Given an array of pairs, find all symmetric pairs in it

Two pairs (a, b) and (c, d) are said to be symmetric if c is equal to b and a is equal to d. For example, (10, 20) and (20, 10) are symmetric. Given an array of pairs find all symmetric pairs in it.

It may be assumed that the first elements of all pairs are distinct.

Example:

Input: arr[] = {{11, 20}, {30, 40}, {5, 10}, {40, 30}, {10, 5}}
Output: Following pairs have symmetric pairs
        (30, 40)
        (5, 10)

We strongly recommend you to minimize your browser and try this yourself first.

A Simple Solution is to go through every pair, and check every other pair for symmetric. This solution requires O(n²) time.

A Better Solution is to use sorting. Sort all pairs by the first element. For every pair, do a binary search for the second element in the given array, i.e., check if the second element of this pair exists as the first element in the array. If found, then compare the first element of pair with the second element. Time Complexity of this solution is O(nLogn).

An Efficient Solution is to use Hashing. The first element of pair is used as key and the second element is used as the value. The idea is to traverse all pairs one by one. For every pair, check if its second element is in the hash table. If yes, then compare the first element with the value of the matched entry of the hash table. If the value and the first element match, then we found symmetric pairs. Else, insert the first element as a key and second element as value.

Following is the implementation of this idea.

C/C++

#include<bits/stdc++.h> 
using namespace std; 
  
// A C++ program to find all symmetric pairs in a given array of pairs 
// Print all pairs that have a symmetric counterpart 
void findSymPairs(int arr[][2], int row) 
{ 
    // Creates an empty hashMap hM 
    unordered_map<int, int> hM; 
  
    // Traverse through the given array 
    for (int i = 0; i < row; i++) 
    { 
        // First and second elements of current pair 
        int first = arr[i][0]; 
        int sec   = arr[i][1]; 
  
        // If found and value in hash matches with first 
        // element of this pair, we found symmetry 
        if (hM.find(sec) != hM.end() && hM[sec] == first) 
            cout << "(" << sec << ", " << first << ")" <<endl; 
  
        else  // Else put sec element of this pair in hash 
            hM[first] = sec; 
    } 
} 
  
// Driver method 
int main() 
{ 
    int arr[5][2]; 
    arr[0][0] = 11; arr[0][1] = 20; 
    arr[1][0] = 30; arr[1][1] = 40; 
    arr[2][0] = 5;  arr[2][1] = 10; 
    arr[3][0] = 40;  arr[3][1] = 30; 
    arr[4][0] = 10;  arr[4][1] = 5; 
    findSymPairs(arr, 5); 
} 
  
//This is contributed by Chhavi 

Java

// A Java program to find all symmetric pairs in a given array of pairs 
import java.util.HashMap; 
   
class SymmetricPairs { 
   
    // Print all pairs that have a symmetric counterpart 
    static void findSymPairs(int arr[][]) 
    { 
        // Creates an empty hashMap hM 
        HashMap<Integer, Integer> hM = new HashMap<Integer, Integer>(); 
   
        // Traverse through the given array 
        for (int i = 0; i < arr.length; i++) 
        { 
            // First and second elements of current pair 
            int first = arr[i][0]; 
            int sec   = arr[i][1]; 
              
            // Look for second element of this pair in hash 
            Integer val = hM.get(sec); 
   
            // If found and value in hash matches with first 
            // element of this pair, we found symmetry 
            if (val != null && val == first) 
               System.out.println("(" + sec + ", " + first + ")"); 
                 
            else  // Else put sec element of this pair in hash 
               hM.put(first, sec); 
        } 
    } 
   
    // Driver method 
    public static void main(String arg[]) 
    { 
        int arr[][] = new int[5][2]; 
        arr[0][0] = 11; arr[0][1] = 20; 
        arr[1][0] = 30; arr[1][1] = 40; 
        arr[2][0] = 5;  arr[2][1] = 10; 
        arr[3][0] = 40;  arr[3][1] = 30; 
        arr[4][0] = 10;  arr[4][1] = 5; 
        findSymPairs(arr); 
    } 
} 

Python3

# A Python3 program to find all symmetric  
# pairs in a given array of pairs. 
  
# Print all pairs that have 
# a symmetric counterpart 
def findSymPairs(arr, row): 
  
    # Creates an empty hashMap hM 
    hM = dict() 
  
    # Traverse through the given array 
    for i in range(row): 
          
        # First and second elements  
        # of current pair 
        first = arr[i][0] 
        sec = arr[i][1] 
  
        # If found and value in hash matches with first 
        # element of this pair, we found symmetry 
        if (sec in hM.keys() and hM[sec] == first): 
            print("(", sec,",", first, ")") 
  
        else: # Else put sec element of 
              # this pair in hash 
            hM[first] = sec 
  
# Driver Code 
if __name__ == '__main__': 
    arr = [[0 for i in range(2)]  
              for i in range(5)] 
    arr[0][0], arr[0][1] = 11, 20
    arr[1][0], arr[1][1] = 30, 40
    arr[2][0], arr[2][1] = 5, 10
    arr[3][0], arr[3][1] = 40, 30
    arr[4][0], arr[4][1] = 10, 5
    findSymPairs(arr, 5) 
  
# This code is contributed by Mohit Kumar 

C#

// C# program to find all symmetric  
// pairs in a given array of pairs  
using System; 
using System.Collections.Generic; 
  
public class SymmetricPairs  
{ 
  
    // Print all pairs that have a symmetric counterpart 
    static void findSymPairs(int [,]arr) 
    { 
        // Creates an empty hashMap hM 
        Dictionary<int,int> hM = new Dictionary<int,int>(); 
        int val = 0; 
          
        // Traverse through the given array 
        for (int i = 0; i < arr.GetLength(0); i++) 
        { 
            // First and second elements of current pair 
            int first = arr[i, 0]; 
            int sec = arr[i, 1]; 
              
            // Look for second element of this pair in hash 
            if(hM.ContainsKey(sec)) 
            val = hM[sec]; 
              
  
            // If found and value in hash matches with first 
            // element of this pair, we found symmetry 
            if (val != 0 && val == first) 
            Console.WriteLine("(" + sec + ", " + first + ")"); 
                  
            else // Else put sec element of this pair in hash 
            hM.Add(first, sec); 
        } 
    } 
  
    // Driver code 
    public static void Main(String []arg) 
    { 
        int [,]arr = new int[5, 2]; 
        arr[0, 0] = 11; arr[0, 1] = 20; 
        arr[1, 0] = 30; arr[1, 1] = 40; 
        arr[2, 0] = 5; arr[2, 1] = 10; 
        arr[3, 0] = 40; arr[3, 1] = 30; 
        arr[4, 0] = 10; arr[4, 1] = 5; 
        findSymPairs(arr); 
    } 
} 
  
// This code has been contributed by 29AjayKumar 

Output:

Following pairs have symmetric pairs
(30, 40)
(5, 10)

Time Complexity of this solution is O(n) under the assumption that hash search and insert methods work in O(1) time.

This article is contributed by Shivam Agrawal. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.

My Personal Notes

C/C++

Java

Python3

C#

Recommended Posts: