Question

There are two boxes, A1×B1×C1 and A2×B2×C2 are size of boxes. Define if it is possible to totally cover one box in the another. (Hint: 1x1x1 can be covered by 2x1x1 box)

Input format

A1, B1, C1, A2, B2, C2.

Output format

The program should bring out one of the following lines:

Boxes are equal, if the boxes are the same,

the first box is smaller than the second one, if the first box can be put in the second,

the first box is larger than the second one, if the second box can be put in the first, Boxes are incomparable, in all other cases

Answer 1

import numpy as np

def fit(inner_dims, outer_dims):
    inner_dims.sort()
    outer_dims.sort()
    x1, y1, z1 = inner_dims
    x2, y2, z2 = outer_dims
    
    # Volume Test
    
    inner_volume = x1 * y1 * z1
    outer_volume = x2 * y2 * z2    
    if inner_volume > outer_volume:
        return False
        
    # Edge Test
    
    diffs = np.greater_equal(outer_dims, inner_dims)
    if np.all(diffs):
        return True

    # Rotation Test
    
    inner_perms = [(x1, y1, z1), (x1, z1, y1), (z1, y1, x1)]
    outer_perms = [(x2, y2, z2), (x2, z2, y2), (z2, y2, x2)]
    
    for i, j in zip(inner_perms, outer_perms):
        if rotation_test(i, j):
            return True

    # Diagonal Test
    
    diag = np.sqrt(x2**2 + y2**2 + z2**2)
    if x1 + y1 + z1 <= diag:
        return True
                
    return False

def rotation_test(inner_dims, outer_dims):
    x1, y1, z1 = inner_dims
    x2, y2, z2 = outer_dims
    diag = np.sqrt(x2**2 + y2**2)
    if x1 + y1 <= diag and z1 <= z2:
        return True
    else:
        return False

def main():
  n = 3 
  first = []
  second = []
# iterating till the range 
  for i in range(0, n): 
    ele = int(input()) 
    first.append(ele)
  for i in range(0, n): 
    ele = int(input()) 
    second.append(ele) 
  # first = [1,1,1]
  # second = [2,2,2]
  first.sort()
  second.sort()
  if first == second:
    print("Boxes are of same size")
  elif fit(first,second):
    print("Box 1 fits in Box 2")
  elif fit(second,first):
    print("Box 2 fits in Box 2")
  else:
    print("Boxes are incomparable")
  
main()

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