Let \([x,y]\) denote the segment formed by all real numbers between \(x\) and \(y\), inclusive.

First, let us consider a one-dimensional problem.

one-dimensional problem

Problem: determine if two segments \([a,b]\) and \([c,d]\) has an intersection of a positive length.

There are various ways to determine it. One ways is to check if the intersection has a length of \(0\), and take its negation. The length of intersection is \(0\) for one of the following cases:

• \([a,b]\) is to the left of \([c,d]\).
• \([a,b]\) is to the right of \([c,d]\).

In Pythonic pseudocode, it can be written as follows:

if b <= c  or  d <= a:
  print("0 intersection")
else:
  print("positive intersection")

three-dimensional problem

Solve the one-dimensional problem for the three coordinates \(x\), \(y\), and \(z\); if the length of the intersection is all positive, then the intersection of the cuboids has a positive volume; otherwise, it is \(0\).

As we are solving one-dimensional problem three times, it is good idea to extract that part into a function in order to simplify the implementation.

Sample code (Python)

x1,y1,z1,x2,y2,z2 = map(int,input().split())
x3,y3,z3,x4,y4,z4 = map(int,input().split())

def f(l1,r1,l2,r2):
  # returns True if the intersection of [l1,r1] and [l2,r2] has a positive length
  return not (r1<=l2 or r2<=l1)

if f(x1,x2,x3,x4) and f(y1,y2,y3,y4) and f(z1,z2,z3,z4):
  print("Yes")
else:
  print("No")