Count cubes of size K inscribed in a cube of size N

Given two integers N and K, the task is to find the number of cubes of size K that can be contained in a cube of size N.

Examples:

Input: N = 2, K = 1
Output: 8
Explanation:
There are 8 cubes of size 1 that can be drawn inside the bigger cube of size 2. 
 

 Input: N = 5, K = 2
Output: 64
Explanation:
There are 64 cubes of size 2 can be drawn inside the bigger cube of size 5.



Approach: The key observation to solve the problem is that the number of cubes inside the cube of size N is (N2 * (N+1)2)/4. Therefore, the cubes of size K inside the cube of size N is:

(N - K +1 )^3

Below is the implementation of the above approach:

C++

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// C++ implementation of the
// above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the number
// of the cubes of the size K
int No_of_cubes(int N, int K)
{
    int No = 0;
 
    // Stores the number of cubes
    No = (N - K + 1);
 
    // Stores the number of cubes
    // of size k
    No = pow(No, 3);
    return No;
}
 
// Driver Code
int main()
{
    // Size of the bigger cube
    int N = 5;
 
    // Size of the smaller cube
    int K = 2;
 
    cout << No_of_cubes(N, K);
    return 0;
}

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Java

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// Java implementation of the
// above approach
class GFG{
 
// Function to find the number
// of the cubes of the size K
static int No_of_cubes(int N,
                       int K)
{
  int No = 0;
 
  // Stores the number of cubes
  No = (N - K + 1);
 
  // Stores the number of cubes
  // of size k
  No = (int) Math.pow(No, 3);
  return No;
}
 
// Driver Code
public static void main(String[] args)
{
  // Size of the bigger cube
  int N = 5;
 
  // Size of the smaller cube
  int K = 2;
 
  System.out.print(No_of_cubes(N, K));
}
}
 
// This code is contributed by Princi Singh

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Python3

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# Python3 implementation of the
# above approach
  
# Function to find the number
# of the cubes of the size K
def No_of_cubes(N, K):
     
    No = 0
  
    # Stores the number of cubes
    No = (N - K + 1)
  
    # Stores the number of cubes
    # of size k
    No = pow(No, 3)
    return No
 
# Driver Code
 
# Size of the bigger cube
N = 5
  
# Size of the smaller cube
K = 2
  
print(No_of_cubes(N, K))
 
# This code is contributed by sanjoy_62

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C#

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// C# implementation of the
// above approach
using System;
  
class GFG{
      
// Function to find the number
// of the cubes of the size K
static int No_of_cubes(int N, int K)
{
    int No = 0;
     
    // Stores the number of cubes
    No = (N - K + 1);
     
    // Stores the number of cubes
    // of size k
    No = (int)Math.Pow(No, 3);
    return No;
}
  
// Driver Code
public static void Main()
{
     
    // Size of the bigger cube
    int N = 5;
     
    // Size of the smaller cube
    int K = 2;
     
    Console.Write(No_of_cubes(N, K));
}
}
 
// This code is contributed by sanjoy_62

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Output: 

64









 

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

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Improved By : princi singh, sanjoy_62