Question

Write a function that returns a chessboard pattern ("B" for black squares, "W" for white squares). The function takes a number N as input and generates the corresponding board.
Input The first line of the input consists of an integer- num, representing the size of the chessboard.
Output Print N lines consist of N space-separated characters representing the chessboard pattern.

Answer 1

Answer:

Here is the C++ program.

#include <iostream>  //to use input output functions

using namespace std;  // to access objects like cin cout

 

void chessboard(int N){  // function that takes a number N as parameter generates corresponding board

   int i, j;  

   string black = "B";  // B for black squares

   string white = "W"; // W for white squares

   for(i=1;i<=N;i++){  //iterates through each column of the board

       for(j=1;j<=N;j++){  //iterates through each row of the board

           if((i+j)%2==0)  // if sum of i and j is completely divisible by 2

               cout<<black<<" ";  //displays B when above if condition is true

           else  //if (i+j)%2 is not equal to 0

           cout<<white<<" ";  }  // displays W when above if condition is false

      cout<<endl;    }    }  //prints the new line

       

int main(){    //start of the main function

   int num;  //declares an integer num

   cout << "Enter an integer representing the size of the chessboard: ";  //prompts user to enter size of chess board

   cin >> num;  //reads value of num from user

   chessboard(num); } //calls chessboard function to display N lines consist of N space-separated characters representing the chessboard pattern

Explanation:

The function works as follows:

Lets say that N = 2

two string variables black and white are declared. The value of black is set to "B" and value of white is set to "W" to return a chessboard pattern in B and W squares.

The outer loop for(i=1;i<=N;i++) iterates through each column of the chess board. The inner loop  for(j=1;j<=N;j++) iterates through each row of chess board.

At first iteration of outer loop:

N = 2

outer loop:

i=1

i<=N is true because i=1 and 1<=2

So the program enters the body of the outer for loop. It has an inner for loop:

for(j=1;j<=N;j++)

At first iteration of inner loop:

j = 1

j<=N is true because j=1 and 1<=2

So the program enters the body of the inner for loop. It has an if statement:

if((i+j)%2==0) this statement works as:

if(1+1) % 2 == 0

(1+1 )% 2 takes the mod of 1+1 with 2 which gives the remainder of the division.

2%2 As 2 is completely divisible by 2 so 2%2 == 0

Hence the if condition evaluates to true. So the statement in if part executes:

cout<<black<<" ";

This prints B on the output screen with a space.

B

The value of j is incremented to 1.

j = 2

At second iteration of inner loop:

j = 2

j<=N is true because j=2 and 2=2

So the program enters the body of the inner for loop. It has an if statement:

if((i+j)%2==0) this statement works as:

if(1+2) % 2 == 0

(1+2 )% 2 takes the mod of 1+2 with 2 which gives the remainder of the division.

3%2 As 3 is not completely divisible by 2

Hence the if condition evaluates to false. So the statement in else part executes:

cout<<white<<" ";

This prints W on the output screen with a space.

B W

The value of j is incremented to 1.

j = 3

Now  

j<=N is false because j=3 and 3>2

So the loop breaks and program moves to the outer loop to iterate through the next row.

At second iteration of outer loop:

N = 2

outer loop:

i=2

i<=N is true because i=2 and 2 = 2

So the program enters the body of the outer for loop. It has an inner for loop:

for(j=1;j<=N;j++)

At first iteration of inner loop:

j = 1

j<=N is true because j=1 and 1<=2

So the program enters the body of the inner for loop. It has an if statement:

if((i+j)%2==0) this statement works as:

if(2+1) % 2 == 0

(2+1 )% 2 takes the mod of 2+1 with 2 which gives the remainder of the division.

3%2 As 3 is not completely divisible by 2

Hence the if condition evaluates to false. So the statement in else part executes:

cout<<white<<" ";

This prints W on the output screen with a space.

B W

W

The value of j is incremented to 1.

j = 2

At second iteration of inner loop:

j = 2

j<=N is true because j=2 and 2=2

So the program enters the body of the inner for loop. It has an if statement:

if((i+j)%2==0) this statement works as:

if(2+2) % 2 == 0

(2+2 )% 2 takes the mod of 2+2 with 2 which gives the remainder of the division.

4%2 As 4 is completely divisible by 2 so 4%2 == 0

Hence the if condition evaluates to false. So the statement in if part executes:

cout<<black<<" ";

This prints B on the output screen with a space.

B W

W B

The value of j is incremented to 1.

j = 3

Now  

j<=N is false because j=3 and 3>2

So the loop breaks and program moves to the outer loop. The value of outer loop variable i is incremented to 1 so i = 3

N = 2

outer loop:

i=3

i<=N is false because i=3 and 3>2

So this outer loop ends.

Now the output of this program is:

B W

W B

Screenshot of this program along with its output is attached.