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Tæl alle par med givet XOR

Givet en matrix af distinkte positive heltal og et tal x find antallet af par heltal i matrixen, hvis XOR er lig med x. 

Eksempler:  

Input : arr[] = {5 4 10 15 7 6} x = 5 Output : 1 Explanation : (10 ^ 15) = 5 Input : arr[] = {3 6 8 10 15 50} x = 5 Output : 2 Explanation : (3 ^ 6) = 5 and (10 ^ 15) = 5 

EN Simpel løsning er at krydse hvert element og kontrollere, om der er et andet tal, hvis XOR med det er lig med x. Denne løsning tager O(n2) tid.  An effektiv løsning til dette problem tager O(n) tid. Ideen er baseret på det faktum, at arr[i] ^ arr[j] er lig med x hvis og kun hvis arr[i] ^ x er lig med arr[j].  



1) Initialize result as 0. 2) Create an empty hash set 's'. 3) Do following for each element arr[i] in arr[] (a) If x ^ arr[i] is in 's' then increment result by 1. (b) Insert arr[i] into the hash set 's'. 3) return result.

Implementering:

C++
// C++ program to Count all pair with given XOR // value x #include   using namespace std; // Returns count of pairs in arr[0..n-1] with XOR // value equals to x. int xorPairCount(int arr[] int n int x) {  int result = 0; // Initialize result  // create empty set that stores the visiting   // element of array.   // Refer below post for details of unordered_set  // https://www.geeksforgeeks.org/cpp/unordered_set-in-cpp-stl/  unordered_set<int> s;  for (int i=0; i<n ; i++)  {  // If there exist an element in set s  // with XOR equals to x^arr[i] that means  // there exist an element such that the  // XOR of element with arr[i] is equal to  // x then increment count.  if (s.find(x^arr[i]) != s.end())  result++;  // Make element visited  s.insert(arr[i]);  }  // return total count of pairs with XOR equal to x  return result; } // driver program int main() {  int arr[] = {5  4 10 15 7 6};  int n = sizeof(arr)/sizeof(arr[0]);  int x = 5;  cout << 'Count of pairs with given XOR = '  << xorPairCount(arr n x);  return 0; } 
Java
// Java program to Count all pair with  // given XOR value x  import java.util.*; class GFG  {  // Returns count of pairs in arr[0..n-1] with XOR   // value equals to x.   static int xorPairCount(int arr[] int n int x)   {  int result = 0; // Initialize result   // create empty set that stores the visiting   // element of array.   // Refer below post for details of unordered_set   // https://www.geeksforgeeks.org/cpp/unordered_set-in-cpp-stl/   HashSet<Integer> s = new HashSet<Integer>();  for (int i = 0; i < n; i++)   {  // If there exist an element in set s   // with XOR equals to x^arr[i] that means   // there exist an element such that the   // XOR of element with arr[i] is equal to   // x then increment count.   if (s.contains(x ^ arr[i]) &&   (x ^ arr[i]) == (int) s.toArray()[s.size() - 1])   {  result++;  }  // Make element visited   s.add(arr[i]);  }  // return total count of   // pairs with XOR equal to x   return result;  }  // Driver code   public static void main(String[] args)   {  int arr[] = {5 4 10 15 7 6};  int n = arr.length;  int x = 5;  System.out.print('Count of pairs with given XOR = '  + xorPairCount(arr n x));  } } // This code contributed by Rajput-Ji 
