Number of squares of side length required to cover an N*M rectangle

• Last Updated : 20 May, 2021

Given three numbers   . Find Number of squares of dimension required to cover rectangle.
Note

• It’s allowed to cover the surface larger than the rectangle, but the rectangle has to be covered.
• It’s not allowed to break a square.
• The sides of squares should be parallel to the sides of the rectangle.

Examples

Input: N = 6, M = 6, a = 4
Output: 4

Input: N = 2, M = 3, a = 1
Output: 6

Approach: An efficient approach is to make an observation and find a formula. The constraint that edges of each square must be parallel to the edges of the rectangle allows to analyze X and Y axes separately, that is, how many squares of length ‘a’ are needed to cover squares of length ‘m’ and ‘n’ and take the product of these two quantities. The number of small squares of side length ‘a’ required to cover ‘m’ sized square are ceil(m/a). Similarly, number of ‘a’ sized squares required to cover ‘n’ sized square are ceil(n/a).
So, the answer will be ceil(m/a)*ceil(n/a).
Below is the implementation of the above approach:

C++

 // CPP program to find number of squares// of a*a required to cover n*m rectangle#include using namespace std; // function to find number of squares// of a*a required to cover n*m rectangleint Squares(int n, int m, int a){    return ((m + a - 1) / a) * ((n + a - 1) / a);} // Driver codeint main(){    int n = 6, m = 6, a = 4;     // function call    cout << Squares(n, m, a);     return 0;}

Java

 // Java program to find number of squares// of a*a required to cover n*m rectangleimport java.util.*; class solution{ // function to find a number of squares// of a*a required to cover n*m rectanglestatic int Squares(int n, int m, int a){     return ((m + a - 1) / a) * ((n + a - 1) / a); } // Driver codepublic static void main(String arr[]){    int n = 6, m = 6, a = 4;     // function call    System.out.println(Squares(n, m, a)); } }//This code is contributed by Surendra_Gangwar

Python 3

 # Python 3 program to find number# of squares of a*a required to# cover n*m rectangle # function to find number of# squares of a*a required to# cover n*m rectangledef Squares(n, m, a):    return (((m + a - 1) // a) *            ((n + a - 1) // a)) # Driver codeif __name__ == "__main__":    n = 6    m = 6    a = 4     # function call    print(Squares(n, m, a)) # This code is contributed# by ChitraNayal

C#

 // CSHARP program to find number of squares// of a*a required to cover n*m rectangle using System; class GFG{    // function to find a number of squares    // of a*a required to cover n*m rectangle    static int Squares(int n, int m, int a)    {             return ((m + a - 1) / a) * ((n + a - 1) / a);         }     static void Main()    {          int n = 6, m = 6, a = 4;          // function call         Console.WriteLine(Squares(n, m, a));    }    // This code is contributed by ANKITRAI1}



Javascript


Output:
4

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