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Minimum number of blocks required to form Hollow Rectangular Prism

  • Last Updated : 18 Mar, 2021

Given the dimensions of a block L, B and H, the task is to form a Hollow Rectangular prism of length A and height Ht such that minimum no of blocks are required.
Examples: 
 

Input: L = 40, B = 30, H = 10 & A = 500, Ht = 300 
Output: 500
Input: L = 30, B = 20, H = 20, & A = 600, Ht =240 
Output: 960 
 

 

 



Approach: 
Calculate the minimum number of blocks required in each layer which can be done by setting the blocks in such a way that it occupies maximum length by finding the number of blocks required for the 4 sides of the rectangular prism, then choose for the block side which can be taken as the height of the block. From width or the height whichever is greater is taken as height. 
Below is the implementation of the above approach: 
 

C++




// C++ Implementation to find the minimum
// no of blocks required to form
// hollow rectangular prism
#include <bits/stdc++.h>
using namespace std;
 
// Function to display output
void disp(int row_no, int block)
{
    cout << row_no * block;
}
 
// Function to return minimum no of layers
// required to form the hollow prism
int row(int ht, int h)
{
    return ht / h;
}
 
// Function to calculate no of blocks
// required for each layer
void calculate(int l, int w, int h, int a, int ht)
{
    // No of blocks required for each row
    int no_block = (4 * a) / l;
    int row_no;
 
    // Check for no of layers is minimum
    if (h < w)
        row_no = row(ht, w);
    else
        row_no = row(ht, h);
    disp(row_no, no_block);
}
 
// Driver function
int main()
{
    // Length, width, height of each block
    int l = 50, w = 20, h = 35;
 
    // Side of one wall
    int a = 700;
 
    // height of each wall
    int ht = 140;
 
    calculate(l, w, h, a, ht);
    return 0;
}

Java




// Java Implementation to find the minimum
// no of blocks required to form
// hollow rectangular prism
import java.util.*;
 
class GFG{
  
// Function to display output
static void disp(int row_no, int block)
{
    System.out.print(row_no * block);
}
  
// Function to return minimum no of layers
// required to form the hollow prism
static int row(int ht, int h)
{
    return ht / h;
}
  
// Function to calculate no of blocks
// required for each layer
static void calculate(int l, int w, int h, int a, int ht)
{
    // No of blocks required for each row
    int no_block = (4 * a) / l;
    int row_no;
  
    // Check for no of layers is minimum
    if (h < w)
        row_no = row(ht, w);
    else
        row_no = row(ht, h);
    disp(row_no, no_block);
}
  
// Driver function
public static void main(String[] args)
{
    // Length, width, height of each block
    int l = 50, w = 20, h = 35;
  
    // Side of one wall
    int a = 700;
  
    // height of each wall
    int ht = 140;
  
    calculate(l, w, h, a, ht);
}
}
 
// This code is contributed by PrinciRaj1992

Python 3




# Python 3 Implementation to find the minimum
# no of blocks required to form
# hollow rectangular prism
 
# Function to display output
def disp(row_no,block):
    print(row_no * block)
 
# Function to return minimum no of layers
# required to form the hollow prism
def row(ht, h):
    return ht // h
 
# Function to calculate no of blocks
# required for each layer
def calculate(l, w, h, a, ht):
     
        # No of blocks required for each row
    no_block = (4 * a) // l
     
    # Check for no of layers is minimum
    if (h < w):
        row_no = row(ht, w)
    else:
        row_no = row(ht, h)
    disp(row_no, no_block)
 
# Driver function
if __name__ == '__main__':
    # Length, width, height of each block
    l = 50
    w = 20
    h = 35
 
    # Side of one wall
    a = 700
 
    # height of each wall
    ht = 140
 
    calculate(l, w, h, a, ht)
 
# This code is contributed by Surendra_Gangwar

C#




// C# Implementation to find the minimum
// no of blocks required to form
// hollow rectangular prism
using System;
 
class GFG{
 
// Function to display output
static void disp(int row_no, int block)
{
    Console.Write(row_no * block);
}
 
// Function to return minimum no of layers
// required to form the hollow prism
static int row(int ht, int h)
{
    return ht / h;
}
 
// Function to calculate no of blocks
// required for each layer
static void calculate(int l, int w, int h,
                        int a, int ht)
{
    // No of blocks required for each row
    int no_block = (4 * a) / l;
    int row_no;
 
    // Check for no of layers is minimum
    if (h < w)
        row_no = row(ht, w);
    else
        row_no = row(ht, h);
    disp(row_no, no_block);
}
 
// Driver function
public static void Main(String[] args)
{
    // Length, width, height of each block
    int l = 50, w = 20, h = 35;
 
    // Side of one wall
    int a = 700;
 
    // height of each wall
    int ht = 140;
 
    calculate(l, w, h, a, ht);
}
}
 
// This code is contributed by PrinciRaj1992

Javascript




<script>
// javascript Implementation to find the minimum
// no of blocks required to form
// hollow rectangular prism
 
// Function to display output
function disp( row_no,  block)
{
     document.write( row_no * block);
}
 
// Function to return minimum no of layers
// required to form the hollow prism
function row( ht,  h)
{
    return ht / h;
}
 
// Function to calculate no of blocks
// required for each layer
function calculate( l,  w,  h,  a,  ht)
{
 
    // No of blocks required for each row
    let no_block = (4 * a) / l;
    let row_no;
 
    // Check for no of layers is minimum
    if (h < w)
        row_no = row(ht, w);
    else
        row_no = row(ht, h);
    disp(row_no, no_block);
}
 
// Driver function
 
    // Length, width, height of each block
    let l = 50, w = 20, h = 35;
 
    // Side of one wall
    let a = 700;
 
    // height of each wall
    let ht = 140;
    calculate(l, w, h, a, ht);
        
// This code is contributed by Rajput-Ji
 
</script>
Output: 
224

 




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