Find Number of Border Cells in a Grid using C++

Suppose, we are given a grid of dimensions h * w. We have to color the border cells of the grid (i.e. the outermost cells of the grid) with a special color. We have to find out how many border cells we have to color.

Problem Category

Various problems in programming can be solved through different techniques. To solve a problem, we have to devise an algorithm first, and to do that we have to study the particular problem in detail. A recursive approach can be used if there is a recurring appearance of the same problem over and over again; alternatively, we can use iterative structures also. Control statements such as if-else and switch cases can be used to control the flow of logic in the program. Efficient usage of variables and data structures provides an easier solution and a lightweight, low-memory-requiring program. We have to look at the existing programming techniques, such as Divide-and-conquer, Greedy Programming, Dynamic Programming, and find out if they can be used. This problem can be solved by some basic logic or a brute-force approach. Follow the following contents to understand the approach better.

So, if the input of our problem is like h = 4, w = 4, then the output will be 12.

Steps

To solve this, we will follow these steps −

return (2 * ((h - 2) + 2 * (w - 2)))

Example

Let us see the following implementation to get better understanding −

#include<bits/stdc++.h>
using namespace std;
void solve(int h, int w) {
   cout<< 2 * (h - 2) + 2 * (w - 2) + 4 ;
}
int main() {
   int h = 4, w = 4;
   solve(h, w);
   return 0;
}

Input

4, 4

Output

12