Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Find perimeter of shapes formed with 1s in binary matrix in 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
#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
179 Views
