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Program to find number of squares in a chessboard in C++
In this problem, we are given the size of a chessboard. Our task is to create a program to find number of squares in a chessboard in C++.
Problem Description − To find the number of squares in a chessboard. We will have to calculate all the combinations of the square that are inside the chessboard i.e. we will consider squares of side 1x1, 2x2, 3x3 … nxn.
Let’s take an example to understand the problem,
Input: n = 4.
Output: 30
Squares of size 1x1 -> 16 Squares of size 2x2 -> 9 Squares of size 3x3 -> 4 Squares of size 4x4 -> 1 Total number of squares = 16+9+4+1 = 30
Solution Approach:
A simple approach is by using the sum formula for nxn grid. Let’s deduct the general formula for the sum, sum(1) = 1 sum(2) = 1 + 4 = 5 sum(3) = 1 + 4 + 9 = 14 sum(4) = 1 + 4 + 9 + 16 = 30 The sum is can be generalised as sum = 12 + 22 + 32 + 42 + … n2 sum = ( (n*(n+1)*((2*n) + 1))/6 )
Example
#include <iostream>
using namespace std;
int calcSquaresCount(int n){
int squareCount = ( (n * (n+1) * (2*n + 1))/6 );
return squareCount;
}
int main() {
int n = 6;
cout<<"The total number of squares of size "<<n<<"X"<<n<<" is
"<<calcSquaresCount(n);
}Output:
The total number of squares of size 6X6 is 91
Updated on: 01-Oct-2020
2K+ Views
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