[CF Hardcore] Mind-Blowing Solution for Problem B in Codeforces Contest

Contest Background

In the recent Codeforces Round 1103 (Div. 3), participant vishwanth2002 presented a mind-blowing solution that sparked discussions around Problem B.

Solution Analysis

Although the solution is practically unhackable, it remains theoretically hackable. Participants engaged in discussions regarding its randomized approach, although a formal proof has yet to be established.

Code Implementation

Here’s a Python code example provided by participants that demonstrates how to perform random testing given n:

import random

def test(n: int, results: list):
    l = [random.randint(1, n) for i in range(4)]
    l.sort()
    if l[0] == l[1] or l[1] == l[2] or l[2] == l[3]:
        return
    d1 = l[1] - l[0]
    d2 = l[2] - l[1]
    d3 = l[3] - l[2]
    if d1 == d2 or d2 == d3 or d1 == d3:
        results[1] += 1
    else:
        results[0] += 1

Result Analysis

According to the simulation results, with n = 20000, the failure probability was 0.000296, yielding a total failure probability of about 583%. This result sparked debates on the reliability of randomized algorithms.

Blogger's Review: The randomized approach in this solution is indeed refreshing, yet the challenge of theoretical proof should not be underestimated. The reliability of the algorithm and its practical applications in competitions require further research and practical validation. I hope to see more systematic analyses and optimization strategies emerge in the future.