Find Perimeter of Shapes in Binary Matrix using C++

In this problem, we are given a binary matrix bin[][] of size nXm consisting of 0’s and 1’s only. Our task is to Find perimeter of shapes formed with 1s in a binary matrix.

The perimeter taken will cover the figure from all sides, i.e.

For 1 single value, the perimeter is 4.

Let’s take an example to understand the problem,

Input

bin[][] = [1, 0]
   [1, 0]

Output

6

Explanation

The cells (0,0) and (1, 0) are connected making a rectangle of sides 2 and 1. The perimeter is 6.

Solution Approach

A simple solution to the problem is simply finding all one and their contributions to the perimeter and then add all to find the value.

The contribution of a 1 to the perimeter in matrix is, The maximum contribution is 4, when the 1 alone contributes to the perimeter

The minimum contribution is 0, when the 1 is surrounded by 1’s by all sides.

So, for each element of the matrix, we need to check if it is 1 or not. For all 1’s, we will find its neighbours and then contribution to the perimeter and then finally the perimeter.

Program to illustrate the working of our solution,

Example

 Live Demo

#include<iostream>
using namespace std;
#define R 3
#define C 5
int contibutionToPerimeter(int mat[][C], int i, int j) {
   int neighbours = 0;
   if (i > 0 && mat[i - 1][j])
      neighbours++;
   if (j > 0 && mat[i][j - 1])
      neighbours++;
   if (i < R-1 && mat[i + 1][j])
      neighbours++;
   if (j < C-1 && mat[i][j + 1])
      neighbours++;
   return (4 - neighbours);
}
int calcPerimeter(int mat[R][C]){
   int perimeter = 0;
   for (int i = 0; i < R; i++)
      for (int j = 0; j < C; j++)
         if (mat[i][j] == 1)
            perimeter += contibutionToPerimeter(mat, i ,j);
   return perimeter;
}
int main() {
   int mat[R][C] = { {0, 1, 0, 0, 0},
   {1, 1, 1, 1, 0},
   {1, 1, 0, 1, 1} };
   cout<<"The perimeter of shapes from formed with 1s is "<<calcPerimeter(mat);
   return 0;
}

Output

The perimeter of shapes from formed with 1s is 18