Python3
# Python3 program to count all the pair  # with given xor # Returns count of pairs in arr[0..n-1]  # with XOR value equals to x. def xorPairCount(arr n x): result = 0 # Initialize result # create empty set that stores the  # visiting element of array.  s = set() for i in range(0 n): # If there exist an element in set s # with XOR equals to x^arr[i] that  # means there exist an element such  # that the XOR of element with arr[i]  # is equal to x then increment count. if(x ^ arr[i] in s): result = result + 1 # Make element visited s.add(arr[i]) return result # Driver Code if __name__ == '__main__': arr = [5 4 10 15 7 6] n = len(arr) x = 5 print('Count of pair with given XOR = ' + str(xorPairCount(arr n x))) # This code is contributed by Anubhav Natani 
C#
// C# program to Count all pair with  // given XOR value x  using System; using System.Collections.Generic; class GFG  {  // Returns count of pairs in arr[0..n-1] with XOR   // value equals to x.   static int xorPairCount(int []arr int n int x)   {  int result = 0; // Initialize result   // create empty set that stores the visiting   // element of array.   // Refer below post for details of unordered_set   // https://www.geeksforgeeks.org/cpp/unordered_set-in-cpp-stl/   HashSet<int> s = new HashSet<int>();  for (int i = 0; i < n; i++)   {  // If there exist an element in set s   // with XOR equals to x^arr[i] that means   // there exist an element such that the   // XOR of element with arr[i] is equal to   // x then increment count.   if (s.Contains(x ^ arr[i]))   {  result++;  }  // Make element visited   s.Add(arr[i]);  }  // return total count of   // pairs with XOR equal to x   return result;  }  // Driver code   public static void Main()   {  int []arr = {5 4 10 15 7 6};  int n = arr.Length;  int x = 5;  Console.WriteLine('Count of pairs with given XOR = '  + xorPairCount(arr n x));  } } /* This code contributed by PrinciRaj1992 */ 
JavaScript
<script> // Javascript program to Count all pair with  // given XOR value x     // Returns count of pairs in arr[0..n-1] with XOR   // value equals to x.   function xorPairCount(arrnx)  {  let result = 0; // Initialize result     // create empty set that stores the visiting   // element of array.   // Refer below post for details of unordered_set   // https://www.geeksforgeeks.org/cpp/unordered_set-in-cpp-stl/   let s = new Set();    for (let i = 0; i < n; i++)   {  // If there exist an element in set s   // with XOR equals to x^arr[i] that means   // there exist an element such that the   // XOR of element with arr[i] is equal to   // x then increment count.   if (s.has(x ^ arr[i]) )   {  result++;  }    // Make element visited   s.add(arr[i]);  }    // return total count of   // pairs with XOR equal to x   return result;  }    // Driver code   let arr=[5 4 10 15 7 6];  let n = arr.length;  let x = 5;  document.write('Count of pairs with given XOR = '  + xorPairCount(arr n x));      // This code is contributed by unknown2108 </script> 

