# Find all permuted rows of a given row in a matrix

Last Updated : 11 Sep, 2023

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 ` `#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

## 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 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 ``=` `4` `n ``=` `4` `r ``=` `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 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

 ``

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 ` `#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

## 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 ``=` `4` `n ``=` `4` `r ``=` `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

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)

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