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عد جميع الأزواج مع XOR معين

بمعلومية مصفوفة من الأعداد الصحيحة الموجبة المميزة ورقم x، أوجد عدد أزواج الأعداد الصحيحة في المصفوفة التي يساوي XOR فيها x. 

أمثلة:  

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 

أ حل بسيط هو اجتياز كل عنصر والتحقق مما إذا كان هناك رقم آخر يساوي XOR معه x. يأخذ هذا الحل O(n2) وقت.  ان حل فعال لهذه المشكلة يستغرق O(n) الوقت. تعتمد الفكرة على حقيقة أن arr[i] ^ arr[j] يساوي x إذا وفقط إذا كان arr[i] ^ x يساوي 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.

تطبيق:

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> 

الإخراج
Count of pairs with given XOR = 1

التعقيد الزمني : على)
المساحة المساعدة: O(n)

كيفية التعامل مع التكرارات؟  
لا يعمل الحل الفعال أعلاه في حالة وجود نسخ مكررة في مصفوفة الإدخال. على سبيل المثال، ينتج عن الحل أعلاه نتائج مختلفة لـ {2 2 5} و{5 2 2}. للتعامل مع التكرارات، نقوم بتخزين عدد مرات ظهور جميع العناصر. نستخدم unordered_map بدلاً من unordered_set.  

تطبيق:

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> 

الإخراج
Count of pairs with given XOR = 1

التعقيد الزمني : O(n)
المساحة المساعدة: O(n)