# Count squares of size K inscribed in a square of size N

• Difficulty Level : Medium
• Last Updated : 16 Apr, 2021

Given two integers N and K, the task is to find the number of squares of size K that is inscribed in a square of size N. Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

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Examples:

Input: N = 4, K = 2
Output: 9
Explanation:
There are 9 squares of size 2 inscribed in a square of size 4.

Input: N = 5, K = 3
Output: 9
Explanation:
There are 9 squares of size 3 inscribed in a square of size 5.

Approach: The key observation to solve the problem is that the total number of squares in a square of size N is (N * (N + 1)* (2*N + 1)) / 6. Therefore, the total number of squares of size K possible from a square of size N are: Below is the implementation of the above approach:

## C++

 `// C++ implementation of the``// above approach` `#include ``using` `namespace` `std;` `// Function to calculate the number``// of squares of size K in a square``// of size N``int` `No_of_squares(``int` `N, ``int` `K)``{``    ``// Stores the number of squares``    ``int` `no_of_squares = 0;` `    ``no_of_squares``        ``= (N - K + 1) * (N - K + 1);` `    ``return` `no_of_squares;``}` `// Driver Code``int` `main()``{``    ``// Size of the``    ``// bigger square``    ``int` `N = 5;` `    ``// Size of``    ``// smaller square``    ``int` `K = 3;``    ``cout << No_of_squares(N, K);``    ``return` `0;``}`

## Java

 `// Java implementation of the``// above approach``import` `java.util.*;``class` `GFG{` `// Function to calculate the``// number of squares of size``// K in a square of size N``static` `int` `No_of_squares(``int` `N,``                         ``int` `K)``{``  ``// Stores the number``  ``// of squares``  ``int` `no_of_squares = ``0``;` `  ``no_of_squares = (N - K + ``1``) *``                  ``(N - K + ``1``);` `  ``return` `no_of_squares;``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``  ``// Size of the``  ``// bigger square``  ``int` `N = ``5``;` `  ``// Size of``  ``// smaller square``  ``int` `K = ``3``;``  ``System.out.print(No_of_squares(N, K));``}``}` `// This code is contributed by Princi Singh`

## Python3

 `# Python3 implementation of the``# above approach` `# Function to calculate the``# number of squares of size``# K in a square of size N``def` `No_of_squares(N, K):``  ` `    ``# Stores the number``    ``# of squares``    ``no_of_squares ``=` `0``;``    ``no_of_squares ``=` `(N ``-` `K ``+` `1``) ``*` `(N ``-` `K ``+` `1``);``    ``return` `no_of_squares;` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``  ` `    ``# Size of the``    ``# bigger square``    ``N ``=` `5``;` `    ``# Size of``    ``# smaller square``    ``K ``=` `3``;``    ``print``(No_of_squares(N, K));` `# This code is contributed by 29AjayKumar`

## C#

 `// C# implementation of the``// above approach``using` `System;` `class` `GFG{` `// Function to calculate the``// number of squares of size``// K in a square of size N``static` `int` `No_of_squares(``int` `N, ``int` `K)``{``    ` `    ``// Stores the number``    ``// of squares``    ``int` `no_of_squares = 0;``    ` `    ``no_of_squares = (N - K + 1) *``                    ``(N - K + 1);``    ` `    ``return` `no_of_squares;``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ` `    ``// Size of the``    ``// bigger square``    ``int` `N = 5;``    ` `    ``// Size of``    ``// smaller square``    ``int` `K = 3;``    ` `    ``Console.Write(No_of_squares(N, K));``}``}` `// This code is contributed by Amit Katiyar`

## Javascript

 ``
Output:
`9`

Time Complexity: O(1)
Auxiliary Space: O(1)

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