We are given an m*n matrix of positive integers and a row number. The task is to find all rows in given matrix which are permutations of given row elements. It is also given that values in every row are distinct.
Examples:
Input : mat[][] = {{3, 1, 4, 2},
{1, 6, 9, 3},
{1, 2, 3, 4},
{4, 3, 2, 1}}
row = 3
Output: 0, 2
Rows at indexes 0 and 2 are permutations of
row at index 3.
A simple solution is to one by one sort all rows and check all rows. If any row is completely equal to the given row, that means the current row is a permutation of the given row. The time complexity for this approach will be O(m*n log n).
An efficient approach is to use hashing. Simply create a hash set for the given row. After hash set creation, traverse through the remaining rows, and for every row check if all of its elements are present in the hash set or not.
Implementation:
CPP
// C++ program to find all permutations of a given row #include<bits/stdc++.h> #define MAX 100 using namespace std; // Function to find all permuted rows of a given row r void permutatedRows(int mat[][MAX], int m, int n, int r) { // Creating an empty set unordered_set<int> s; // Count frequencies of elements in given row r for (int j=0; j<n; j++) s.insert(mat[r][j]); // Traverse through all remaining rows for (int i=0; i<m; i++) { // we do not need to check for given row r if (i==r) continue; // initialize hash i.e; count frequencies // of elements in row i int j; for (j=0; j<n; j++) if (s.find(mat[i][j]) == s.end()) break; if (j != n) continue; cout << i << ", "; } } // Driver program to run the case int main() { int m = 4, n = 4,r = 3; int mat[][MAX] = {{3, 1, 4, 2}, {1, 6, 9, 3}, {1, 2, 3, 4}, {4, 3, 2, 1}}; permutatedRows(mat, m, n, r); return 0; } |
Java
// Java program to find all permutations of a given row import java.util.*; class GFG { static int MAX = 100; // Function to find all permuted rows of a given row r static void permutatedRows(int mat[][], int m, int n, int r) { // Creating an empty set LinkedHashSet<Integer> s = new LinkedHashSet<>(); // Count frequencies of elements in given row r for (int j = 0; j < n; j++) s.add(mat[r][j]); // Traverse through all remaining rows for (int i = 0; i < m; i++) { // we do not need to check for given row r if (i == r) continue; // initialize hash i.e; count frequencies // of elements in row i int j; for (j = 0; j < n; j++) if (!s.contains(mat[i][j])) break; if (j != n) continue; System.out.print(i+", "); } } // Driver program to run the case public static void main(String[] args) { int m = 4, n = 4,r = 3; int mat[][] = {{3, 1, 4, 2}, {1, 6, 9, 3}, {1, 2, 3, 4}, {4, 3, 2, 1}}; permutatedRows(mat, m, n, r); } } // This code has been contributed by 29AjayKumar |
Python3
# Python program to find all # permutations of a given row # Function to find all # permuted rows of a given row r def permutatedRows(mat, m, n, r): # Creating an empty set s=set() # Count frequencies of # elements in given row r for j in range(n): s.add(mat[r][j]) # Traverse through all remaining rows for i in range(m): # we do not need to check # for given row r if i == r: continue # initialize hash i.e # count frequencies # of elements in row i for j in range(n): if mat[i][j] not in s: # to avoid the case when last # element does not match j = j - 2 break; if j + 1 != n: continue print(i) # Driver program to run the case m = 4n = 4r = 3mat = [[3, 1, 4, 2], [1, 6, 9, 3], [1, 2, 3, 4], [4, 3, 2, 1]] permutatedRows(mat, m, n, r) # This code is contributed # by Upendra Singh Bartwal. |
C#
// C# program to find all permutations of a given row using System; using System.Collections.Generic; class GFG { static int MAX = 100; // Function to find all permuted rows of a given row r static void permutatedRows(int [,]mat, int m, int n, int r) { // Creating an empty set HashSet<int> s = new HashSet<int>(); // Count frequencies of elements in given row r for (int j = 0; j < n; j++) s.Add(mat[r, j]); // Traverse through all remaining rows for (int i = 0; i < m; i++) { // we do not need to check for given row r if (i == r) continue; // initialize hash i.e; count frequencies // of elements in row i int j; for (j = 0; j < n; j++) if (!s.Contains(mat[i,j])) break; if (j != n) continue; Console.Write(i+", "); } } // Driver program to run the case public static void Main(String[] args) { int m = 4, n = 4,r = 3; int [,]mat = {{3, 1, 4, 2}, {1, 6, 9, 3}, {1, 2, 3, 4}, {4, 3, 2, 1}}; permutatedRows(mat, m, n, r); } } /* This code contributed by PrinciRaj1992 */ |
Javascript
