Find duplicate rows in a binary matrix

Given a binary matrix whose elements are only 0 and 1, we need to print the rows which are duplicates of rows that are already present in the matrix.

Examples: 

Input : {1, 1, 0, 1, 0, 1},
    {0, 0, 1, 0, 0, 1},
    {1, 0, 1, 1, 0, 0},
    {1, 1, 0, 1, 0, 1},
    {0, 0, 1, 0, 0, 1},
    {0, 0, 1, 0, 0, 1}.

Output :
There is a duplicate row at position: 4 
There is a duplicate row at position: 5 
There is a duplicate row at position: 6 

This problem is mainly an extension of find unique rows in a binary matrix.

A Simple Solution is to traverse all rows one by one. For every row, check if it is present anywhere else. If yes print the row. 

• Time complexity : O(ROW^2 x COL) 
• Auxiliary Space : O(1)

Optimal solution using Trie Trie is an efficient data structure used for storing and retrieval of data where the character set is small. The searching complexity is optimal as key length. 

The solution approach towards the question is to first insert the matrix in the binary trie and then if the new added row is already present in the trie then we will now that it is a duplicate row 

Implementation:

C++

// C++ program to find duplicate rows
// in a binary matrix.
#include<bits/stdc++.h>

const int MAX = 100;

/*struct the Trie*/
struct Trie
{
    bool leaf;
    Trie* children[2];
};

/*function to get Trienode*/
Trie* getNewTrieNode()
{
    Trie* node = new Trie;
    node->children[0] = node->children[1] = NULL;
    node->leaf = false;
    return node;
}

/* function to insert a row in Trie*/
bool insert(Trie*& head, bool* arr, int N)
{
    Trie* curr = head;

    for (int i = 0; i < N; i++)
    {
        /*creating a new path if it don not exist*/
        if (curr->children[arr[i]] == NULL)
            curr->children[arr[i]] = getNewTrieNode();

        curr = curr->children[arr[i]];
    }

    /*if the row already exist return false*/
    if (curr->leaf)
        return false;

    /* making leaf node tree and return true*/
    return (curr->leaf = true);
}

void printDuplicateRows(bool mat[][MAX], int M, int N)
{
    Trie* head = getNewTrieNode();

    /*inserting into Trie and checking for duplicates*/
    for (int i = 0; i < M; i++)

        // If already exists
        if (!insert(head, mat[i], N))
            printf("There is a duplicate row"
                  " at position: %d \n", i+1);

}

/*driver function to check*/
int main()
{
    bool mat[][MAX] =
    {
        {1, 1, 0, 1, 0, 1},
        {0, 0, 1, 0, 0, 1},
        {1, 0, 1, 1, 0, 0},
        {1, 1, 0, 1, 0, 1},
        {0, 0, 1, 0, 0, 1},
        {0, 0, 1, 0, 0, 1},
    };

    printDuplicateRows(mat, 6, 6);
    return 0;
}

Java

// Java program to find duplicate rows
// in a binary matrix.

class GFG
{
  static final int MAX = 100;

  static class Trie
  {
    public boolean leaf;
    public Trie children[] = new Trie[2];
  };

  //function to get Trienode/
  static Trie getNewTrieNode()
  {
    Trie node = new Trie();
    node.children[0] = null;
    node.children[1] = null;
    node.leaf = false;
    return node;
  }

  // function to insert a row in Trie/
  static boolean insert(Trie head, int[] arr, int N)
  {
    Trie curr = head;

    for (int i = 0; i < N; i++)
    {
      //creating a new path if it don not exist/
      if (curr.children[arr[i] ] == null)
        curr.children[arr[i]] = getNewTrieNode();

      curr = curr.children[arr[i]];
    }

    //if the row already exist return false/
    if (curr.leaf)
      return false;

    // making leaf node tree and return true/
    curr.leaf = true;
    return true;
  }

  static void printDuplicateRows(int[][] mat, int M, int N)
  {
    Trie head = getNewTrieNode();

    //inserting into Trie and checking for duplicates
    for (int i = 0; i < M; i++)

      // If already exists
      if (!insert(head, mat[i], N))
        System.out.printf("There is a duplicate row at position: %d \n", i+1);

  }

  // driver function to check/
  public static void main(String[] args)
  {
    int mat[][] =
    {
      {1, 1, 0, 1, 0, 1},
      {0, 0, 1, 0, 0, 1},
      {1, 0, 1, 1, 0, 0},
      {1, 1, 0, 1, 0, 1},
      {0, 0, 1, 0, 0, 1},
      {0, 0, 1, 0, 0, 1},
    };

    printDuplicateRows(mat, 6, 6);
  }
}

// This code is contributed by phasing17.

