count_pairs(arr): # Create a dictionary to store the elements of the array and their frequencies mp = {} # Initialize the dictionary with the frequencies of the elements in the array for num in arr: if num in mp: mp[num] += 1 else: mp[num] = 1 count = 0 # Initialize the count of pairs to zero # Traverse the array and check if arr[i] has a factor in the dictionary for num in arr: for j in range(1 int(num ** 0.5) + 1): if num % j == 0: factor1 = j factor2 = num // j # If both factors are present in the dictionary  # then increment the count of pairs if factor1 in mp and factor2 in mp: if factor1 == factor2 and mp[factor1] < 2: continue count += 1 return count # Driver code if __name__ == '__main__': # Example input arr = [6 2 4 12 5 3] # Count pairs whose product value is present in the array count = count_pairs(arr) # Print the count print(count) 
C#
using System; using System.Collections.Generic; class GFG {  // Function to count pairs whose product value is  // present in array  static int CountPairs(int[] arr int n)  {  Dictionary<int int> mp = new Dictionary<  int int>(); // Create a dictionary to store the  // elements of the array and their  // frequencies  // Initialize the dictionary with the frequencies of  // the elements in the array  for (int i = 0; i < n; i++) {  if (!mp.ContainsKey(arr[i]))  mp[arr[i]] = 1;  else  mp[arr[i]]++;  }  int count  = 0; // Initialize the count of pairs to zero  // Traverse the array and check if arr[i] has a  // factor in the dictionary  for (int i = 0; i < n; i++) {  for (int j = 1; j * j <= arr[i]; j++) {  if (arr[i] % j == 0) {  int factor1 = j;  int factor2 = arr[i] / j;  // If both factors are present in the  // dictionary then increment the count  // of pairs  if (mp.ContainsKey(factor1)  && mp.ContainsKey(factor2)) {  if (factor1 == factor2  && mp[factor1] < 2) {  continue;  }  count++;  }  }  }  }  // Return the count of pairs  return count;  }  // Driver code  static void Main(string[] args)  {  // Example input  int[] arr = { 6 2 4 12 5 3 };  int n = arr.Length;  // Count pairs whose product value is present in  // array  int count = CountPairs(arr n);  // Print the count  Console.WriteLine(count);  } } 
JavaScript
// Function to count pairs whose product value is present in the array function GFG(arr) {  // Create a map to store the elements of the array   // and their frequencies  const mp = new Map();  // Initialize the map with the frequencies of the elements   // in the array  for (let i = 0; i < arr.length; i++) {  if (!mp.has(arr[i])) {  mp.set(arr[i] 0);  }  mp.set(arr[i] mp.get(arr[i]) + 1);  }  let count = 0; // Initialize the count of pairs to zero  // Traverse the array and check if arr[i] has a factor in the map  for (let i = 0; i < arr.length; i++) {  for (let j = 1; j * j <= arr[i]; j++) {  if (arr[i] % j === 0) {  const factor1 = j;  const factor2 = arr[i] / j;  // If both factors are present in the map  // then increment the count of pairs  if (mp.has(factor1) && mp.has(factor2)) {  if (factor1 === factor2 && mp.get(factor1) < 2) {  continue;  }  count++;  }  }  }  }  // Return the count of pairs  return count; } // Driver code function main() {  // Example input  const arr = [6 2 4 12 5 3];  // Count pairs whose product value is present in the array  const count = GFG(arr);  // Print the count  console.log(count); } main(); 

Producción:

    3     

Complejidad del tiempo: O(n iniciar sesión n)

Espacio Auxiliar: En)

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