Checks whether there are T consecutive blocks of 0's in the given binary matrix

Introduction

Binary matrices are widely used in computer science and various fields to effectively represent data or solve complex problems. In some cases, it becomes important to identify whether a given binary matrix contains consecutive blocks of zeros. In this article, we will explore an elegant solution using C code that allows us to detect the presence of T consecutive blocks of zeros in a given binary matrix. This approach is both intuitive and efficient, making it suitable for practical implementation.

Check whether there are T consecutive 0 blocks

Given a two-dimensional binary matrix of dimensions N x M and integers T, we need to determine whether there are T consecutive blocks of zeros in the matrix (where "contiguous" means adjacent horizontally or vertically). To achieve this, let's break down the process step by step using logical and algorithmic methods.

Input verification

Before delving deeper into exploring patterns in a binary matrix, it is important to verify the appropriate size and relevant characteristics of the user input. We must ensure that T is within an acceptable range to provide feasible results while maintaining computational efficiency

Traverse rows and columns

In order to efficiently determine consecutive blocks of zeros, we must analyze rows and columns separately. For example, starting from the first row (topmost), we will iterate through all elements column-wise until row N (bottommost). Traversing columns simultaneously helps capture horizontal and vertical sequences naturally without missing any potential combinations

Detect continuous blocks

Identifying consecutive zeros forms the cornerstone of detecting blocks of consecutive zeros as we iterate through each column of each row.

A binary matrix is ​​an array consisting only of 0s and 1s, where each element represents the "off" or "on" state respectively. By analyzing these two states, we can identify unique patterns that may provide correlations or unique arrangements between adjacent elements.

Example

Binary matrices are treated as,

1 0 0 0 1
1 0 0 0 1
1 1 1 1 1
1 0 0 0 1

We need to find the number of consecutive zero blocks in the matrix. The value of T is 3.

We can use depth-first search (DFS) to find consecutive blocks of zeros in a matrix. We first iterate over the matrix by rows and columns. If we encounter a zero element that has not been accessed before, we push it onto the stack and start DFS from that element.

During the DFS process, we check the four adjacent cells (upper, lower, left, right) of the current cell. If any of these cells are zero and have not been accessed before, we push them onto the stack and continue DFS from that cell.

We also keep track of the number of consecutive zero blocks encountered so far. If this count is greater than or equal to T, we return "yes". Otherwise, we continue DFS until all cells have been visited

In this case, we do a depth-first search (DFS) starting from cell (0,1). We encounter two more zero elements at (0,2) and (0,3) and add them to our current path. We then backtrack to cell (0,1) and check its neighboring cells. We encounter another zero element at (1,1) and add it to our current path. Then we backtrack to cell (0,1) again and check its neighboring cells. We have not encountered any zero elements that have not been visited yet

Then we start DFS from cell (3,1). We encounter two more zero elements at (3,2) and (3,3) and add them to our current path. We then backtrack to cell (3,1) and check its neighboring cells. We will never encounter a zero element that has not been visited before.

We have now found three consecutive blocks of zeros in the matrix. Since this count is greater than or equal to T=3, the output is "Yes"

Method 1: C code checks whether there are T consecutive 0 blocks

To achieve our goal, we can utilize graph traversal techniques on a binary matrix while keeping track of visited cells. We will use the Depth First Search (DFS) algorithm combined with the backtracking principle.

algorithm

Step 1: Initialize necessary variables, such as defining constants `N` and `M` to represent the size of the input binary matrix, declaring auxiliary Boolean arrays 'visited' and 'inCurrentPath', each array's of size N x M and initially sets all elements in both arrays to false

Step 2: Implement the DFS function and include the main function

Step 3: Depending on the input binary matrix, the output is printed as yes or no.

Example

#include<iostream>
#include<stack>
#include<bitset>

#define N 100
#define M 100

struct Node {
   int i;
   int j;
};

bool DFS(bool matrix[], int rows, int cols, int T)
{
   if(matrix == nullptr || rows <= 0 || cols <= 0 || T <= 0) // check for invalid input
      return false;

   std::bitset<N*M> visited; // declare bitset to mark visited cells
   std::bitset<N*M> inCurrentPath; // declare bitset to mark cells in current path
   std::stack<Node> s; // declare stack to store nodes for DFS

   for(int i=0;i<rows;++i){
      for(int j=0;j<cols;++j){

         if(matrix[i*cols+j] == 0 && !visited[i*cols+j]){

            s.push({i,j});
            int count = 0; // initialize count to zero for each new search

            while(!s.empty()){

               Node node = s.top();
               s.pop();

               if(node.i < 0 || node.i >= rows || node.j < 0 || node.j >= cols || visited[node.i*cols+node.j])
                  continue;

               visited[node.i*cols+node.j] = true;

               if(matrix[node.i*cols+node.j] == 0 && !inCurrentPath[node.i*cols+node.j]){
                  inCurrentPath[node.i*cols+node.j] = true;
                  count++;
               }

               if(count >= T){
                  std::cout << "Yes, the path is: "; // print yes and the path
                  for(int k=0;k<N*M;++k){
                     if(inCurrentPath[k]){
                        std::cout << "(" << k/cols << "," << k%cols << ") "; // print the coordinates of the cells in the path
                     }
                  }
                  std::cout << "\n";
                  return true;
               }

               s.push({node.i+1,node.j});
               s.push({node.i-1,node.j});
               s.push({node.i,node.j+1});
               s.push({node.i,node.j-1});
            }

            inCurrentPath.reset(); // reset the path after each search
         }
      }
   }

   std::cout << "No\n"; // print no if no path is found
   return false;
}

int main()
{
   bool matrix[N*M] = {1,1,0,0,1,
                  1,0,0,0,1,
                  1,1,1,1,1,
                  1,1,0,0,1,
                  }; // Binary matrix

   int T = 3; // Number of continuous blocks to find

   DFS(matrix, N, M, T); // call DFS function

   return 0;
}

Output

Yes, the path is: (0,2) (1,0) (1,1)

in conclusion

By leveraging the proposed C code, which employs a graph traversal technique involving depth-first search (DFS), we can conveniently determine whether a given number (T) of consecutive blocks of zeros are present in a binary matrix. This solution provides an efficient way to solve problems related to binary matrices and allows researchers and developers to create powerful algorithms efficiently.

The above is the detailed content of Checks whether there are T consecutive blocks of 0's in the given binary matrix. For more information, please follow other related articles on the PHP Chinese website!