Python3

# Python3 program to find duplicate rows
# in a binary matrix.
class Trie:
    def __init__(self):
        self.leaf = False;
        self.children = [None, None]


MAX = 100;

# function to get Trienode
def getNewTrieNode():

    node = Trie();
    node.children[0] = None;
    node.children[1] = None;
    node.leaf = False;
    return node;

# function to insert a row in Trie/
def insert(head, arr, N):

    curr = head;

    for i in range(N):
        # creating a new path if it don not exist/
        if (curr.children[arr[i]] == None):
            curr.children[arr[i]] = getNewTrieNode();

        curr = curr.children[arr[i]];

    # if the row already exist return False/
    if (curr.leaf):
        return False;

    # making leaf node tree and return True/
    curr.leaf = True;
    return True;


def printDuplicateRows(mat, M, N):

    head = getNewTrieNode();

    # inserting into Trie and checking for duplicates
    for i in range(M):

        # If already exists
        if (not insert(head, mat[i], N)):
            print( "There is a duplicate row at position:", (i + 1));

# driver function to check/
mat = [
    [ 1, 1, 0, 1, 0, 1 ],
    [ 0, 0, 1, 0, 0, 1 ],
    [ 1, 0, 1, 1, 0, 0 ],
    [ 1, 1, 0, 1, 0, 1 ],
    [ 0, 0, 1, 0, 0, 1 ],
    [ 0, 0, 1, 0, 0, 1 ],
];

printDuplicateRows(mat, 6, 6);

# This code is contributed by phasing17

C#

// C# program to find duplicate rows
// in a binary matrix.
using System;
using System.Collections.Generic;

class Trie
{
    public bool leaf;
    public Trie[] children = new Trie[2];
};
class GFG
{
  static int MAX = 100;

  // function to get Trienode/
  static Trie getNewTrieNode()
  {
    Trie node = new Trie();
    node.children[0] = null;
    node.children[1] = null;
    node.leaf = false;
    return node;
  }

  // function to insert a row in Trie/
  static bool insert(Trie head, int[] arr, int N)
  {
    Trie curr = head;

    for (int i = 0; i < N; i++)
    {
      //creating a new path if it don not exist/
      if (curr.children[arr[i] ] == null)
        curr.children[arr[i]] = getNewTrieNode();

      curr = curr.children[arr[i]];
    }

    //if the row already exist return false/
    if (curr.leaf)
      return false;

    // making leaf node tree and return true/
    curr.leaf = true;
    return true;
  }

  static void printDuplicateRows(int[][] mat, int M, int N)
  {
    Trie head = getNewTrieNode();

    // inserting into Trie and checking for duplicates
    for (int i = 0; i < M; i++)

      // If already exists
      if (!insert(head, mat[i], N))
        Console.WriteLine("There is a duplicate row at position: " +  (i+1));

  }

  // driver function to check/
  public static void Main(string[] args)
  {
    int[][] mat =
    {
      new int[] {1, 1, 0, 1, 0, 1},
      new int[] {0, 0, 1, 0, 0, 1},
      new int[] {1, 0, 1, 1, 0, 0},
      new int[] {1, 1, 0, 1, 0, 1},
      new int[] {0, 0, 1, 0, 0, 1},
      new int[] {0, 0, 1, 0, 0, 1},
    };

    printDuplicateRows(mat, 6, 6);
  }
}

// This code is contributed by phasing17.

