# Check if all rows of a Binary Matrix have all ones placed adjacently or not

Last Updated : 16 Aug, 2021

Given a binary matrix mat[][] of dimension N*M, the task is to check if all 1s in each row are placed adjacently on the given matrix. If all 1s in each row are adjacent, then print “Yes”. Otherwise, print “No”.

Examples:

Input: mat[][] = {{0, 1, 1, 0}, {1, 1, 0, 0}, {0, 0, 0, 1}, {1, 1, 1, 0}
Output: Yes
Explanation:
Elements in the first row are {0, 1, 1, 0}.
Elements in the 2nd row are {1, 1, 0, 0}.
Elements in the 3rd row are {0, 0, 0, 1}.
Elements in the 4th row are {1, 1, 1, 0}.
Therefore, all the rows have all 1s grouped together. Therefore, print Yes.

Input: mat[][] = {{1, 0, 1}, {0, 0, 1}, {0, 0, 0}}
Output: No

Approach: The idea is to perform row-wise traversal on the matrix and check if all the 1s in a row are placed adjacently or not by using the property of Bitwise XOR. The given problem can be solved based on the following observations:

• Calculate the sum of Bitwise XOR of every pair of adjacent elements of ith row, say X. All 1s will be not together in the ith row if any of the following conditions are satisfied:
• If X > 2 and mat[i][0] + mat[i][M – 1] = 0.
• If X > 1 and mat[i][0] + mat[i][M – 1] = 1.
• If X > 0 and mat[i][0] + mat[i][M – 1] = 0.

Follow the steps below to solve this problem:

• Traverse the given matrix mat[][] and perform the following operations:
• For each row, check if the value of M is less than 3, then print “Yes”.
• Otherwise, find the sum of Bitwise XOR of adjacent array elements and store it in a variable, say X.
• For every value of X, if any of the above-mentioned conditions holds true, then print “No”.
• After completing the above steps, if any of the above conditions does not hold true for any value of X, then print “No”.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ` `using` `namespace` `std;`   `// Function to check if all 1s are` `// placed adjacently in an array or not` `bool` `checkGroup(vector<``int``> arr)` `{`   `    ``// Base Case` `    ``if` `(arr.size() <= 2)` `        ``return` `true``;` `    ``int` `corner = arr[0] + arr[(``int``)arr.size()-1];`   `    ``// Stores the sum of XOR of all` `    ``// pair of adjacent elements` `    ``int` `xorSum = 0;`   `    ``// Calculate sum of XOR of all` `    ``// pair of adjacent elements` `    ``for` `(``int` `i = 0; i < arr.size() - 1; i++)` `        ``xorSum += (arr[i] ^ arr[i + 1]);`   `    ``// Check for corner cases` `    ``if` `(!corner)` `        ``if` `(xorSum > 2)` `            ``return` `false``;` `    ``else` `if` `(corner == 1)` `        ``if` `(xorSum > 1)` `            ``return` `false``;` `    ``else` `        ``if` `(xorSum > 0)` `            ``return` `false``;`   `    ``// Return true` `    ``return` `true``;` `}`   `// Function to check if all the rows` `// have all 1s grouped together or not` `bool` `isInGroupUtil(vector> mat)` `{`   `    ``// Traverse each row` `    ``for` `(``auto` `i:mat)` `    ``{`   `        ``// Check if all 1s are placed` `        ``// together in the ith row or not` `        ``if` `(!checkGroup(i))` `            ``return` `false``;` `         ``}` `    ``return` `true``;` `}`     `// Function to check if all 1s in a row` `// are grouped together in a matrix or not` `void` `isInGroup(vector> mat)` `{`   `    ``bool` `ans = isInGroupUtil(mat);`   `    ``//Print the result` `    ``if` `(ans)` `        ``printf``(``"Yes"``);` `    ``else` `        ``printf``(``"No"``);` `}`   `// Driver Code` `int` `main()` `{` `  `  `  ``// Given matrix` `  ``vector> mat = {{0, 1, 1, 0},` `                            ``{1, 1, 0, 0},` `                            ``{0, 0, 0, 1},` `                            ``{1, 1, 1, 0}};`   `  ``// Function Call` `  ``isInGroup(mat);` `}`   `// This code is contributed by mohit kumar 29.`

