How print("YNEOS"[(w%2)|(w<=2)::2]) works

Question

I was just trying to solve this problem on Codeforces: Check whether it's posible to split a number w (1 ≤ w ≤ 100) into a sum of 2 even numbers

I solved the problem and started to look others solutions for the problem. The I found that solution:

w=int(input())
print("YNEOS"[(w%2)|(w<=2)::2])

it took half of time to solve the problem then mine. Unfortunately I am not getting how it is working and why it is faster than mine. My solution is :

n = int(input())
if (n-2)%2==0 and n > 2:
    print("YES")
else:
    print("NO")

I am a beginner in python. So it will be very helpful for me it i get a proper explanation.

Answer 1

The :: part is called slicing. The general syntax is start:stop[:step] which will make a new array or string from the original one, beginning from index start to before stop every step (default = 1). It's essentially a syntactic sugar for slice(start, stop, step) which returns a slice object. If stop is omitted then all the elements till the end of the string will be extracted

• Understanding slice notation
• How do I use the slice notation in Python?
• https://docs.python.org/2.3/whatsnew/section-slices.html

You may want to read An Informal Introduction to Python for more information about slicing

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Now (w%2)|(w<=2) calculates the start index. | is the bitwise-OR operator. w<=2 is a bool expression, but in Python "Booleans are a subtype of integers", so True and False will be converted to 1 and 0 respectively

• If w is an odd number then w % 2 == 1. Regardless of the remaining part, (w%2)|(w<=2) will always be 1 in this case and the expression becomes "YNEOS"[1::2] which takes every second letter in the string starting from index 1. The result is the string NO
• If w is an even number then w % 2 == 0. According to the problem description 1 ≤ w ≤ 100 the only valid even numbers belong to the range [2, 100]
  • If w == 2 then w <= 2 returns 1 and the output is NO like above
  • If w > 2 then both the sides of (w%2)|(w<=2) is 0, and "YNEOS"[0::2] takes the 1st, 3rd and 5th letters which is YES

Realizing that the expression always returns 0 or 1 we'll have an alternative more readable solution that uses direct addressing instead of slicing

w=int(input())
print(['YES', 'NO'][(w % 2) | (w <= 2)])

Btw, you have a redundant subtraction: (n-2)%2==0 is exactly the same as n % 2 == 0