Javascript

// JS program to find duplicate rows
// in a binary matrix.

class Trie {
    constructor()
    {
        this.leaf = false;
        this.children = new Array(2);
    }
};

let MAX = 100;

// function to get Trienode/
function getNewTrieNode()
{
    let node = new Trie();
    node.children[0] = null;
    node.children[1] = null;
    node.leaf = false;
    return node;
}

// function to insert a row in Trie/
function insert(head, arr, N)
{
    let curr = head;

    for (let i = 0; i < N; i++) {
        // creating a new path if it don not exist/
        if (curr.children[arr[i]] == null)
            curr.children[arr[i]] = getNewTrieNode();

        curr = curr.children[arr[i]];
    }

    // if the row already exist return false/
    if (curr.leaf)
        return false;

    // making leaf node tree and return true/
    curr.leaf = true;
    return true;
}

function printDuplicateRows(mat, M, N)
{
    let head = getNewTrieNode();

    // inserting into Trie and checking for duplicates
    for (let i = 0; i < M; i++)

        // If already exists
        if (!insert(head, mat[i], N))
            console.log(
                "There is a duplicate row at position: "
                + (i + 1));
}

// driver function to check/
let mat = [
    [ 1, 1, 0, 1, 0, 1 ],
    [ 0, 0, 1, 0, 0, 1 ],
    [ 1, 0, 1, 1, 0, 0 ],
    [ 1, 1, 0, 1, 0, 1 ],
    [ 0, 0, 1, 0, 0, 1 ],
    [ 0, 0, 1, 0, 0, 1 ],
];

printDuplicateRows(mat, 6, 6);

// This code is contributed by phasing17.

Output

There is a duplicate row at position: 4 
There is a duplicate row at position: 5 
There is a duplicate row at position: 6 

Time Complexity: O(M*N)
Auxiliary Space: O(M*N), to build trie.

Another approach without using Trie but does not work for large number of columns :
Another approach is to convert the decimal equivalent of row and check if a new row has the same decimal equivalent then it is a duplicate row. It will not work if the number of columns is large .

Here is the implementation of the above approach.

C++

#include<iostream>
#include<vector>
#include<set>
using namespace std;
vector<int> repeatedRows(vector<vector<int>> matrix, int M, int N)
{

    set<int>s;

    // vector to store the repeated rows
    vector<int>res;

    for(int i=0;i<M;i++){
        // calculating decimal equivalent of the row
        int no=0;
        for(int j=0;j<N;j++){
            no+=(matrix[i][j]<<j);
        }

        /*
        rows with same decimal equivalent will be same,
        therefore, checking through set if the calculated equivalent was
        present before;
        if yes then add to the result otherwise insert in the set
        */
        if(s.find(no)!=s.end()){
            res.push_back(i);
        }
        else{
            s.insert(no);
        }
    }

    return res;

}
int main() {

  vector<vector<int>>matrix={
        {1, 1, 0, 1, 0, 1},
        {0, 0, 1, 0, 0, 1},
        {1, 0, 1, 1, 0, 0},
        {1, 1, 0, 1, 0, 1},
        {0, 0, 1, 0, 0, 1},
        {0, 0, 1, 0, 0, 1},};

  int m=matrix.size();
  int n=matrix[0].size();
  vector<int>res=repeatedRows(matrix,m,n);
  for(int e:res){
     cout<< "There is a duplicate row at position: "<<e+1 << '\n';
  }


    return 0;
}

Java

/*package whatever //do not write package name here */

import java.io.*;
import java.util.*;

class GFG {
  static ArrayList<Integer> repeatedRows(int[][] matrix, int M, int N)
  {

    TreeSet<Integer> s = new TreeSet<>();

    // vector to store the repeated rows
    ArrayList<Integer> res = new ArrayList<>();

    for(int i = 0; i < M; i++)
    {

      // calculating decimal equivalent of the row
      int no = 0;
      for(int j = 0; j < N; j++)
      {
        no+=(matrix[i][j]<<j);
      }

      /*
            rows with same decimal equivalent will be same,
            therefore, checking through set if the calculated equivalent was
            present before;
            if yes then add to the result otherwise insert in the set
            */
      if(s.contains(no)){
        res.add(i);
      }
      else{
        s.add(no);
      }
    }

    return res;

  }

  // Driver Code
  public static void main(String args[])
  {
    int[][] matrix={
      {1, 1, 0, 1, 0, 1},
      {0, 0, 1, 0, 0, 1},
      {1, 0, 1, 1, 0, 0},
      {1, 1, 0, 1, 0, 1},
      {0, 0, 1, 0, 0, 1},
      {0, 0, 1, 0, 0, 1}
    };

    int m = matrix.length;
    int n = matrix[0].length;
    ArrayList<Integer> res = repeatedRows(matrix,m,n);
    for(int e:res){
      System.out.println("There is a duplicate row at position: "+(e+1));
    }
  }
}