Produktion
Count of pairs with given XOR = 1

Tidskompleksitet: På)
Hjælpeplads: O(n)

Hvordan håndterer man dubletter?  
Ovenstående effektive løsning virker ikke, hvis der er dubletter i input-arrayet. For eksempel giver ovenstående løsning forskellige resultater for {2 2 5} og {5 2 2}. For at håndtere dubletter gemmer vi tællinger af forekomster af alle elementer. Vi bruger unordered_map i stedet for unordered_set.  

Implementering:

C++
// C++ program to Count all pair with given XOR // value x #include   using namespace std; // Returns count of pairs in arr[0..n-1] with XOR // value equals to x. int xorPairCount(int arr[] int n int x) {  int result = 0; // Initialize result  // create empty map that stores counts of  // individual elements of array.  unordered_map<int int> m;  for (int i=0; i<n ; i++)  {  int curr_xor = x^arr[i];  // If there exist an element in map m  // with XOR equals to x^arr[i] that means  // there exist an element such that the  // XOR of element with arr[i] is equal to  // x then increment count.  if (m.find(curr_xor) != m.end())  result += m[curr_xor];  // Increment count of current element  m[arr[i]]++;  }  // return total count of pairs with XOR equal to x  return result; } // driver program int main() {  int arr[] = {2 5 2};  int n = sizeof(arr)/sizeof(arr[0]);  int x = 0;  cout << 'Count of pairs with given XOR = '  << xorPairCount(arr n x);  return 0; } 
Java
// Java program to Count all pair with given XOR // value x import java.util.*; class GFG { // Returns count of pairs in arr[0..n-1] with XOR // value equals to x. static int xorPairCount(int arr[] int n int x) {  int result = 0; // Initialize result  // create empty map that stores counts of  // individual elements of array.  Map<IntegerInteger> m = new HashMap<>();  for (int i = 0; i < n ; i++)  {  int curr_xor = x^arr[i];  // If there exist an element in map m  // with XOR equals to x^arr[i] that means  // there exist an element such that the  // XOR of element with arr[i] is equal to  // x then increment count.  if (m.containsKey(curr_xor))  result += m.get(curr_xor);  // Increment count of current element  if(m.containsKey(arr[i]))  {  m.put(arr[i] m.get(arr[i]) + 1);  }  else{  m.put(arr[i] 1);  }  }  // return total count of pairs with XOR equal to x  return result; } // Driver code public static void main(String[] args)  {  int arr[] = {2 5 2};  int n = arr.length;  int x = 0;  System.out.println('Count of pairs with given XOR = '  + xorPairCount(arr n x)); } } // This code has been contributed by 29AjayKumar 
Python3
# Python3 program to Count all pair with  # given XOR value x # Returns count of pairs in arr[0..n-1]  # with XOR value equals to x. def xorPairCount(arr n x): result = 0 # Initialize result # create empty map that stores counts  # of individual elements of array. m = dict() for i in range(n): curr_xor = x ^ arr[i] # If there exist an element in map m # with XOR equals to x^arr[i] that # means there exist an element such that  # the XOR of element with arr[i] is equal  # to x then increment count. if (curr_xor in m.keys()): result += m[curr_xor] # Increment count of current element if arr[i] in m.keys(): m[arr[i]] += 1 else: m[arr[i]] = 1 # return total count of pairs # with XOR equal to x return result # Driver Code arr = [2 5 2] n = len(arr) x = 0 print('Count of pairs with given XOR = ' xorPairCount(arr n x)) # This code is contributed by Mohit Kumar 
C#
// C# program to Count all pair with given XOR // value x using System;  using System.Collections.Generic; class GFG { // Returns count of pairs in arr[0..n-1] with XOR // value equals to x. static int xorPairCount(int []arr int n int x) {  int result = 0; // Initialize result  // create empty map that stores counts of  // individual elements of array.  Dictionary<intint> m = new Dictionary<intint>();  for (int i = 0; i < n ; i++)  {  int curr_xor = x^arr[i];  // If there exist an element in map m  // with XOR equals to x^arr[i] that means  // there exist an element such that the  // XOR of element with arr[i] is equal to  // x then increment count.  if (m.ContainsKey(curr_xor))  result += m[curr_xor];  // Increment count of current element  if(m.ContainsKey(arr[i]))  {  var val = m[arr[i]];  m.Remove(arr[i]);  m.Add(arr[i] val + 1);  }  else  {  m.Add(arr[i] 1);  }  }    // return total count of pairs with XOR equal to x  return result; } // Driver code public static void Main(String[] args)  {  int []arr = {2 5 2};  int n = arr.Length;  int x = 0;  Console.WriteLine('Count of pairs with given XOR = '  + xorPairCount(arr n x)); } } // This code has been contributed by 29AjayKumar 
JavaScript
<script> // Javascript program to Count all pair with given XOR // value x // Returns count of pairs in arr[0..n-1] with XOR // value equals to x. function xorPairCount(arr n x) {  let result = 0; // Initialize result    // create empty map that stores counts of  // individual elements of array.  let m = new Map();    for (let i = 0; i < n ; i++)  {  let curr_xor = x^arr[i];    // If there exist an element in map m  // with XOR equals to x^arr[i] that means  // there exist an element such that the  // XOR of element with arr[i] is equal to  // x then increment count.  if (m.has(curr_xor))  result += m.get(curr_xor);    // Increment count of current element  if(m.has(arr[i]))  {  m.set(arr[i] m.get(arr[i]) + 1);  }  else{  m.set(arr[i] 1);  }  }  // return total count of pairs with XOR equal to x  return result; } // Driver program   let arr = [2 5 2];  let n = arr.length;  let x = 0;  document.write('Count of pairs with given XOR = '  + xorPairCount(arr n x));   </script> 

Produktion
Count of pairs with given XOR = 1

Tidskompleksitet: O(n)
Hjælpeplads: O(n)