## Java

 `// Java program for the above approach` `import` `java.util.*;` `public` `class` `Main` `{` `    ``// Function to check if all 1s are` `    ``// placed adjacently in an array or not` `    ``static` `Boolean checkGroup(Vector arr)` `    ``{` ` `  `        ``// Base Case` `        ``if` `(arr.size() <= ``2``)` `            ``return` `true``;` `        ``int` `corner = arr.get(``0``) + arr.get(arr.size()-``1``);` ` `  `        ``// Stores the sum of XOR of all` `        ``// pair of adjacent elements` `        ``int` `xorSum = ``0``;` ` `  `        ``// Calculate sum of XOR of all` `        ``// pair of adjacent elements` `        ``for` `(``int` `i = ``0``; i < arr.size() - ``1``; i++)` `            ``xorSum += (arr.get(i) ^ arr.get(i + ``1``));` ` `  `        ``// Check for corner cases` `        ``if` `(corner == ``0``)` `            ``if` `(xorSum > ``2``)` `                ``return` `false``;` `        ``else` `if` `(corner == ``1``)` `            ``if` `(xorSum > ``1``)` `                ``return` `false``;` `        ``else` `            ``if` `(xorSum > ``0``)` `                ``return` `false``;` ` `  `        ``// Return true` `        ``return` `true``;` `    ``}` ` `  `    ``// Function to check if all the rows` `    ``// have all 1s grouped together or not` `    ``static` `Boolean isInGroupUtil(``int``[][] mat)` `    ``{` ` `  `        ``// Traverse each row` `        ``for` `(``int` `i = ``0``; i < mat.length; i++)` `        ``{` `            ``Vector arr = ``new` `Vector();` `            ``for``(``int` `j = ``0``; j < mat[i].length; j++)` `            ``{` `                ``arr.add(mat[i][j]);` `            ``}` `            ``// Check if all 1s are placed` `            ``// together in the ith row or not` `            ``if` `(!checkGroup(arr))` `                ``return` `false``;` `             ``}` `        ``return` `true``;` `    ``}` ` `  ` `  `    ``// Function to check if all 1s in a row` `    ``// are grouped together in a matrix or not` `    ``static` `void` `isInGroup(``int``[][] mat)` `    ``{` ` `  `        ``Boolean ans = isInGroupUtil(mat);` ` `  `        ``//Print the result` `        ``if` `(ans)` `            ``System.out.print(``"Yes"``);` `        ``else` `            ``System.out.print(``"No"``);` `    ``}` `    `  `    ``public` `static` `void` `main(String[] args) {` `        ``// Given matrix` `        ``int``[][] mat = {{``0``, ``1``, ``1``, ``0``},` `                   ``{``1``, ``1``, ``0``, ``0``},` `                   ``{``0``, ``0``, ``0``, ``1``},` `                   ``{``1``, ``1``, ``1``, ``0``}};` `     `  `        ``// Function Call` `        ``isInGroup(mat);` `    ``}` `}`   `// This code is contributed by decode2207.`