// This code is contributed by shinjanpatra

Python3

def repeatedRows(matrix, M, N):

    s = set()

    # vector to store the repeated rows
    res = []

    for i in range(M):
        # calculating decimal equivalent of the row
        no = 0
        for j in range(N):
            no += (matrix[i][j] << j)

        # rows with same decimal equivalent will be same,
        # therefore, checking through set if the calculated equivalent was
        # present before
        # if yes then add to the result otherwise insert in the set

        if(no in s):
            res.append(i)

        else:
            s.add(no)

    return res

# driver code
matrix = [
    [1, 1, 0, 1, 0, 1],
    [0, 0, 1, 0, 0, 1],
    [1, 0, 1, 1, 0, 0],
    [1, 1, 0, 1, 0, 1],
    [0, 0, 1, 0, 0, 1],
    [0, 0, 1, 0, 0, 1]
]

m = len(matrix)
n = len(matrix[0])
res = repeatedRows(matrix,m,n)
for e in res:
   print("There is a duplicate row at position: "+str(e+1))

# This code is contributed by shinjanpatra

C#

using System;
using System.Collections.Generic;

class GFG {
  static List<int> repeatedRows(int[, ] matrix, int M, int N)
  {

    HashSet<int> s = new HashSet<int>();

    // vector to store the repeated rows
    List<int> res = new List<int>();

    for(int i = 0; i < M; i++)
    {

      // calculating decimal equivalent of the row
      int no = 0;
      for(int j = 0; j < N; j++)
      {
        no+=(matrix[i, j]<<j);
      }

      /*
            rows with same decimal equivalent will be same,
            therefore, checking through set if the calculated equivalent was
            present before;
            if yes then add to the result otherwise insert in the set
            */
      if(s.Contains(no)){
        res.Add(i);
      }
      else{
        s.Add(no);
      }
    }

    return res;

  }

  // Driver Code
  public static void Main(string[] args)
  {
    int[, ] matrix={
      {1, 1, 0, 1, 0, 1},
      {0, 0, 1, 0, 0, 1},
      {1, 0, 1, 1, 0, 0},
      {1, 1, 0, 1, 0, 1},
      {0, 0, 1, 0, 0, 1},
      {0, 0, 1, 0, 0, 1}
    };

    int m = matrix.GetLength(0);
    int n = matrix.GetLength(1);
    List<int> res = repeatedRows(matrix,m,n);
    foreach (int e in res){
      Console.WriteLine("There is a duplicate row at position: "+(e+1));
    }
  }
}

// This code is contributed by phasing17

Javascript

<script>

function repeatedRows(matrix,M,N)
{

    let s = new Set();

    // vector to store the repeated rows
    let res = [];

    for(let i=0;i<M;i++){
        // calculating decimal equivalent of the row
        let no=0;
        for(let j=0;j<N;j++){
            no+=(matrix[i][j]<<j);
        }

        /*
        rows with same decimal equivalent will be same,
        therefore, checking through set if the calculated equivalent was
        present before;
        if yes then add to the result otherwise insert in the set
        */
        if(s.has(no)){
            res.push(i);
        }
        else{
            s.add(no);
        }
    }

    return res;

}

// driver code

let matrix = [
    [1, 1, 0, 1, 0, 1],
    [0, 0, 1, 0, 0, 1],
    [1, 0, 1, 1, 0, 0],
    [1, 1, 0, 1, 0, 1],
    [0, 0, 1, 0, 0, 1],
    [0, 0, 1, 0, 0, 1]
];

let m = matrix.length;
let n = matrix[0].length;
let res = repeatedRows(matrix,m,n);
for(let e of res){
   document.write("There is a duplicate row at position: "+(e+1),"</br>");
}

// This code is contributed by shinjanpatra

</script>

Output

There is a duplicate row at position: 4
There is a duplicate row at position: 5
There is a duplicate row at position: 6

Time Complexity: O(M*N)
Auxiliary Space: O(M), where M is number of rows

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