Given a binary matrix **mat[][]** of dimension **N*M**, the task is to check if all **1**s in each row are placed adjacently on the given matrix. If all **1**s 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:YesExplanation:

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 **1**s 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
**i**row, say^{th}**X**. All**1s**will be not together in the**i**row if any of the following conditions are satisfied:^{th}- 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**.

- If

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”**.

- For each row, check if the value of
- 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 <bits/stdc++.h>` `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<vector<` `int` `>> 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<vector<` `int` `>> mat)` `{` ` ` `bool` `ans = isInGroupUtil(mat);` ` ` `//Print the result` ` ` `if` `(ans)` ` ` `printf` `(` `"Yes"` `);` ` ` `else` ` ` `printf` `(` `"No"` `);` `}` `// Driver Code` `int` `main()` `{` ` ` ` ` `// Given matrix` ` ` `vector<vector<` `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 mohit kumar 29.` |

## 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)` |

**Output:**

Yes

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

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