<script> // Javascript program to find all permutations of a given row let MAX = 100; // Function to find all permuted rows of a given row r function permutatedRows(mat, m, n, r) { // Creating an empty set let s = new Set(); // Count frequencies of elements in given row r for (let j = 0; j < n; j++) s.add(mat[r][j]); // Traverse through all remaining rows for (let i = 0; i < m; i++) { // we do not need to check for given row r if (i == r) continue; // initialize hash i.e; count frequencies // of elements in row i let j; for (j = 0; j < n; j++) if (!s.has(mat[i][j])) break; if (j != n) continue; document.write(i+", "); } } // Driver program let m = 4, n = 4,r = 3; let mat = [[ 3, 1, 4, 2], [1, 6, 9, 3], [1, 2, 3, 4], [4, 3, 2, 1]]; permutatedRows(mat, m, n, r); </script> |
Output
0, 2,
Time complexity: O(m*n)
Auxiliary space: O(n)
Another approach to the solution is using the Standard Template Library(STL):
CPP
// C++ program to find all permutations of a given row #include<bits/stdc++.h> #define MAX 100 using namespace std; // Function to find all permuted rows of a given row r void permutatedRows(int mat[][MAX], int m, int n, int r) { for (int i=0; i<m&&i!=r; i++){ if(is_permutation(mat[i],mat[i]+n,mat[r])) cout<<i<<","; } } // Driver program to run the case int main() { int m = 4, n = 4,r = 3; int mat[][MAX] = {{3, 1, 4, 2}, {1, 6, 9, 3}, {1, 2, 3, 4}, {4, 3, 2, 1}}; permutatedRows(mat, m, n, r); return 0; } |
Java
// Java program to find all permutations of a given row import java.util.*; class gfg { // This function checks if two arrays are permutations // of each other static boolean is_permutation(int[] a, int[] b) { Arrays.sort(a); Arrays.sort(b); for (int i = 0; i < a.length; i++) { if (a[i] != b[i]) return false; } return true; } // Function to find all permuted rows of a given row r static void permutatedRows(int[][] mat, int m, int n, int r) { for (var i = 0; i < m && i != r; i++) { if (is_permutation(mat[i], mat[r])) System.out.print(i + ","); } } // Driver program to run the case public static void main(String[] args) { int m = 4, n = 4, r = 3; int[][] mat = { { 3, 1, 4, 2 }, { 1, 6, 9, 3 }, { 1, 2, 3, 4 }, { 4, 3, 2, 1 } }; permutatedRows(mat, m, n, r); } } // This code is contributed by karandeep1234 |
Python3
# Python3 program to find all permutations of a given row MAX = 100 # This function checks if two arrays are permutations of each other def is_permutation(a, b): return sorted(a) == sorted(b) # Function to find all permuted rows of a given row r def permutatedRows(mat, m, n, r): for i in range(min(m, r)): if is_permutation(mat[i], mat[r]): print(i, end = ", ") # Driver program to run the case m = 4n = 4r = 3; mat = [[ 3, 1, 4, 2], [1, 6, 9, 3], [1, 2, 3, 4], [4, 3, 2, 1]]; permutatedRows(mat, m, n, r); # This code is contributed by phasing17 |
C#
// C# program to find all permutations of a given row using System; using System.Collections.Generic; class gfg { // This function checks if two arrays are permutations // of each other static bool is_permutation(int[] a, int[] b) { Array.Sort(a); Array.Sort(b); for (int i = 0; i < a.Length; i++) { if (a[i] != b[i]) return false; } return true; } // Function to find all permuted rows of a given row r static void permutatedRows(int[][] mat, int m, int n, int r) { for (var i = 0; i < m && i != r; i++) { if (is_permutation(mat[i], mat[r])) Console.Write(i + ","); } } // Driver program to run the case public static void Main(string[] args) { int m = 4, n = 4, r = 3; int[][] mat = { new [] { 3, 1, 4, 2 }, new [] { 1, 6, 9, 3 }, new [] { 1, 2, 3, 4 }, new [] { 4, 3, 2, 1 } }; permutatedRows(mat, m, n, r); } } // This code is contributed by phasing17 |
Javascript
// JS program to find all permutations of a given row let MAX = 100 // This function checks if two arrays are permutations of each other function is_permutation(a, b) { a.sort() b.sort() return (a.join("#")) == (b.join("#")) } // Function to find all permuted rows of a given row r function permutatedRows(mat, m, n, r) { for (var i=0; i<m&&i!=r; i++){ if(is_permutation(mat[i], mat[r])) process.stdout.write(i + ","); } } // Driver program to run the case let m = 4, n = 4,r = 3; let mat = [[ 3, 1, 4, 2], [1, 6, 9, 3], [1, 2, 3, 4], [4, 3, 2, 1]]; permutatedRows(mat, m, n, r); // This code is contributed by phasing17. |
Output
0,2,
Time Complexity: O(m*n), where m is the number of rows and n is the size of each row. We need to compare each row with the given row, so the time complexity is O(m*n).
Auxiliary Space : O(1). No extra space is used.
Exercise :
Extend the above solution to work for an input matrix where all elements of a row don’t have to be distinct. (Hit: We can use Hash Map instead of a Hash Set)
This article is contributed by Shashank Mishra . If you like neveropen and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the neveropen main page and help other Geeks.
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