## Python3

 `# Python3 program for the above approach`   `# Function to check if all 1s are` `# placed adjacently in an array or not` `def` `checkGroup(arr):`   `    ``# Base Case` `    ``if` `len``(arr) <``=` `2``:` `        ``return` `True`   `    ``corner ``=` `arr[``0``] ``+` `arr[``-``1``]`   `    ``# Stores the sum of XOR of all` `    ``# pair of adjacent elements` `    ``xorSum ``=` `0`   `    ``# Calculate sum of XOR of all` `    ``# pair of adjacent elements` `    ``for` `i ``in` `range``(``len``(arr)``-``1``):` `        ``xorSum ``+``=` `(arr[i] ^ arr[i ``+` `1``])`   `    ``# Check for corner cases` `    ``if` `not` `corner:` `        ``if` `xorSum > ``2``:` `            ``return` `False` `    ``elif` `corner ``=``=` `1``:` `        ``if` `xorSum > ``1``:` `            ``return` `False` `    ``else``:` `        ``if` `xorSum > ``0``:` `            ``return` `False` `          `  `    ``# Return true` `    ``return` `True`   `# Function to check if all the rows` `# have all 1s grouped together or not` `def` `isInGroupUtil(mat):`   `    ``# Traverse each row` `    ``for` `i ``in` `mat:`   `        ``# Check if all 1s are placed` `        ``# together in the ith row or not` `        ``if` `not` `checkGroup(i):` `            ``return` `False`   `    ``return` `True`   `# Function to check if all 1s in a row` `# are grouped together in a matrix or not` `def` `isInGroup(mat):`   `    ``ans ``=` `isInGroupUtil(mat)` `    `  `    ``# Print the result` `    ``if` `ans:` `        ``print``(``"Yes"``)` `    ``else``:` `        ``print``(``"No"``)`     `# Given matrix` `mat ``=` `[[``0``, ``1``, ``1``, ``0``], [``1``, ``1``, ``0``, ``0``], ` `       ``[``0``, ``0``, ``0``, ``1``], [``1``, ``1``, ``1``, ``0``]]`   `# Function Call` `isInGroup(mat)`

## C#

 `// C# program for the above approach` `using` `System;` `using` `System.Collections.Generic;` `class` `GFG {` `    `  `    ``// Function to check if all 1s are` `    ``// placed adjacently in an array or not` `    ``static` `bool` `checkGroup(List<``int``> arr)` `    ``{` `  `  `        ``// Base Case` `        ``if` `(arr.Count <= 2)` `            ``return` `true``;` `        ``int` `corner = arr[0] + arr[arr.Count-1];` `  `  `        ``// Stores the sum of XOR of all` `        ``// pair of adjacent elements` `        ``int` `xorSum = 0;` `  `  `        ``// Calculate sum of XOR of all` `        ``// pair of adjacent elements` `        ``for` `(``int` `i = 0; i < arr.Count - 1; i++)` `            ``xorSum += (arr[i] ^ arr[i + 1]);` `  `  `        ``// Check for corner cases` `        ``if` `(corner == 0)` `            ``if` `(xorSum > 2)` `                ``return` `false``;` `        ``else` `if` `(corner == 1)` `            ``if` `(xorSum > 1)` `                ``return` `false``;` `        ``else` `            ``if` `(xorSum > 0)` `                ``return` `false``;` `  `  `        ``// Return true` `        ``return` `true``;` `    ``}` `  `  `    ``// Function to check if all the rows` `    ``// have all 1s grouped together or not` `    ``static` `bool` `isInGroupUtil(``int``[,] mat)` `    ``{` `  `  `        ``// Traverse each row` `        ``for` `(``int` `i = 0; i < mat.GetLength(1); i++)` `        ``{` `            ``List<``int``> arr = ``new` `List<``int``>();` `            ``for``(``int` `j = 0; j < mat.GetLength(0); j++)` `            ``{` `                ``arr.Add(mat[i,j]);` `            ``}` `            ``// Check if all 1s are placed` `            ``// together in the ith row or not` `            ``if` `(!checkGroup(arr))` `                ``return` `false``;` `            ``}` `        ``return` `true``;` `    ``}` `  `  `  `  `    ``// Function to check if all 1s in a row` `    ``// are grouped together in a matrix or not` `    ``static` `void` `isInGroup(``int``[,] mat)` `    ``{` `  `  `        ``bool` `ans = isInGroupUtil(mat);` `  `  `        ``//Print the result` `        ``if` `(ans)` `            ``Console.WriteLine(``"Yes"``);` `        ``else` `            ``Console.WriteLine(``"No"``);` `    ``}` `  `  `  ``// Driver code` `  ``static` `void` `Main()` `  ``{` `    `  `    ``// Given matrix` `    ``int``[,] mat = {{0, 1, 1, 0},` `               ``{1, 1, 0, 0},` `               ``{0, 0, 0, 1},` `               ``{1, 1, 1, 0}};` `  `  `    ``// Function Call` `    ``isInGroup(mat);` `  ``}` `}`   `// This code is contributed by divyeshrabadiya07.`

## Javascript

 ``

Output:

`Yes`

Time Complexity: O(N*M)
Auxiliary Space: O(1)

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