CF 1523A - Game of Life

Rating: 800
Tags: implementation
Solve time: 12m
Verified: no

Solution

The empty output indicates a runtime crash before any printing happens, not a logical error in the math.

Tracing the execution on the input:

The program first reads t = 3, then processes three test cases. The expected computation per test case is:

For each k, compute:

$$\frac{100}{\gcd(k, 100)}$$

The failure happens earlier than any arithmetic reasoning: the program never reaches print. The usual cause for exactly this symptom (no traceback shown in judge-style harnesses, just empty output) is a missing import or undefined symbol in the actual execution path, most commonly math.gcd or gcd being used without importing math or importing gcd explicitly.

In many Codeforces-style templates, the solution uses gcd directly, but if it was written as math.gcd without import math, or as gcd without from math import gcd, execution stops immediately.

The correct fix is to ensure the gcd function is properly imported and the program never depends on implicit namespace availability.

The algorithm itself is correct: the minimal number of liters is achieved by taking the smallest integer pair proportional to $k : (100-k)$, which reduces to dividing by their greatest common divisor.

Corrected Python Solution

import sys
from math import gcd

input = sys.stdin.readline

t = int(input())
for _ in range(t):
    k = int(input())
    g = gcd(k, 100)
    print(100 // g)

This version ensures:

gcd is defined in all execution environments.
Each test case is processed independently in O(1).
Output is produced immediately per case, avoiding buffering issues in broken early-exit runs.

The logic remains unchanged: reduce the ratio $k/100$ to lowest terms; the denominator gives the minimal total number of operations required to achieve that exact percentage using unit increments.